[latexrefman-commits] [SCM] latexrefman updated: r676 - trunk

jimhefferon at gnu.org.ua jimhefferon at gnu.org.ua
Mon Jul 2 17:52:36 CEST 2018


Author: jimhefferon
Date: 2018-07-02 18:52:35 +0300 (Mon, 02 Jul 2018)
New Revision: 676

Modified:
   trunk/ChangeLog
   trunk/latex2e.html
   trunk/latex2e.info
   trunk/latex2e.pdf
   trunk/latex2e.texi
Log:
Working through the .html files.  Through Modes.html

Modified: trunk/ChangeLog
===================================================================
--- trunk/ChangeLog	2018-07-01 20:07:33 UTC (rev 675)
+++ trunk/ChangeLog	2018-07-02 15:52:35 UTC (rev 676)
@@ -1,3 +1,8 @@
+2018-07-02  Jim Hefferon  <jhefferon at smcvt.edu>
+
+	* latex2e.texi (Many sections) Check entries against
+	latex2e-reference.  Through "Modes".
+
 2018-07-01  Jim Hefferon  <jhefferon at smcvt.edu>
 
 	* latex2e.texi (Many sections) Check entries against

Modified: trunk/latex2e.html
===================================================================
--- trunk/latex2e.html	2018-07-01 20:07:33 UTC (rev 675)
+++ trunk/latex2e.html	2018-07-02 15:52:35 UTC (rev 676)
@@ -352,7 +352,7 @@
       <li><a name="toc-Blackboard-bold-1" href="#Blackboard-bold">16.2.1 Blackboard bold</a></li>
       <li><a name="toc-Calligraphic-1" href="#Calligraphic">16.2.2 Calligraphic</a></li>
       <li><a name="toc-_005cboldmath-_0026-_005cunboldmath-1" href="#g_t_005cboldmath-_0026-_005cunboldmath">16.2.3 <code>\boldmath</code> & <code>\unboldmath</code></a></li>
-      <li><a name="toc-Ellipses-1" href="#Ellipses">16.2.4 Ellipses</a></li>
+      <li><a name="toc-Dots_002c-horizontal-or-vertical" href="#Dots">16.2.4 Dots, horizontal or vertical</a></li>
     </ul></li>
     <li><a name="toc-Math-functions-1" href="#Math-functions">16.3 Math functions</a></li>
     <li><a name="toc-Math-accents-1" href="#Math-accents">16.4 Math accents</a></li>
@@ -4650,7 +4650,7 @@
 \end{array}
 </pre></div>
 
-<p>or
+<p>or:
 </p>
 <div class="example">
 <pre class="example">\begin{array}[<var>pos</var>]{<var>cols</var>}
@@ -4661,10 +4661,25 @@
 
 <p>Produce a mathematical array.  This environment can only be used in math
 mode, and normally appears within a displayed mathematics environment
-such as <code>equation</code> (see <a href="#equation">equation</a>).  Column entries are
-separated by an ampersand (<code>&</code>).  Rows are terminated with
-double-backslashes (see <a href="#g_t_005c_005c">\\</a>).  
+such as <code>equation</code> (see <a href="#equation">equation</a>).  Inside of each row the
+column entries are separated by an ampersand, (<code>&</code>).  Rows are
+terminated with double-backslashes (see <a href="#g_t_005c_005c">\\</a>).
 </p>
+<p>This example shows a three by three array.
+</p>
+<div class="example">
+<pre class="example">\begin{equation*}
+  \chi(x) =
+  \left|              % vertical bar fence
+    \begin{array}{ccc}
+      x-a  &-b  &-c  \\
+      -d   &x-e &-f  \\
+      -g   &-h  &x-i
+    \end{array}
+ \right|
+\end{equation*}
+</pre></div>
+
 <p>The required argument <var>cols</var> describes the number of columns, their
 alignment, and the formatting of the intercolumn regions.  For instance,
 <code>\begin{array}{rcl}...\end{array}</code> gives three columns: the
@@ -4675,14 +4690,15 @@
 </p>
 <p>There are two ways that <code>array</code> diverges from <code>tabular</code>.  The
 first is that <code>array</code> entries are typeset in math mode, in
-textstyle (except if the <var>cols</var> definition specifies the column with
-<code>p{...}</code>, which causes the entry to be typeset in text mode).
-The second is that, instead of <code>tabular</code>’s parameter
-<code>\tabcolsep</code>, LaTeX’s intercolumn space in an <code>array</code> is governed
-by
+textstyle (see <a href="#Modes">Modes</a>) except if the <var>cols</var> definition specifies
+the column with <code>p{...}</code>, which causes the entry to be typeset in
+text mode.  The second is that, instead of <code>tabular</code>’s parameter
+<code>\tabcolsep</code>, LaTeX’s intercolumn space in an <code>array</code> is
+governed by
 <a name="index-_005carraycolsep"></a>
 <code>\arraycolsep</code>, which gives half the width between columns. The
-default for this is ‘<samp>5pt</samp>’.
+default for this is ‘<samp>5pt</samp>’ so that between two columns comes
+10pt of space.
 </p>
 <a name="index-package_002c-amsmath"></a>
 <a name="index-amsmath-package"></a>
@@ -4696,30 +4712,34 @@
 <code>Vmatrix</code> for an array surrounded by double vertical
 bars <code>||...||</code>, along with a number of other array constructs.
 </p>
-<p>Here is an example of an array:
+<a name="index-package_002c-amsmath-1"></a>
+<a name="index-amsmath-package-1"></a>
+
+<p>The next example uses the <samp>amsmath</samp> package.
 </p>
 <div class="example">
-<pre class="example">\begin{equation}
-  \begin{array}{cr}
-    \sqrt{y}  &12.3 \\
-    x^2       &3.4       
-  \end{array}
-\end{equation}
-</pre></div>
+<pre class="example">\usepackage{amsmath}  % in preamble
 
-<p>The next example works if <code>\usepackage{amsmath}</code> is in the
-preamble:
-</p>
-<div class="example">
-<pre class="example">\begin{equation}
-  \begin{vmatrix}{cc}
+\begin{equation}    
+  \begin{vmatrix}{cc}  % array with vert lines
     a  &b \\
     c  &d       
   \end{vmatrix}=ad-bc
 \end{equation}
 </pre></div>
 
+<a name="index-package_002c-array-_0028package_0029"></a>
+<a name="index-array-_0028package_0029-package"></a>
 
+<a name="index-package_002c-dcolumn"></a>
+<a name="index-dcolumn-package"></a>
+
+<p>There are many packages concerning arrays.  The <samp>array</samp> package has
+many useful extensions, including more column types.  The <samp>dcolumn</samp>
+package adds a column type to center on a decimal point.  For both see
+the documentation on CTAN.
+</p>
+
 <hr>
 <a name="center"></a>
 <div class="header">
@@ -4738,22 +4758,14 @@
 </p>
 <div class="example">
 <pre class="example">\begin{center}
-  ... text ...
-\end{center}
-</pre></div>
-
-<p>or
-</p>
-<div class="example">
-<pre class="example">\begin{center}
-  text on first line \\
-  text on second line \\
+  <var>line1</var> \\
+  <var>line2</var> \\
   ...
 \end{center}
 </pre></div>
 
 <p>Create a new paragraph consisting of a sequence of lines that are
-centered within the left and right margins on the current page.  Use
+centered within the left and right margins.  Use
 double-backslash, <code>\\</code>, to get a line break (see <a href="#g_t_005c_005c">\\</a>).
 <a name="index-_005c_005c-_0028for-center_0029"></a>
 If some text is too long to fit on a line then LaTeX will insert line
@@ -4789,8 +4801,12 @@
 \end{center}
 </pre></div>
 
-<p>A double backslash after the final line is optional.
+<p>A double backslash after the final line is optional.  If present it
+doesn’t add any vertical space.
 </p>
+<p>In a two-column document the text is centered in a column, not in the
+entire page.
+</p>
 <table class="menu" border="0" cellspacing="0">
 <tr><td align="left" valign="top">• <a href="#g_t_005ccentering" accesskey="1">\centering</a>:</td><td>  </td><td align="left" valign="top">Declaration form of the <code>center</code> environment.
 </td></tr>
@@ -4876,9 +4892,9 @@
 </p>
 <div class="example">
 <pre class="example">\begin{description}
-\item[<var>label of first item</var>] <var>text of first item</var>
-\item[<var>label of second item</var>] <var>text of second item</var>
-  ...
+  \item[<var>label of first item</var>] <var>text of first item</var>
+  \item[<var>label of second item</var>] <var>text of second item</var>
+   ...
 \end{description}
 </pre></div>
 
@@ -4889,8 +4905,6 @@
 missing \item</samp>’.
 </p>
 <p>This example shows the environment used for a sequence of definitions.
-The labels ‘<samp>lama</samp>’ and ‘<samp>llama</samp>’ come out in boldface with their
-left edges aligned on the left margin.
 </p>
 <div class="example">
 <pre class="example">\begin{definition}
@@ -4899,6 +4913,9 @@
 \end{definition}
 </pre></div>
 
+<p>The labels ‘<samp>lama</samp>’ and ‘<samp>llama</samp>’ are output in boldface, with the
+left edge on the left margin.
+</p>
 <a name="index-_005citem"></a>
 <p>Start list items with the <code>\item</code> command (see <a href="#g_t_005citem">\item</a>).  Use the
 optional labels, as in <code>\item[Main point]</code>, because there is
@@ -4911,10 +4928,10 @@
 change given in argument style (see <a href="#Font-styles">Font styles</a>) then it will come
 out bold.  For instance, if the label text calls for typewriter with
 <code>\item[\texttt{label text}]</code> then it will appear in bold
-typewriter, if that is available. The simplest way to get non-bold
-typewriter is to use declarative style: <code>\item[{\tt label
-text}]</code>.  Similarly, get the standard roman font with <code>\item[{\rm
-label text}]</code>.
+typewriter, if that is available. The simplest way around this, in this
+example to get non-bold typewriter, is to use declarative style:
+<code>\item[{\tt label text}]</code>.  Similarly, get the standard roman
+font with <code>\item[{\rm label text}]</code>.
 </p>
 <p>For other major LaTeX labelled list environments, see <a href="#itemize">itemize</a>
 and <a href="#enumerate">enumerate</a>.  Unlike those environments, nesting
@@ -4951,7 +4968,7 @@
 </p>
 <div class="example">
 <pre class="example">\begin{displaymath}
-<var>math text</var>
+  <var>mathematical text</var>
 \end{displaymath}
 </pre></div>
 
@@ -4965,8 +4982,8 @@
 </p>
 <p>LaTeX will not break the <var>math text</var> across lines.
 </p>
-<a name="index-package_002c-amsmath-1"></a>
-<a name="index-amsmath-package-1"></a>
+<a name="index-package_002c-amsmath-2"></a>
+<a name="index-amsmath-package-2"></a>
 
 <p>Note that the <samp>amsmath</samp> package has significantly more extensive
 displayed equation facilities.  For example, there are a number of
@@ -5096,9 +5113,9 @@
 </p>
 <div class="example">
 <pre class="example">\begin{enumerate}
-\item[<var>optional label of first item</var>] text of first item
-\item[<var>optional label of second item</var>] text of second item
-...
+  \item[<var>optional label of first item</var>] <var>text of first item</var>
+  \item[<var>optional label of second item</var>] <var>text of second item</var>
+  ...
 \end{enumerate}
 </pre></div>
 
@@ -5277,18 +5294,21 @@
 </p>
 <div class="example">
 <pre class="example">\begin{equation}
-  math text
+  <var>mathematical text</var>
 \end{equation}
 </pre></div>
 
-<p>Make a <code>displaymath</code> environment (see <a href="#displaymath">displaymath</a>) with an
-equation number in the right margin.  The equation number is generated
-using the <code>equation</code> counter.
+<p>The same as a <code>displaymath</code> environment (see <a href="#displaymath">displaymath</a>)
+except that LaTeX puts an equation number flush to the right margin.
+The equation number is generated using the <code>equation</code> counter.
 </p>
 <p>You should have no blank lines between <code>\begin{equation}</code> and
-<code>\begin{equation}</code> or LaTeX will tell you that there is a
+<code>\begin{equation}</code>, or LaTeX will tell you that there is a
 missing dollar sign.
 </p>
+<a name="index-package_002c-amsmath-3"></a>
+<a name="index-amsmath-package-3"></a>
+
 <p>The package <samp>amsmath</samp> package has extensive displayed equation
 facilities.  New documents should include this package.
 </p>
@@ -5312,30 +5332,31 @@
 </p>
 <div class="example">
 <pre class="example">\begin{figure}[<var>placement</var>]
-  figure body
+  <var>figure body</var>
   \caption[<var>loftitle</var>]{<var>title</var>}  % optional
   \label{<var>label}</var>              % optional
 \end{figure}
 </pre></div>
 
-<p>or
+<p>or:
 </p>
 <div class="example">
 <pre class="example">\begin{figure*}[<var>placement</var>]
-  figure body
+  <var>figure body</var>
   \caption[<var>loftitle</var>]{<var>title</var>}  % optional
   \label{<var>label}</var>              % optional  
 \end{figure*}
 </pre></div>
 
-<p>The figure body is made up of imported graphics, or text, LaTeX
-commands, etc.  It is typeset in a <code>parbox</code> of width
-<code>\textwidth</code>.
+<p>Figures are for material that is not part of the normal text.  An
+example is material that you cannot have split between two pages, such
+as a graphic.  Because of this, LaTeX does not typeset figures in
+sequence with normal text but instead “floats” them to a convenient
+place, such as the top of a following page (see <a href="#Floats">Floats</a>).
 </p>
-<p>Figures are not part of the normal text.  A long figure will not be
-split between two pages.  Because of this, they are not typeset in
-sequence with the normal text but instead are “floated” to a
-convenient place, such as the top of a following page (see <a href="#Floats">Floats</a>).
+<p>The <var>figure body</var> can consist of imported graphics
+(see <a href="#Graphics">Graphics</a>), or text, LaTeX commands, etc.  It is typeset in a
+<code>parbox</code> of width <code>\textwidth</code>.
 </p>
 <p>The possible values of <var>placement</var> are <code>h</code> for ‘<samp>here</samp>’,
 <code>t</code> for ‘<samp>top</samp>’, <code>b</code> for ‘<samp>bottom</samp>’, and <code>p</code> for
@@ -5354,13 +5375,14 @@
 figure.  By default it is numbered.  If <var>loftitle</var> is present, it is
 used in the list of figures instead of <var>title</var> (see <a href="#Table-of-contents-etc_002e">Table of contents etc.</a>).
 </p>
-<p>This example makes a figure out of a graphic.  It requires one of the
-packages <samp>graphics</samp> or <samp>graphicx</samp>.  The graphic, with its
-caption, will be placed at the top of a page or, if it is pushed to the
+<p>This example makes a figure out of a graphic.  LaTeX will place that
+graphic and its caption at the top of a page or, if it is pushed to the
 end of the document, on a page of floats.
 </p>
 <div class="example">
-<pre class="example">\begin{figure}[t]
+<pre class="example">\usepackage{graphicx}  % in preamble
+  ...
+\begin{figure}[t]
   \centering
   \includegraphics[width=0.5\textwidth]{CTANlion.png}
   \caption{The CTAN lion, by Duane Bibby}
@@ -5470,9 +5492,10 @@
 
 <a name="index-_005c_005c-for-flushleft"></a>
 <p>An environment that creates a paragraph whose lines are flush to the
-left-hand margin and ragged right. LaTeX will break long lines to
-avoid hyphenation and stretching or shrinking spaces.  Force a new line
-with a double backslash <code>\\</code>.  For the declaration form
+left-hand margin, and ragged right. If you have lines that are too long
+then LaTeX will linebreak them in a way that avoids hyphenation and
+stretching or shrinking spaces.  To force a new line use a double
+backslash, <code>\\</code>.  For the declaration form
 see <a href="#g_t_005craggedright">\raggedright</a>.
 </p>
 <p>This creates a box of text that is at most 3 inches wide, with the text
@@ -5573,9 +5596,10 @@
 
 <a name="index-_005c_005c-_0028for-flushright_0029"></a>
 <p>An environment that creates a paragraph whose lines are flush to the
-right-hand margin and ragged left. LaTeX will break long lines to
-avoid hyphenation and stretching or shrinking spaces.  Force a new line
-with a double backslash <code>\\</code>.  For the declaration form
+right-hand margin and ragged left. If you have lines that are too long
+to fit the margins then LaTeX will linebreak them in a way that
+avoids hyphenation and stretching or shrinking spaces.  To force a new
+line use a double backslash, <code>\\</code>.  For the declaration form
 see <a href="#g_t_005craggedleft">\raggedleft</a>.
 </p>
 <p>For an example related to this environment, see <a href="#flushleft">flushleft</a>.
@@ -5644,24 +5668,23 @@
 <a name="index-lists-of-items"></a>
 <a name="index-unordered-lists"></a>
 <a name="index-bulleted-lists"></a>
+<a name="index-bullet-lists"></a>
 
 <p>Synopsis:
 </p>
 <div class="example">
 <pre class="example">\begin{itemize}
-\item[<var>optional label of first item</var>] text of first item
-\item[<var>optional label of second item</var>] text of second item
-...
+  \item[<var>optional label of first item</var>] <var>text of first item</var>
+  \item[<var>optional label of second item</var>] <var>text of second item</var>
+  ...
 \end{itemize}
 </pre></div>
 
-<p>Produces an “unordered,” or “bulleted,” list.  The format of the
-labelling depends on the nesting level; see below.  Each <code>itemize</code>
-list environment must have at least one item; having none causes the
+<p>Produce a list that is unordered, sometimes called a bullet list.  The
+environment must have at least one <code>\item</code>; having none causes the
 LaTeX error ‘<samp>Something's wrong--perhaps a missing \item</samp>’.
 </p>
-<p>This example gives a two-item list.  As a top-level list each label
-would come out as a bullet, •.
+<p>This gives a two-item list.
 </p>
 <div class="example">
 <pre class="example">\begin{itemize}
@@ -5670,6 +5693,9 @@
 \end{itemize}
 </pre></div>
 
+<p>As a top-level list each label would come out as a bullet, •.
+The format of the labeling depends on the nesting level; see below.
+</p>
 <a name="index-_005citem-3"></a>
 <p>Start list items with the <code>\item</code> command (see <a href="#g_t_005citem">\item</a>).  If you
 give <code>\item</code> an optional argument by following it with square
@@ -5785,21 +5811,24 @@
 </p>
 <div class="example">
 <pre class="example">\begin{list}{<var>labeling</var>}{<var>spacing</var>}
-\item[<var>optional label of first item</var>] text of first item
-\item[<var>optional label of second item</var>] text of second item
-...
+  \item[<var>optional label of first item</var>] <var>text of first item</var>
+  \item[<var>optional label of second item</var>] <var>text of second item</var>
+  ...
 \end{list}
 </pre></div>
 
-<p>A generic environment for constructing more specialized lists.  It is
-most often used to create lists via the <code>description</code>,
-<code>enumerate</code>, and <code>itemize</code> environments (see <a href="#description">description</a>,
-<a href="#enumerate">enumerate</a>, and <a href="#itemize">itemize</a>).  Also, many standard LaTeX
-environments that are not visually lists are constructed using
-<code>list</code>, including <code>quotation</code>, <code>quote</code>, <code>center</code>,
-<code>verbatim</code>, and plenty more (see <a href="#quotation-_0026-quote">quotation & quote</a>,
-see <a href="#center">center</a>, see <a href="#flushright">flushright</a>).
+<p>An environment for constructing lists.
 </p>
+<p>Note that this environment does not typically appear in the document
+body.  Most lists created by LaTeX authors are the ones that come
+standard: the <code>description</code>, <code>enumerate</code>, and <code>itemize</code>
+environments (see <a href="#description">description</a>, <a href="#enumerate">enumerate</a>, and <a href="#itemize">itemize</a>).
+</p>
+<p>Instead, the <code>list</code> environment is most often used in macros.  For
+example, many standard LaTeX environments that do not immediately
+appear to be lists are in fact constructed using <code>list</code>, including
+<code>quotation</code>, <code>quote</code>, and <code>center</code> (see <a href="#quotation-_0026-quote">quotation & quote</a>, see <a href="#center">center</a>).
+</p>
 <p>This uses the <code>list</code> environment to define a new custom
 environment.
 </p>
@@ -5807,9 +5836,9 @@
 <pre class="example">\newcounter{namedlistcounter}  % number the items
 \newenvironment{named}
   {\begin{list}
-     {Item~\Roman{namedlistcounter}.} % labeling argument
-     {\usecounter{namedlistcounter}   % spacing argument
-      \setlength{\leftmargin}{3.5em}} % still spacing arg
+     {Item~\Roman{namedlistcounter}.} % labeling 
+     {\usecounter{namedlistcounter}   % set counter
+      \setlength{\leftmargin}{3.5em}} % set spacing 
   }
   {\end{list}}
 
@@ -5830,19 +5859,21 @@
 optional argument by including square braces and the text, as in the
 above <code>\item[Special label.]</code>; see <a href="#g_t_005citem">\item</a>.
 </p>
-<p>The mandatory second argument <var>spacing</var> has a list of commands.  One
-that goes in here is <code>\usecounter{<var>countername</var>}</code>
-(see <a href="#g_t_005cusecounter">\usecounter</a>).  Use this to tell LaTeX to number the items
-using the given counter.  The counter will be reset to zero each time
-LaTeX enters the environment, and the counter is incremented by one
-each time LaTeX encounters an <code>\item</code>.
+<p>The mandatory second argument <var>spacing</var> has a list of commands.
+This list can be empty.  A command that can go in here is
+<code>\usecounter{<var>countername</var>}</code> (see <a href="#g_t_005cusecounter">\usecounter</a>).  Use this
+to tell LaTeX to number the items using the given counter.  The
+counter will be reset to zero each time LaTeX enters the environment,
+and the counter is incremented by one each time LaTeX encounters an
+<code>\item</code> that does not have an optional argument.
 </p>
 <a name="index-_005cmakelabel"></a>
-<a name="list-makelabel"></a><p>Another command that can go in <var>spacing</var> is <code>\makelabel</code>, which
-constructs the label box.  By default it puts the contents flush
-right.  Its only argument is the label, which it typesets in
-LR mode. One example of changing its definition is that to the above
-<code>named</code> example before the definition of the environment add
+<a name="list-makelabel"></a><p>Another command that can go in <var>spacing</var> is
+<code>\makelabel</code>, which constructs the label box.  By default it puts
+the contents flush right.  Its only argument is the label, which it
+typesets in LR mode (see <a href="#Modes">Modes</a>). One example of changing its
+definition is that to the above <code>named</code> example, before the
+definition of the environment add
 <code>\newcommand{\namedmakelabel}[1]{\textsc{#1}}</code>, and between
 the <code>\setlength</code> command and the parenthesis that closes the
 <var>spacing</var> argument also add <code>\let\makelabel\namedmakelabel</code>.
@@ -6296,24 +6327,21 @@
 is similar to <code>\parbox</code> (see <a href="#g_t_005cparbox">\parbox</a>) but here you can have
 paragraphs.
 </p>
-<p>This puts the footnote at the bottom of the table, not the bottom of the
-page.
+<p>This example will be 3 inches wide, and has two paragraphs.
 </p>
 <div class="example">
-<pre class="example">\begin{center}           % center the minipage on the line
-\begin{minipage}{2.5in}
-  \begin{center}         % center the table inside the minipage
-    \begin{tabular}{ll}
-      \textsc{Monarch}  &\textsc{Reign}             \\ \hline
-      Elizabeth II      &63 years\footnote{to date} \\
-      Victoria          &63 years                   \\
-      George III        &59 years
-    \end{tabular}
-  \end{center}  
+<pre class="example">\begin{minipage}{3in}
+  Stephen Kleene was a founder of the Theory of Computation.
+
+  He was a student of Church, wrote three influential texts,
+  was President of the Association for Symbolic Logic,
+  and won the National Medal of Science.
 \end{minipage}
-\end{center}
 </pre></div>
 
+<p>See below for a discussion of the paragraph indent inside a
+<code>minipage</code>.
+</p>
 <p>The required argument <var>width</var> is a rigid length (see <a href="#Lengths">Lengths</a>).
 It gives the width of the box into which <var>contents</var> are typeset.
 </p>
@@ -6415,6 +6443,24 @@
 uses the <code>\mpfootnote</code> counter instead of the ordinary
 <code>footnote</code> counter (see <a href="#Counters">Counters</a>).
 </p>
+<p>This puts the footnote at the bottom of the table, not the bottom of the
+page.
+</p>
+<div class="example">
+<pre class="example">\begin{center}           % center the minipage on the line
+\begin{minipage}{2.5in}
+  \begin{center}         % center the table inside the minipage
+    \begin{tabular}{ll}
+      \textsc{Monarch}  &\textsc{Reign}             \\ \hline
+      Elizabeth II      &63 years\footnote{to date} \\
+      Victoria          &63 years                   \\
+      George III        &59 years
+    \end{tabular}
+  \end{center}  
+\end{minipage}
+\end{center}
+</pre></div>
+
 <p>If you nest minipages then there is an oddness when using footnotes.
 Footnotes appear at the bottom of the text ended by the next
 <code>\end{minipage}</code> which may not be their logical place.
@@ -6810,8 +6856,9 @@
 </pre></div>
 
 <p>Draw a line.  It slopes such that it vertically rises <var>y_rise</var> for
-every horizontal <var>x_run</var>, and such that the total horizontal change
-is <var>travel</var>.  In the special case of vertical lines, where
+every horizontal <var>x_run</var>.  The <var>travel</var> is the total horizontal
+change — it is not the length of the vector, it is the change in
+<em>x</em>.  In the special case of vertical lines, where
 (<var>x_run</var>,<var>y_rise</var>)=(0,1), the <var>travel</var> gives the change in
 <em>y</em>.
 </p>
@@ -7092,20 +7139,21 @@
 <pre class="example">\vector(<var>x_run</var>,<var>y_rise</var>){<var>travel</var>}
 </pre></div>
 
-<p>Draw a line ending in an arrow.  It slopes such that it vertically rises
-<var>y_rise</var> for every horizontal <var>x_run</var>, and such that the total
-horizontal change is <var>travel</var>.  In the special case of vertical
-vectors, if (<var>x_run</var>,<var>y_rise</var>)=(0,1), then <var>travel</var> gives
-the change in <em>y</em>.
+<p>Draw a line ending in an arrow.  The slope of that line is: it
+vertically rises <var>y_rise</var> for every horizontal <var>x_run</var>.  The
+<var>travel</var> is the total horizontal change — it is not the
+length of the vector, it is the change in <em>x</em>.  In the special case
+of vertical vectors, if (<var>x_run</var>,<var>y_rise</var>)=(0,1), then
+<var>travel</var> gives the change in <em>y</em>.
 </p>
 <p>For an example see <a href="#picture">picture</a>.
 </p>
 <p>For elaboration on <var>x_run</var> and <var>y_rise</var> see <a href="#g_t_005cline">\line</a>.  As
-there, the values of <var>x_run</var> and <var>y_rise</var> are limited.  You must
-chooses integers between -4 and 4, inclusive.  Also, the two you
-choose must be relatively prime.  Thus, <code>\vector(2,1){4}</code> is
-acceptable but <code>\vector(4,2){4}</code> is not (if you use the latter
-then you get a sequence of arrowheads).
+there, the values of <var>x_run</var> and <var>y_rise</var> are limited.  For
+<code>\vector</code> you must chooses integers between -4 and 4,
+inclusive.  Also, the two you choose must be relatively prime.  Thus,
+<code>\vector(2,1){4}</code> is acceptable but <code>\vector(4,2){4}</code> is
+not (if you use the latter then you get a sequence of arrowheads).
 </p>
 
 <hr>
@@ -8018,24 +8066,24 @@
 bar <code>|</code> is more common.  This command is rarely used in the
 body of a table; typically a table’s vertical lines are specified in
 <code>tabular</code>’s <var>cols</var> argument and overridden as needed with
-<code>\multicolumn</code>.
+<code>\multicolumn</code> (see <a href="#tabular">tabular</a>).
 </p>
-<p>This example illustrates some pitfalls.  In the first line’s second
+<p>The example below illustrates some pitfalls.  In the first row’s second
 entry the <code>\hfill</code> moves the <code>\vline</code> to the left edge of the
 cell.  But that is different than putting it halfway between the two
-columns, so in that row between the first and second columns there are
-two vertical rules, with the one from the <code>{c|cc}</code> specifier
-coming before the one produced by the <code>\vline\hfill</code>.  In contrast,
-the first line’s third entry shows the usual way to put a vertical bar
-between two columns.  In the second line, the <code>ghi</code> is the widest
-entry in its column so in the <code>\vline\hfill</code> the <code>\hfill</code> has
-no effect and the vertical line in that entry appears immediately next
-to the <code>g</code>, with no whitespace.
+columns, so between the first and second columns there are two vertical
+rules, with the one from the <code>{c|cc}</code> specifier coming before the
+one produced by the <code>\vline\hfill</code>.  In contrast, the first row’s
+third entry shows the usual way to put a vertical bar between two
+columns.  In the second row, the <code>ghi</code> is the widest entry in its
+column so in the <code>\vline\hfill</code> the <code>\hfill</code> has no effect and
+the vertical line in that entry appears immediately next to the
+<code>g</code>, with no whitespace.
 </p>
 <div class="example">
 <pre class="example">\begin{tabular}{c|cc}
-  x   &\vline\hfill y   &\multicolumn{1}{|r}{z} \\  
-  abc &def &\vline\hfill ghi 
+  x   &\vline\hfill y   &\multicolumn{1}{|r}{z} \\ % row 1  
+  abc &def &\vline\hfill ghi                       % row 2  
 \end{tabular}
 </pre></div>
 
@@ -8478,8 +8526,8 @@
 \end{thm}
 </pre></div>
 
-<a name="index-package_002c-amsmath-2"></a>
-<a name="index-amsmath-package-2"></a>
+<a name="index-package_002c-amsmath-4"></a>
+<a name="index-amsmath-package-4"></a>
 
 <a name="index-package_002c-amsthm"></a>
 <a name="index-amsthm-package"></a>
@@ -8646,17 +8694,7 @@
 
 <p>Typeset <var>literal-text</var> as it is input, including special characters
 and spaces, using the typewriter (<code>\tt</code>) font.
-<a name="index-visible-space"></a>
-The <code>*</code>-form differs only in that spaces are printed with a visible
-space character.
 </p>
-<p>The single-character delimiter <var>char</var> surrounds <var>literal-text</var>;
-it is the same character before and after.  No spaces come between
-<code>\verb</code> or <code>\verb*</code> and <var>char</var>, or between <var>char</var> and
-<var>literal-text</var>, or between <var>literal-text</var> and the second
-occurrence of <var>char</var>.  The delimiter must not appear in
-<var>literal-text</var>. The <var>literal-text</var> cannot include a line break.
-</p>
 <p>This example shows two different invocations of <code>\verb</code>.
 </p>
 <div class="example">
@@ -8668,6 +8706,25 @@
 exclamation point, <code>!</code>.  The second instead uses plus, <code>+</code>,
 because the exclamation point is part of <code>literal-text</code>.
 </p>
+<p>The single-character delimiter <var>char</var> surrounds
+<var>literal-text</var> — it must be the same character before and
+after.  No spaces come between <code>\verb</code> or <code>\verb*</code> and
+<var>char</var>, or between <var>char</var> and <var>literal-text</var>, or between
+<var>literal-text</var> and the second occurrence of <var>char</var> (the synopsis
+shows a space only to distinguish one component from the other).  The
+delimiter must not appear in <var>literal-text</var>. The <var>literal-text</var>
+cannot include a line break.
+</p>
+<a name="index-visible-space"></a>
+<p>The <code>*</code>-form differs only in that spaces are printed with a visible
+space character.
+</p>
+<p>The output from this will include a character showing the spaces.
+</p>
+<div class="example">
+<pre class="example">The commands's first argument is \verb*!filename with extension! and ...
+</pre></div>
+
 <a name="index-package_002c-url"></a>
 <a name="index-url-package"></a>
 
@@ -8675,6 +8732,15 @@
 provides an option that is better than the <code>\verb</code> command, since
 it allows line breaks.
 </p>
+<a name="index-package_002c-listings-2"></a>
+<a name="index-listings-package-2"></a>
+
+<a name="index-package_002c-minted-2"></a>
+<a name="index-minted-package-2"></a>
+
+<p>For computer code there are many packages with advantages over
+<code>\verb</code>.  One is <samp>listings</samp>, another is <samp>minted</samp>.
+</p>
 <a name="index-package_002c-cprotect-1"></a>
 <a name="index-cprotect-package-1"></a>
 
@@ -10956,11 +11022,11 @@
 </pre></div>
 
 <p>Used in the second argument of the <code>list</code> environment
-(see <a href="#list">list</a>).  It sets up <var>counter</var> to number the list items.  It
-initializes <var>counter</var> to zero, and arranges that when <code>\item</code>
-is called without its optional argument then <var>counter</var> is
-incremented by <code>\refstepcounter</code>, making its value be the current
-<code>ref</code> value (see <a href="#g_t_005cref">\ref</a>).  This command is fragile
+(see <a href="#list">list</a>), this declares that list items will be numbered by
+<var>counter</var>.  It initializes <var>counter</var> to zero, and arranges that
+when <code>\item</code> is called without its optional argument then
+<var>counter</var> is incremented by <code>\refstepcounter</code>, making its value
+be the current <code>ref</code> value (see <a href="#g_t_005cref">\ref</a>).  This command is fragile
 (see <a href="#g_t_005cprotect">\protect</a>).
 </p>
 <p>Put in the document preamble, this example makes a new list environment
@@ -10996,14 +11062,9 @@
 <pre class="example">\value{<var>counter</var>}
 </pre></div>
 
-<p>Expands to the value of <var>counter</var>.  It is often used in
-<code>\setcounter</code> or <code>\addtocounter</code> but <code>\value</code> can be used
-anywhere that LaTeX expects a number.  It must not be preceded by
-<code>\protect</code> (see <a href="#g_t_005cprotect">\protect</a>).
+<p>Expands to the value of the counter <var>counter</var>. (Note that the name
+of a counter does not begin with a backslash.)
 </p>
-<p>The <code>\value</code> command is not used for typesetting the value of the
-counter.  See <a href="#g_t_005calph-_005cAlph-_005carabic-_005croman-_005cRoman-_005cfnsymbol">\alph \Alph \arabic \roman \Roman \fnsymbol</a>.
-</p>
 <p>This example outputs ‘<samp>Test counter is 6. Other counter
 is 5.</samp>’.
 </p>
@@ -11016,6 +11077,14 @@
 Other counter is \arabic{other}.
 </pre></div>
 
+<p>The <code>\value</code> command is not used for typesetting the value of the
+counter.  For that, see <a href="#g_t_005calph-_005cAlph-_005carabic-_005croman-_005cRoman-_005cfnsymbol">\alph \Alph \arabic \roman \Roman \fnsymbol</a>.
+</p>
+<p>It is often used in <code>\setcounter</code> or <code>\addtocounter</code> but
+<code>\value</code> can be used anywhere that LaTeX expects a number, such
+as in <code>\hspace{\value{foo}\parindent}</code>.  It must not be
+preceded by <code>\protect</code> (see <a href="#g_t_005cprotect">\protect</a>).
+</p>
 <p>This example inserts <code>\hspace{4\parindent}</code>.
 </p>
 <div class="example">
@@ -11859,41 +11928,39 @@
 <a name="index-remarks-in-the-margin"></a>
 <a name="index-_005cmarginpar"></a>
 
-<p>Synopsis:
+<p>Synopsis, one of:
 </p>
 <div class="example">
-<pre class="example">\marginpar[<var>left</var>]{<var>right</var>}
+<pre class="example">\marginpar{<var>right</var>}
+\marginpar[<var>left</var>]{<var>right</var>}
 </pre></div>
 
 <p>Create a note in the margin.  The first line of the note will have the
 same baseline as the line in the text where the <code>\marginpar</code>
 occurs.
 </p>
-<p>When you only specify the mandatory argument <var>right</var>, the text
-will be placed
+<p>The margin that LaTeX uses for the note depends on the current layout
+(see <a href="#Document-class-options">Document class options</a>) and also on <code>\reversemarginpar</code>
+(see below).  If you are using one-sided layout (document option
+<code>oneside</code>) then it goes in the right margin.  If you are using
+two-sided layout (document option <code>twoside</code>) then it goes in the
+outside margin.  If you are in two-column layout (document option
+<code>twocolumn</code>) then it goes in the nearest margin.
 </p>
-<ul>
-<li> in the right margin for one-sided layout (option <code>oneside</code>, see
-<a href="#Document-class-options">Document class options</a>);
-
-</li><li> in the outside margin for two-sided layout (option <code>twoside</code>, see
-<a href="#Document-class-options">Document class options</a>);
-
-</li><li> in the nearest margin for two-column layout (option <code>twocolumn</code>,
-see <a href="#Document-class-options">Document class options</a>).
-</li></ul>
-
 <a name="index-_005creversemarginpar"></a>
 <a name="index-_005cnormalmarginpar"></a>
-<p>The command <code>\reversemarginpar</code> places subsequent marginal notes
-in the opposite (inside) margin.  <code>\normalmarginpar</code> places them
-in the default position.
+<p>If you declare <code>\reversemarginpar</code> then LaTeX will place
+subsequent marginal notes in the opposite margin to that given in the
+prior paragraph.  Revert that to the default position with
+<code>\normalmarginpar</code>.
 </p>
-<p>When you specify both arguments, <var>left</var> is used for the left
-margin, and <var>right</var> is used for the right margin.
+<p>When you specify the optional argument <var>left</var> then it is used for a
+note in the left margin, while the mandatory argument <var>right</var> is
+used for a note in the the right margin.
 </p>
-<p>The first word will normally not be hyphenated; you can enable
-hyphenation there by beginning the node with <code>\hspace{0pt}</code>.
+<p>Normally, a note’s first word will not be hyphenated.  You can enable
+hyphenation there by beginning <var>left</var> or <var>right</var> with
+<code>\hspace{0pt}</code>.
 </p>
 <p>These parameters affect the formatting of the note:
 </p>
@@ -11960,40 +12027,25 @@
 where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.
 </pre></div>
 
-<p>Math mode is for inline mathematics.  It is invoked by the starting
-<code>\(</code> and finished by the matching ending <code>\)</code>.  Display math
-mode is for displayed equations and here is invoked by the
+<p>Math mode is for inline mathematics.  In the above example it is invoked
+by the starting <code>\(</code> and finished by the matching ending <code>\)</code>.
+Display math mode is for displayed equations and here is invoked by the
 <code>displaymath</code> environment.  Note that any mathematical text
-whatever, including that consisting of single characters, is handled in
-math mode.
+whatever, including mathematical text consisting of just one character,
+is handled in math mode.
 </p>
-<a name="index-package_002c-amsmath-3"></a>
-<a name="index-amsmath-package-3"></a>
-<a name="index-package_002c-amsfonts"></a>
-<a name="index-amsfonts-package"></a>
-<a name="index-package_002c-mathtools"></a>
-<a name="index-mathtools-package"></a>
-
-<p>The American Mathematical Society has made freely available a set of
-packages that greatly expand your options for writing mathematics,
-<samp>amsmath</samp> and <samp>amssymb</samp> (also be aware of the
-<samp>mathtools</samp> package that is an extension to, and loads,
-<samp>amsmath</samp>).  New documents that will have mathematical text should
-use these packages.  Descriptions of these packages is outside the scope
-of this document; see their documentation on CTAN.
-</p>
 <p>When in math mode or display math mode, LaTeX handles many aspects of
 your input text differently than in other text modes.  For example,
 </p>
 <div class="example">
-<pre class="example">contrast x+y with \( x+y \).
+<pre class="example">contrast x+y with \( x+y \)
 </pre></div>
 
 <p>in math mode the letters are in italics and the spacing around the plus
 sign is different.
 </p>
-<p>To make inline formulas, put LaTeX in math mode with one of these
-three.
+<p>There are three ways to make inline formulas, to put LaTeX in math
+mode.
 </p>
 <div class="example">
 <pre class="example">\( <var>mathematical material</var> \)
@@ -12001,9 +12053,10 @@
 \begin{math} <var>mathematical material</var> \end{math}
 </pre></div>
 
-<p>The first form is preferred, and the third form is very rarely used.
-You can mix them, sometimes using one and sometimes another.  These can
-be used in paragraph mode or in LR mode (see <a href="#Modes">Modes</a>).
+<p>The first form is preferred and the second is quite common, but the
+third form is rarely used.  You can sometimes use one and sometimes
+another, as in <code>\(x\) and $y$</code>.  You can use these in paragraph
+mode or in LR mode (see <a href="#Modes">Modes</a>).
 </p>
 <p>To make displayed formulas, put LaTeX into display math mode with
 either:
@@ -12022,10 +12075,10 @@
 \end{equation}
 </pre></div>
 
-<p>The only difference is that with the <code>equation</code> environment,
-LaTeX puts a formula number alongside the formula, which by default
-has the form ‘<samp>(<var>arabic number</var>)</samp>’.  The construct <code>\[
-<var>math</var> \]</code> is equivalent to <code>\begin{displaymath} <var>math</var>
+<p>(see <a href="#displaymath">displaymath</a>, see <a href="#equation">equation</a>).  The only difference is that
+with the <code>equation</code> environment, LaTeX puts a formula number
+alongside the formula.  The construct <code>\[ <var>math</var> \]</code> is
+equivalent to <code>\begin{displaymath} <var>math</var>
 \end{displaymath}</code>.  These environments can only be used in paragraph
 mode (see <a href="#Modes">Modes</a>).
 </p>
@@ -12035,12 +12088,12 @@
 math mode they are further apart and in inline math mode they are closer
 together.
 </p>
-<p>Sometimes you want the display math treatment to happen in the inline
-math mode.  For this, the <code>\displaystyle</code> declaration forces the
-size and style of the formula to be that of <code>displaymath</code>.  Thus
-<code>\(\displaystyle \sum_{n=0}^\infty x_n\)</code> will have the limits
-above and below the summation sign, not next to it.  Another example is
-that
+<p>Sometimes you want the display math typographical treatment to happen in
+the inline math mode.  For this, the <code>\displaystyle</code> declaration
+forces the size and style of the formula to be that of
+<code>displaymath</code>.  Thus <code>\(\displaystyle \sum_{n=0}^\infty
+x_n\)</code> will have the limits above and below the summation sign, not next
+to it.  Another example is that
 </p>
 <div class="example">
 <pre class="example">\begin{tabular}{r|cc}
@@ -12057,6 +12110,23 @@
 the ‘<samp>Geometric</samp>’ line’s fraction will be easy to read, with
 characters the same size as in the rest of the line.
 </p>
+<a name="index-package_002c-amsmath-5"></a>
+<a name="index-amsmath-package-5"></a>
+
+<a name="index-package_002c-amsfonts"></a>
+<a name="index-amsfonts-package"></a>
+
+<a name="index-package_002c-mathtools"></a>
+<a name="index-mathtools-package"></a>
+
+<p>The American Mathematical Society has made freely available a set of
+packages that greatly expand your options for writing mathematics,
+<samp>amsmath</samp> and <samp>amssymb</samp> (also be aware of the <samp>mathtools</samp>
+package that is an extension to, and loads, <samp>amsmath</samp>).  New
+documents that will have mathematical text should use these packages.
+Descriptions of these packages is outside the scope of this document;
+see their documentation on CTAN.
+</p>
 <table class="menu" border="0" cellspacing="0">
 <tr><td align="left" valign="top">• <a href="#Subscripts-_0026-superscripts" accesskey="1">Subscripts & superscripts</a>:</td><td>  </td><td align="left" valign="top">Also known as exponent or index.
 </td></tr>
@@ -13756,7 +13826,7 @@
 </td></tr>
 <tr><td align="left" valign="top">• <a href="#g_t_005cboldmath-_0026-_005cunboldmath" accesskey="3">\boldmath & \unboldmath</a>:</td><td>  </td><td align="left" valign="top">Symbols in boldface.
 </td></tr>
-<tr><td align="left" valign="top">• <a href="#Ellipses" accesskey="4">Ellipses</a>:</td><td>  </td><td align="left" valign="top">Dots.
+<tr><td align="left" valign="top">• <a href="#Dots" accesskey="4">Dots</a>:</td><td>  </td><td align="left" valign="top">Ellipses, etc.
 </td></tr>
 </table>
 
@@ -13838,7 +13908,7 @@
 <a name="g_t_005cboldmath-_0026-_005cunboldmath"></a>
 <div class="header">
 <p>
-Next: <a href="#Ellipses" accesskey="n" rel="next">Ellipses</a>, Previous: <a href="#Calligraphic" accesskey="p" rel="prev">Calligraphic</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
+Next: <a href="#Dots" accesskey="n" rel="next">Dots</a>, Previous: <a href="#Calligraphic" accesskey="p" rel="prev">Calligraphic</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
 </div>
 <a name="g_t_005cboldmath-_0026-_005cunboldmath-1"></a>
 <h4 class="subsection">16.2.3 <code>\boldmath</code> & <code>\unboldmath</code></h4>
@@ -13903,13 +13973,13 @@
 </p>
 
 <hr>
-<a name="Ellipses"></a>
+<a name="Dots"></a>
 <div class="header">
 <p>
 Previous: <a href="#g_t_005cboldmath-_0026-_005cunboldmath" accesskey="p" rel="prev">\boldmath & \unboldmath</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
 </div>
-<a name="Ellipses-1"></a>
-<h4 class="subsection">16.2.4 Ellipses</h4>
+<a name="Dots_002c-horizontal-or-vertical"></a>
+<h4 class="subsection">16.2.4 Dots, horizontal or vertical</h4>
 
 <a name="index-ellipses"></a>
 <a name="index-dots"></a>
@@ -13940,7 +14010,7 @@
 <dt><code>\ddots</code>
 <a name="index-_005cddots"></a>
 </dt>
-<dd><p>Diagonal ellipsis, &#x22F1;.  See the above example for a
+<dd><p>Diagonal ellipsis, &#x22F1;.  See the above array example for a
 usage.
 </p>
 <a name="ellipses-ldots"></a></dd>
@@ -13948,25 +14018,26 @@
 <a name="index-_005cldots"></a>
 </dt>
 <dd><p>Ellipsis on the baseline, &#x2026;.  Used as: <code>\(
-x_0,\ldots x_{n-1} \)</code>.  A synonym is <code>\mathellipsis</code>.  A synonym
-from the <samp>amsmath</samp> package is <code>\hdots</code>.
+x_0,\ldots x_{n-1} \)</code>.  Another example is the above array example. A
+synonym is <code>\mathellipsis</code>.  A synonym from the <samp>amsmath</samp>
+package is <code>\hdots</code>.
 </p>
 <p>You can also use this command outside of mathematical text, as in
-<code>The gears, brakes, \ldots{} are all broken</code>.  (In a text mode a
-synonym for <code>\ldots</code> is <code>\dots</code>.)
+<code>The gears, brakes, \ldots{} are all broken</code>.  (In a paragraph
+mode or LR mode a synonym for <code>\ldots</code> is <code>\dots</code>.)
 </p>
 <a name="ellipses-vdots"></a></dd>
 <dt><code>\vdots</code>
 <a name="index-_005cvdots"></a>
 </dt>
-<dd><p>Vertical ellipsis, &#x22EE;.  See the above example for a
+<dd><p>Vertical ellipsis, &#x22EE;.  See the above array example for a
 usage.
 </p>
 </dd>
 </dl>
 
-<a name="index-package_002c-amsmath-4"></a>
-<a name="index-amsmath-package-4"></a>
+<a name="index-package_002c-amsmath-6"></a>
+<a name="index-amsmath-package-6"></a>
 
 <p>The <samp>amsmath</samp> package has the command <code>\dots</code> to semantically
 mark up ellipses.  This example produces two different-looking outputs
@@ -14215,8 +14286,8 @@
 </dd>
 </dl>
 
-<a name="index-package_002c-amsmath-5"></a>
-<a name="index-amsmath-package-5"></a>
+<a name="index-package_002c-amsmath-7"></a>
+<a name="index-amsmath-package-7"></a>
 
 <p>The <samp>amsmath</samp> package adds improvements on some of these, and also
 allows you to define your own.  The full documentation is on CTAN, but
@@ -14569,15 +14640,15 @@
 <pre class="example">With side ratios \( 3:4 \) and \( 4:5 \), the triangle is right.
 </pre></div>
 
-<a name="index-package_002c-amsmath-6"></a>
-<a name="index-amsmath-package-6"></a>
+<a name="index-package_002c-amsmath-8"></a>
+<a name="index-amsmath-package-8"></a>
 
 <p>Ordinary LaTeX defines <code>\colon</code> to produce the colon character
 with the spacing appropriate for punctuation, as in set-builder notation
 <code>\{x\colon 0\leq x<1\}</code>.
 </p>
-<a name="index-package_002c-amsmath-7"></a>
-<a name="index-amsmath-package-7"></a>
+<a name="index-package_002c-amsmath-9"></a>
+<a name="index-amsmath-package-9"></a>
 
 <p>But the widely-used <samp>amsmath</samp> package defines <code>\colon</code> for use
 in the definition of functions <code>f\colon D\to C</code>.  So if you want
@@ -14768,7 +14839,7 @@
 the math modes), and error messages will refer to these.
 </p>
 <ul>
-<li><a name="modes-paragraph-mode"></a></li><li> <a name="index-paragraph-mode"></a>
+<li> <a name="modes-paragraph-mode"></a><a name="index-paragraph-mode"></a>
 <em>Paragraph mode</em> is what LaTeX is in when processing ordinary
 text.  It breaks the input text into lines and breaks the lines into
 pages.  This is the mode LaTeX is in most of the time.
@@ -14780,16 +14851,17 @@
 making a box with an <code>\mbox</code> command.  As in paragraph mode,
 LaTeX’s output is a string of words with spaces between them.  Unlike
 in paragraph mode, in LR mode LaTeX never starts a new line, it just
-keeps going from left to right.  (When it tries to put that box into a
-line, most likely LaTeX will complain because the box is too wide to
-fit.)
+keeps going from left to right.  (Although LaTeX will not complain
+that the LR box is too long, when it is finished and next tries to put
+that box into a line, it could very well complain that the finished LR
+box won’t fit there.)
 </p>
 </li><li> <a name="index-math-mode"></a>
-<a name="modes-math-mode"></a><em>Math mode</em> happens when LaTeX is generating an inline
-mathematical formula.
+<a name="modes-math-mode"></a><em>Math mode</em> is when LaTeX is generating
+an inline mathematical formula.
 
 <a name="index-display-math-mode"></a>
-<p><em>Display math mode</em> happens when LaTeX is generating a displayed
+<p><em>Display math mode</em> is when LaTeX is generating a displayed
 mathematical formula.  (Displayed formulas differ somewhat from inline
 ones.  One example is that the placement of the subscript on <code>\int</code>
 differs in the two situations.)
@@ -14805,21 +14877,21 @@
 </p>
 </li></ul>
 
-<p>For instance, if you begin a LaTeX article with
-‘<samp>Let \( x \) be ...</samp>’ then these are the modes.  First, LaTeX
-starts every document in vertical mode.  It reads the ‘<samp>L</samp>’ and
-switches to paragraph mode.  The next switch happens at the ‘<samp>\(</samp>’,
-where LaTeX changes to math mode.  Then, when it leaves the formula,
-it resets itself to paragraph mode.
+<p>For instance, if you begin a LaTeX article with ‘<samp>Let \( x \) be
+...</samp>’ then these are the modes: first LaTeX starts every document in
+vertical mode, then it reads the ‘<samp>L</samp>’ and switches to paragraph
+mode, then the next switch happens at the ‘<samp>\(</samp>’ where LaTeX
+changes to math mode, and then when it leaves the formula it pops
+back to paragraph mode.
 </p>
 <a name="index-inner-paragraph-mode"></a>
 <a name="index-outer-paragraph-mode"></a>
 <a name="modes-inner-paragraph-mode"></a><a name="modes-outer-paragraph-mode"></a><p>Paragraph mode has two subcases.  If you use a <code>\parbox</code> command or
-<code>minipage</code> environment then LaTeX is put into paragraph mode; it
-is dividing string of words into lines.  But it will not put a page
-break here.  Inside one of these boxes, called a <em>parbox</em>, LaTeX
-is in <em>inner paragraph mode</em>.  Its more usual situation, where it
-can put page breaks, is <em>outer paragraph mode</em> (see <a href="#Page-breaking">Page breaking</a>).
+or a <code>minipage</code> then LaTeX is put into paragraph mode.  But it
+will not put a page break here.  Inside one of these boxes, called a
+<em>parbox</em>, LaTeX is in <em>inner paragraph mode</em>.  Its more usual
+situation, where it can put page breaks, is <em>outer paragraph mode</em>
+(see <a href="#Page-breaking">Page breaking</a>).
 </p>
 <table class="menu" border="0" cellspacing="0">
 <tr><td align="left" valign="top">• <a href="#g_t_005censuremath" accesskey="1">\ensuremath</a>:</td><td>  </td><td align="left" valign="top">Ensure that math mode is active
@@ -16283,8 +16355,8 @@
 between the questions.
 </p>
 <p>If you use <code>\vspace</code> in the middle of a paragraph (i.e., in
-horizontal mode) then the space is inserted after the line with the
-<code>\vspace</code> command; it does not start a new paragraph at the
+horizontal mode) then the space is inserted after the line containing
+the <code>\vspace</code> command; it does not start a new paragraph at the
 <code>\vspace</code> command.
 </p>
 <p>In this example the two questions will be evenly spaced vertically on
@@ -16329,17 +16401,18 @@
 <code>\vfill</code> ends the current paragraph whereas <code>\vspace{\fill}</code>
 adds the infinite vertical space below its line, irrespective of the
 paragraph structure.  In both cases that space will disappear at a page
-boundary; to circumvent this see <a href="#g_t_005cvspace">\vspace</a>.
+boundary; to circumvent this see the starred option
+in <a href="#g_t_005cvspace">\vspace</a>.
 </p>
 <p>In this example the page is filled, so the top and bottom lines contain
-the text ‘<samp>Lost Dog!</samp>’ and the third ‘<samp>Lost Dog!</samp>’ is exactly
+the text ‘<samp>Lost Dog!</samp>’ and the second ‘<samp>Lost Dog!</samp>’ is exactly
 halfway between them.
 </p> 
 <div class="example">
 <pre class="example">\begin{document}
 Lost Dog!
 \vfill
-Lost Dog!
+Lost Dog!  % perfectly in the middle
 \vfill
 Lost Dog!
 \end{document}
@@ -16965,9 +17038,11 @@
 <pre class="example">\usebox{<var>box-cmd</var>}
 </pre></div>
 
-<p>Produce the box most recently saved in the bin <var>box-cmd</var> by
-<code>\sbox</code>, or <code>\savebox</code>, or <code>lrbox</code>. See <a href="#g_t_005csbox-_0026-_005csavebox">\sbox & \savebox</a> for more information and examples.  This command is robust
-(see <a href="#g_t_005cprotect">\protect</a>).
+<p>Produce the box most recently saved in the bin <var>box-cmd</var> by the
+commands <code>\sbox</code> or <code>\savebox</code>, or the <code>lrbox</code>
+environment. See <a href="#g_t_005csbox-_0026-_005csavebox">\sbox & \savebox</a> for more information and examples.
+(Note that <var>box-cmd</var> starts with a backslash.)  This command is
+robust (see <a href="#g_t_005cprotect">\protect</a>).
 </p>
 
 <hr>
@@ -20938,7 +21013,7 @@
   <var>letter body</var>
 \closing{<var>closing text</var>}
 \end{letter}
-...  more letters ...
+   ...
 \end{document}
 </pre></div>
 
@@ -20950,7 +21025,7 @@
 </p>
 <div class="example">
 <pre class="example"> \begin{letter}{Ninon de l'Enclos \\
-   l'h\^otel Sagonne}
+                l'h\^otel Sagonne}
    ...
  \end{letter}
 </pre></div>
@@ -20964,7 +21039,7 @@
 contains multiple lines separated by a double
 backslash (<code>\\</code>).  LaTeX will put the <var>sender name</var>
 under the closing, after a vertical space for the traditional
-hand-written signature; it also can contain multiple lines.
+hand-written signature.
 </p>
 <p>Each <code>letter</code> environment body begins with a required
 <code>\opening</code> command such as <code>\opening{Dear Madam or Sir:}</code>.
@@ -20980,13 +21055,13 @@
 Boss \\ the Boss's Boss}</code>.  There’s a similar <code>\encl</code> command for
 a list of enclosures.  And, you can add a postscript with <code>\ps</code>.
 </p>
-<p>LaTeX’s default is to indent the signature and the <code>\closing</code>
-above it by a length of <code>\longindentation</code>.  By default this is
+<p>LaTeX’s default is to indent the sender name and the closing above it
+by a length of <code>\longindentation</code>.  By default this is
 <code>0.5\textwidth</code>. To make them flush left, put
 <code>\setlength{\longindentation}{0em}</code> in your preamble.
 </p>
 <p>To set a fixed date use something like
-<code>\renewcommand{\today}{2015-Oct-12}</code>.  If put in your preamble
+<code>\renewcommand{\today}{1958-Oct-12}</code>.  If put in your preamble
 then it will apply to all the letters.
 </p>
 <p>This example shows only one <code>letter</code> environment.  The three lines
@@ -22411,7 +22486,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005ccaption-1"><code>\caption</code></a>:</td><td> </td><td valign="top"><a href="#table">table</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccc"><code>\cc</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ccc">\cc</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccdot"><code>\cdot</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005ccdots"><code>\cdots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005ccdots"><code>\cdots</code></a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccentering"><code>\centering</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ccentering">\centering</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cchapter"><code>\chapter</code></a>:</td><td> </td><td valign="top"><a href="#Sectioning">Sectioning</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cchapter-1"><code>\chapter</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cchapter">\chapter</a></td></tr>
@@ -22469,7 +22544,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005cddag"><code>\ddag</code></a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cddagger"><code>\ddagger</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cddot"><code>\ddot</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cddots"><code>\ddots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cddots"><code>\ddots</code></a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cDeclareGraphicsExtensions"><code>\DeclareGraphicsExtensions</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cDeclareGraphicsExtensions">\DeclareGraphicsExtensions</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cDeclareGraphicsRule"><code>\DeclareGraphicsRule</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cDeclareGraphicsRule">\DeclareGraphicsRule</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cDeclareOption"><code>\DeclareOption</code></a>:</td><td> </td><td valign="top"><a href="#Class-and-package-commands">Class and package commands</a></td></tr>
@@ -22660,7 +22735,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005clbrace"><code>\lbrace</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005clbrack"><code>\lbrack</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005clceil"><code>\lceil</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cldots"><code>\ldots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cldots"><code>\ldots</code></a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cldots-1"><code>\ldots</code></a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cle"><code>\le</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cleadsto"><code>\leadsto</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
@@ -23145,7 +23220,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005cvarsigma"><code>\varsigma</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvartheta"><code>\vartheta</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvdash"><code>\vdash</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cvdots"><code>\vdots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cvdots"><code>\vdots</code></a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvec"><code>\vec</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvector"><code>\vector</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cvector">\vector</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvee"><code>\vee</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
@@ -23222,13 +23297,15 @@
 <tr><td></td><td valign="top"><a href="#index-alignment-via-tabbing">alignment via tabbing</a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsfonts-package"><code>amsfonts</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-1"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-2"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-3"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-4"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-5"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-6"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-7"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-1"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-2"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-3"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#equation">equation</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-4"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-5"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-6"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-7"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-8"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-9"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package_002c-replacing-eqnarray">amsmath <span class="roman">package, replacing <code>eqnarray</code></span></a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsthm-package"><code>amsthm</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsthm-package-1"><code>amsthm</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#g_t_005crule">\rule</a></td></tr>
@@ -23236,6 +23313,7 @@
 <tr><td></td><td valign="top"><a href="#index-appendix">appendix</a>:</td><td> </td><td valign="top"><a href="#g_t_005cappendix">\appendix</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-appendix-package"><code>appendix</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#g_t_005cappendix">\appendix</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-aring">aring</a>:</td><td> </td><td valign="top"><a href="#Additional-Latin-letters">Additional Latin letters</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-array-_0028package_0029-package"><code>array (package)</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-array-environment"><code><code>array</code> <span class="roman">environment</span></code></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-arrays_002c-math">arrays, math</a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-arrow_002c-left_002c-in-text">arrow, left, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
@@ -23307,6 +23385,7 @@
 <tr><td></td><td valign="top"><a href="#index-breve-accent">breve accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-breve-accent_002c-math">breve accent, math</a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bug-reporting">bug reporting</a>:</td><td> </td><td valign="top"><a href="#About-this-document">About this document</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-bullet-lists">bullet lists</a>:</td><td> </td><td valign="top"><a href="#itemize">itemize</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bullet-symbol">bullet symbol</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bullet_002c-in-text">bullet, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bulleted-lists">bulleted lists</a>:</td><td> </td><td valign="top"><a href="#itemize">itemize</a></td></tr>
@@ -23416,6 +23495,7 @@
 <tr><td></td><td valign="top"><a href="#index-datetime-package"><code>datetime</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#g_t_005ctoday">\today</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dbltopnumber"><code>dbltopnumber</code></a>:</td><td> </td><td valign="top"><a href="#Floats">Floats</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dbltopnumber-1"><code>dbltopnumber</code></a>:</td><td> </td><td valign="top"><a href="#Floats">Floats</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-dcolumn-package"><code>dcolumn</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dd"><code>dd</code></a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-define-color">define color</a>:</td><td> </td><td valign="top"><a href="#Define-colors">Define colors</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-defining-a-new-command">defining a new command</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewcommand-_0026-_005crenewcommand">\newcommand & \renewcommand</a></td></tr>
@@ -23459,7 +23539,7 @@
 <tr><td></td><td valign="top"><a href="#index-dotless-i_002c-math">dotless i, math</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dotless-j">dotless j</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dotless-j_002c-math">dotless j, math</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-dots">dots</a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-dots">dots</a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-angle-quotation-marks">double angle quotation marks</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-dagger_002c-in-text">double dagger, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-dagger_002c-in-text-1">double dagger, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
@@ -23480,7 +23560,7 @@
 <tr><th><a name="Index_cp_letter-E">E</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-e_002ddash">e-dash</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-e_002dTeX">e-TeX</a>:</td><td> </td><td valign="top"><a href="#TeX-engines">TeX engines</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-ellipses">ellipses</a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-ellipses">ellipses</a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-ellipsis">ellipsis</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-em">em</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-em-1"><code>em</code></a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
@@ -23791,6 +23871,7 @@
 <tr><td></td><td valign="top"><a href="#index-list-of-tables-file">list of tables file</a>:</td><td> </td><td valign="top"><a href="#Output-files">Output files</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-listings-package"><code>listings</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-listings-package-1"><code>listings</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-listings-package-2"><code>listings</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#g_t_005cverb">\verb</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-lists-of-items">lists of items</a>:</td><td> </td><td valign="top"><a href="#itemize">itemize</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-lists-of-items_002c-generic">lists of items, generic</a>:</td><td> </td><td valign="top"><a href="#list">list</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-lists-of-items_002c-numbered">lists of items, numbered</a>:</td><td> </td><td valign="top"><a href="#enumerate">enumerate</a></td></tr>
@@ -23849,6 +23930,7 @@
 <tr><td></td><td valign="top"><a href="#index-minipage_002c-creating-a">minipage, creating a</a>:</td><td> </td><td valign="top"><a href="#minipage">minipage</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-minted-package"><code>minted</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-minted-package-1"><code>minted</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-minted-package-2"><code>minted</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#g_t_005cverb">\verb</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-mm"><code>mm</code></a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-modes">modes</a>:</td><td> </td><td valign="top"><a href="#Modes">Modes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-monospace-font">monospace font</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
@@ -23918,16 +24000,19 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-algorithm2e"><span class="roman">package</span>, <code>algorithm2e</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsfonts"><span class="roman">package</span>, <code>amsfonts</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsmath"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-1"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-2"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-3"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-4"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-5"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-6"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-7"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-1"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-2"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-3"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#equation">equation</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-4"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-5"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-6"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Dots">Dots</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-7"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-8"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-9"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsthm"><span class="roman">package</span>, <code>amsthm</code></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsthm-1"><span class="roman">package</span>, <code>amsthm</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005crule">\rule</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-appendix"><span class="roman">package</span>, <code>appendix</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cappendix">\appendix</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-array-_0028package_0029"><span class="roman">package</span>, <code>array (package)</code></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-Asymptote"><span class="roman">package</span>, <code>Asymptote</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cline">\line</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-Asymptote-1"><span class="roman">package</span>, <code>Asymptote</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cstrut">\strut</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-Asymptote-2"><span class="roman">package</span>, <code>Asymptote</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmbox-_0026-_005cmakebox">\mbox & \makebox</a></td></tr>
@@ -23945,6 +24030,7 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-cprotect"><span class="roman">package</span>, <code>cprotect</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-cprotect-1"><span class="roman">package</span>, <code>cprotect</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cverb">\verb</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-datetime"><span class="roman">package</span>, <code>datetime</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ctoday">\today</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-dcolumn"><span class="roman">package</span>, <code>dcolumn</code></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-enumitem"><span class="roman">package</span>, <code>enumitem</code></a>:</td><td> </td><td valign="top"><a href="#list">list</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-envlab"><span class="roman">package</span>, <code>envlab</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmakelabels">\makelabels</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-etoolbox"><span class="roman">package</span>, <code>etoolbox</code></a>:</td><td> </td><td valign="top"><a href="#Class-and-package-commands">Class and package commands</a></td></tr>
@@ -23970,6 +24056,7 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-index"><span class="roman">package</span>, <code>index</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cindex">\index</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-listings"><span class="roman">package</span>, <code>listings</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-listings-1"><span class="roman">package</span>, <code>listings</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-listings-2"><span class="roman">package</span>, <code>listings</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cverb">\verb</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-macros2e"><span class="roman">package</span>, <code>macros2e</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmakeatletter-_0026-_005cmakeatother">\makeatletter & \makeatother</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-mathtools"><span class="roman">package</span>, <code>mathtools</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-mathtools-1"><span class="roman">package</span>, <code>mathtools</code></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
@@ -23978,6 +24065,7 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-mhchem"><span class="roman">package</span>, <code>mhchem</code></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-minted"><span class="roman">package</span>, <code>minted</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-minted-1"><span class="roman">package</span>, <code>minted</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-minted-2"><span class="roman">package</span>, <code>minted</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cverb">\verb</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-multind"><span class="roman">package</span>, <code>multind</code></a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-pict2e"><span class="roman">package</span>, <code>pict2e</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cline">\line</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-polyglossia"><span class="roman">package</span>, <code>polyglossia</code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>

Modified: trunk/latex2e.info
===================================================================
--- trunk/latex2e.info	2018-07-01 20:07:33 UTC (rev 675)
+++ trunk/latex2e.info	2018-07-02 15:52:35 UTC (rev 676)
@@ -2901,7 +2901,7 @@
        ...
      \end{array}
 
-or
+or:
 
      \begin{array}[POS]{COLS}
        COLUMN 1 ENTRY &COLUMN 2 ENTRY ... &COLUMN N ENTRY \\
@@ -2910,10 +2910,23 @@
 
    Produce a mathematical array.  This environment can only be used in
 math mode, and normally appears within a displayed mathematics
-environment such as 'equation' (*note equation::).  Column entries are
-separated by an ampersand ('&').  Rows are terminated with
-double-backslashes (*note \\::).
+environment such as 'equation' (*note equation::).  Inside of each row
+the column entries are separated by an ampersand, ('&').  Rows are
+terminated with double-backslashes (*note \\::).
 
+   This example shows a three by three array.
+
+     \begin{equation*}
+       \chi(x) =
+       \left|              % vertical bar fence
+         \begin{array}{ccc}
+           x-a  &-b  &-c  \\
+           -d   &x-e &-f  \\
+           -g   &-h  &x-i
+         \end{array}
+      \right|
+     \end{equation*}
+
    The required argument COLS describes the number of columns, their
 alignment, and the formatting of the intercolumn regions.  For instance,
 '\begin{array}{rcl}...\end{array}' gives three columns: the first flush
@@ -2922,12 +2935,13 @@
 features of the two environments, including the optional POS argument.
 
    There are two ways that 'array' diverges from 'tabular'.  The first
-is that 'array' entries are typeset in math mode, in textstyle (except
-if the COLS definition specifies the column with 'p{...}', which causes
-the entry to be typeset in text mode).  The second is that, instead of
-'tabular''s parameter '\tabcolsep', LaTeX's intercolumn space in an
-'array' is governed by '\arraycolsep', which gives half the width
-between columns.  The default for this is '5pt'.
+is that 'array' entries are typeset in math mode, in textstyle (*note
+Modes::) except if the COLS definition specifies the column with
+'p{...}', which causes the entry to be typeset in text mode.  The second
+is that, instead of 'tabular''s parameter '\tabcolsep', LaTeX's
+intercolumn space in an 'array' is governed by '\arraycolsep', which
+gives half the width between columns.  The default for this is '5pt' so
+that between two columns comes 10pt of space.
 
    To obtain arrays with braces the standard is to use the 'amsmath'
 package.  It comes with environments 'pmatrix' for an array surrounded
@@ -2937,24 +2951,22 @@
 bars '|...|', and 'Vmatrix' for an array surrounded by double vertical
 bars '||...||', along with a number of other array constructs.
 
-   Here is an example of an array:
+   The next example uses the 'amsmath' package.
 
-     \begin{equation}
-       \begin{array}{cr}
-         \sqrt{y}  &12.3 \\
-         x^2       &3.4
-       \end{array}
-     \end{equation}
+     \usepackage{amsmath}  % in preamble
 
-   The next example works if '\usepackage{amsmath}' is in the preamble:
-
      \begin{equation}
-       \begin{vmatrix}{cc}
+       \begin{vmatrix}{cc}  % array with vert lines
          a  &b \\
          c  &d
        \end{vmatrix}=ad-bc
      \end{equation}
 
+   There are many packages concerning arrays.  The 'array' package has
+many useful extensions, including more column types.  The 'dcolumn'
+package adds a column type to center on a decimal point.  For both see
+the documentation on CTAN.
+
 
 File: latex2e.info,  Node: center,  Next: description,  Prev: array,  Up: Environments
 
@@ -2964,22 +2976,16 @@
 Synopsis:
 
      \begin{center}
-       ... text ...
-     \end{center}
-
-or
-
-     \begin{center}
-       text on first line \\
-       text on second line \\
+       LINE1 \\
+       LINE2 \\
        ...
      \end{center}
 
    Create a new paragraph consisting of a sequence of lines that are
-centered within the left and right margins on the current page.  Use
-double-backslash, '\\', to get a line break (*note \\::).  If some text
-is too long to fit on a line then LaTeX will insert line breaks that
-avoid hyphenation and avoid stretching or shrinking any interword space.
+centered within the left and right margins.  Use double-backslash, '\\',
+to get a line break (*note \\::).  If some text is too long to fit on a
+line then LaTeX will insert line breaks that avoid hyphenation and avoid
+stretching or shrinking any interword space.
 
    This environment inserts space above and below the text body.  See
 *note \centering:: to avoid such space, for example inside a 'figure'
@@ -3006,8 +3012,12 @@
        I grew up in that belief.  --Richard Burton
      \end{center}
 
-   A double backslash after the final line is optional.
+   A double backslash after the final line is optional.  If present it
+doesn't add any vertical space.
 
+   In a two-column document the text is centered in a column, not in the
+entire page.
+
 * Menu:
 
 * \centering::          Declaration form of the 'center' environment.
@@ -3066,9 +3076,9 @@
 Synopsis:
 
      \begin{description}
-     \item[LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
-     \item[LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
-       ...
+       \item[LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
+       \item[LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
+        ...
      \end{description}
 
    Environment to make a list of labeled items.  Each item's LABEL is
@@ -3078,14 +3088,16 @@
 \item'.
 
    This example shows the environment used for a sequence of
-definitions.  The labels 'lama' and 'llama' come out in boldface with
-their left edges aligned on the left margin.
+definitions.
 
      \begin{definition}
        \item[lama] A priest.
        \item[llama] A beast.
      \end{definition}
 
+The labels 'lama' and 'llama' are output in boldface, with the left edge
+on the left margin.
+
    Start list items with the '\item' command (*note \item::).  Use the
 optional labels, as in '\item[Main point]', because there is no sensible
 default.  Following the '\item' is optional text, which may contain
@@ -3095,9 +3107,10 @@
 font change given in argument style (see *note Font styles::) then it
 will come out bold.  For instance, if the label text calls for
 typewriter with '\item[\texttt{label text}]' then it will appear in bold
-typewriter, if that is available.  The simplest way to get non-bold
-typewriter is to use declarative style: '\item[{\tt label text}]'.
-Similarly, get the standard roman font with '\item[{\rm label text}]'.
+typewriter, if that is available.  The simplest way around this, in this
+example to get non-bold typewriter, is to use declarative style:
+'\item[{\tt label text}]'.  Similarly, get the standard roman font with
+'\item[{\rm label text}]'.
 
    For other major LaTeX labelled list environments, see *note itemize::
 and *note enumerate::.  Unlike those environments, nesting 'description'
@@ -3122,7 +3135,7 @@
 Synopsis:
 
      \begin{displaymath}
-     MATH TEXT
+       MATHEMATICAL TEXT
      \end{displaymath}
 
    Environment to typeset the math text on its own line, in display
@@ -3221,9 +3234,9 @@
 Synopsis:
 
      \begin{enumerate}
-     \item[OPTIONAL LABEL OF FIRST ITEM] text of first item
-     \item[OPTIONAL LABEL OF SECOND ITEM] text of second item
-     ...
+       \item[OPTIONAL LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
+       \item[OPTIONAL LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
+       ...
      \end{enumerate}
 
    Environment to produce a numbered list of items.  The format of the
@@ -3348,16 +3361,16 @@
 Synopsis:
 
      \begin{equation}
-       math text
+       MATHEMATICAL TEXT
      \end{equation}
 
-   Make a 'displaymath' environment (*note displaymath::) with an
-equation number in the right margin.  The equation number is generated
-using the 'equation' counter.
+   The same as a 'displaymath' environment (*note displaymath::) except
+that LaTeX puts an equation number flush to the right margin.  The
+equation number is generated using the 'equation' counter.
 
    You should have no blank lines between '\begin{equation}' and
-'\begin{equation}' or LaTeX will tell you that there is a missing dollar
-sign.
+'\begin{equation}', or LaTeX will tell you that there is a missing
+dollar sign.
 
    The package 'amsmath' package has extensive displayed equation
 facilities.  New documents should include this package.
@@ -3371,27 +3384,29 @@
 Synopsis:
 
      \begin{figure}[PLACEMENT]
-       figure body
+       FIGURE BODY
        \caption[LOFTITLE]{TITLE}  % optional
        \label{LABEL}              % optional
      \end{figure}
 
-or
+or:
 
      \begin{figure*}[PLACEMENT]
-       figure body
+       FIGURE BODY
        \caption[LOFTITLE]{TITLE}  % optional
        \label{LABEL}              % optional
      \end{figure*}
 
-   The figure body is made up of imported graphics, or text, LaTeX
-commands, etc.  It is typeset in a 'parbox' of width '\textwidth'.
-
-   Figures are not part of the normal text.  A long figure will not be
-split between two pages.  Because of this, they are not typeset in
-sequence with the normal text but instead are "floated" to a convenient
+   Figures are for material that is not part of the normal text.  An
+example is material that you cannot have split between two pages, such
+as a graphic.  Because of this, LaTeX does not typeset figures in
+sequence with normal text but instead "floats" them to a convenient
 place, such as the top of a following page (*note Floats::).
 
+   The FIGURE BODY can consist of imported graphics (*note Graphics::),
+or text, LaTeX commands, etc.  It is typeset in a 'parbox' of width
+'\textwidth'.
+
    The possible values of PLACEMENT are 'h' for 'here', 't' for 'top',
 'b' for 'bottom', and 'p' for 'on a separate page of floats'.  For the
 effect of these options on the float placement algorithm, see *note
@@ -3409,11 +3424,12 @@
 is used in the list of figures instead of TITLE (*note Table of contents
 etc.::).
 
-   This example makes a figure out of a graphic.  It requires one of the
-packages 'graphics' or 'graphicx'.  The graphic, with its caption, will
-be placed at the top of a page or, if it is pushed to the end of the
-document, on a page of floats.
+   This example makes a figure out of a graphic.  LaTeX will place that
+graphic and its caption at the top of a page or, if it is pushed to the
+end of the document, on a page of floats.
 
+     \usepackage{graphicx}  % in preamble
+       ...
      \begin{figure}[t]
        \centering
        \includegraphics[width=0.5\textwidth]{CTANlion.png}
@@ -3489,10 +3505,10 @@
      \end{flushleft}
 
    An environment that creates a paragraph whose lines are flush to the
-left-hand margin and ragged right.  LaTeX will break long lines to avoid
-hyphenation and stretching or shrinking spaces.  Force a new line with a
-double backslash '\\'.  For the declaration form see *note
-\raggedright::.
+left-hand margin, and ragged right.  If you have lines that are too long
+then LaTeX will linebreak them in a way that avoids hyphenation and
+stretching or shrinking spaces.  To force a new line use a double
+backslash, '\\'.  For the declaration form see *note \raggedright::.
 
    This creates a box of text that is at most 3 inches wide, with the
 text flush left and ragged right.
@@ -3558,9 +3574,10 @@
      \end{flushright}
 
    An environment that creates a paragraph whose lines are flush to the
-right-hand margin and ragged left.  LaTeX will break long lines to avoid
-hyphenation and stretching or shrinking spaces.  Force a new line with a
-double backslash '\\'.  For the declaration form see *note
+right-hand margin and ragged left.  If you have lines that are too long
+to fit the margins then LaTeX will linebreak them in a way that avoids
+hyphenation and stretching or shrinking spaces.  To force a new line use
+a double backslash, '\\'.  For the declaration form see *note
 \raggedleft::.
 
    For an example related to this environment, see *note flushleft::.
@@ -3606,24 +3623,25 @@
 Synopsis:
 
      \begin{itemize}
-     \item[OPTIONAL LABEL OF FIRST ITEM] text of first item
-     \item[OPTIONAL LABEL OF SECOND ITEM] text of second item
-     ...
+       \item[OPTIONAL LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
+       \item[OPTIONAL LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
+       ...
      \end{itemize}
 
-   Produces an "unordered," or "bulleted," list.  The format of the
-labelling depends on the nesting level; see below.  Each 'itemize' list
-environment must have at least one item; having none causes the LaTeX
-error 'Something's wrong--perhaps a missing \item'.
+   Produce a list that is unordered, sometimes called a bullet list.
+The environment must have at least one '\item'; having none causes the
+LaTeX error 'Something's wrong--perhaps a missing \item'.
 
-   This example gives a two-item list.  As a top-level list each label
-would come out as a bullet, *.
+   This gives a two-item list.
 
      \begin{itemize}
       \item Pencil and watercolor sketch by Cassandra
       \item Rice portrait
      \end{itemize}
 
+As a top-level list each label would come out as a bullet, *.  The
+format of the labeling depends on the nesting level; see below.
+
    Start list items with the '\item' command (*note \item::).  If you
 give '\item' an optional argument by following it with square brackets,
 as in '\item[Optional label]', then by default it will appear in bold
@@ -3699,27 +3717,31 @@
 Synopsis:
 
      \begin{list}{LABELING}{SPACING}
-     \item[OPTIONAL LABEL OF FIRST ITEM] text of first item
-     \item[OPTIONAL LABEL OF SECOND ITEM] text of second item
-     ...
+       \item[OPTIONAL LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
+       \item[OPTIONAL LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
+       ...
      \end{list}
 
-   A generic environment for constructing more specialized lists.  It is
-most often used to create lists via the 'description', 'enumerate', and
-'itemize' environments (*note description::, *note enumerate::, and
-*note itemize::).  Also, many standard LaTeX environments that are not
-visually lists are constructed using 'list', including 'quotation',
-'quote', 'center', 'verbatim', and plenty more (*note quotation &
-quote::, *note center::, *note flushright::).
+   An environment for constructing lists.
 
+   Note that this environment does not typically appear in the document
+body.  Most lists created by LaTeX authors are the ones that come
+standard: the 'description', 'enumerate', and 'itemize' environments
+(*note description::, *note enumerate::, and *note itemize::).
+
+   Instead, the 'list' environment is most often used in macros.  For
+example, many standard LaTeX environments that do not immediately appear
+to be lists are in fact constructed using 'list', including 'quotation',
+'quote', and 'center' (*note quotation & quote::, *note center::).
+
    This uses the 'list' environment to define a new custom environment.
 
      \newcounter{namedlistcounter}  % number the items
      \newenvironment{named}
        {\begin{list}
-          {Item~\Roman{namedlistcounter}.} % labeling argument
-          {\usecounter{namedlistcounter}   % spacing argument
-           \setlength{\leftmargin}{3.5em}} % still spacing arg
+          {Item~\Roman{namedlistcounter}.} % labeling
+          {\usecounter{namedlistcounter}   % set counter
+           \setlength{\leftmargin}{3.5em}} % set spacing
        }
        {\end{list}}
 
@@ -3738,18 +3760,19 @@
 by giving '\item' an optional argument by including square braces and
 the text, as in the above '\item[Special label.]'; *note \item::.
 
-   The mandatory second argument SPACING has a list of commands.  One
-that goes in here is '\usecounter{COUNTERNAME}' (*note \usecounter::).
-Use this to tell LaTeX to number the items using the given counter.  The
-counter will be reset to zero each time LaTeX enters the environment,
-and the counter is incremented by one each time LaTeX encounters an
-'\item'.
+   The mandatory second argument SPACING has a list of commands.  This
+list can be empty.  A command that can go in here is
+'\usecounter{COUNTERNAME}' (*note \usecounter::).  Use this to tell
+LaTeX to number the items using the given counter.  The counter will be
+reset to zero each time LaTeX enters the environment, and the counter is
+incremented by one each time LaTeX encounters an '\item' that does not
+have an optional argument.
 
    Another command that can go in SPACING is '\makelabel', which
 constructs the label box.  By default it puts the contents flush right.
-Its only argument is the label, which it typesets in LR mode.  One
-example of changing its definition is that to the above 'named' example
-before the definition of the environment add
+Its only argument is the label, which it typesets in LR mode (*note
+Modes::).  One example of changing its definition is that to the above
+'named' example, before the definition of the environment add
 '\newcommand{\namedmakelabel}[1]{\textsc{#1}}', and between the
 '\setlength' command and the parenthesis that closes the SPACING
 argument also add '\let\makelabel\namedmakelabel'.  Then the items will
@@ -4103,22 +4126,18 @@
 floats.)  This box will not be broken across pages.  So 'minipage' is
 similar to '\parbox' (*note \parbox::) but here you can have paragraphs.
 
-   This puts the footnote at the bottom of the table, not the bottom of
-the page.
+   This example will be 3 inches wide, and has two paragraphs.
 
-     \begin{center}           % center the minipage on the line
-     \begin{minipage}{2.5in}
-       \begin{center}         % center the table inside the minipage
-         \begin{tabular}{ll}
-           \textsc{Monarch}  &\textsc{Reign}             \\ \hline
-           Elizabeth II      &63 years\footnote{to date} \\
-           Victoria          &63 years                   \\
-           George III        &59 years
-         \end{tabular}
-       \end{center}
+     \begin{minipage}{3in}
+       Stephen Kleene was a founder of the Theory of Computation.
+
+       He was a student of Church, wrote three influential texts,
+       was President of the Association for Symbolic Logic,
+       and won the National Medal of Science.
      \end{minipage}
-     \end{center}
 
+See below for a discussion of the paragraph indent inside a 'minipage'.
+
    The required argument WIDTH is a rigid length (*note Lengths::).  It
 gives the width of the box into which CONTENTS are typeset.
 
@@ -4198,6 +4217,22 @@
 '\mpfootnote' counter instead of the ordinary 'footnote' counter (*note
 Counters::).
 
+   This puts the footnote at the bottom of the table, not the bottom of
+the page.
+
+     \begin{center}           % center the minipage on the line
+     \begin{minipage}{2.5in}
+       \begin{center}         % center the table inside the minipage
+         \begin{tabular}{ll}
+           \textsc{Monarch}  &\textsc{Reign}             \\ \hline
+           Elizabeth II      &63 years\footnote{to date} \\
+           Victoria          &63 years                   \\
+           George III        &59 years
+         \end{tabular}
+       \end{center}
+     \end{minipage}
+     \end{center}
+
    If you nest minipages then there is an oddness when using footnotes.
 Footnotes appear at the bottom of the text ended by the next
 '\end{minipage}' which may not be their logical place.
@@ -4490,9 +4525,10 @@
      \line(X_RUN,Y_RISE){TRAVEL}
 
    Draw a line.  It slopes such that it vertically rises Y_RISE for
-every horizontal X_RUN, and such that the total horizontal change is
-TRAVEL.  In the special case of vertical lines, where
-(X_RUN,Y_RISE)=(0,1), the TRAVEL gives the change in y.
+every horizontal X_RUN.  The TRAVEL is the total horizontal change -- it
+is not the length of the vector, it is the change in x.  In the special
+case of vertical lines, where (X_RUN,Y_RISE)=(0,1), the TRAVEL gives the
+change in y.
 
    This draws a line starting at coordinates (1,3).
 
@@ -4677,16 +4713,17 @@
 
      \vector(X_RUN,Y_RISE){TRAVEL}
 
-   Draw a line ending in an arrow.  It slopes such that it vertically
-rises Y_RISE for every horizontal X_RUN, and such that the total
-horizontal change is TRAVEL.  In the special case of vertical vectors,
-if (X_RUN,Y_RISE)=(0,1), then TRAVEL gives the change in y.
+   Draw a line ending in an arrow.  The slope of that line is: it
+vertically rises Y_RISE for every horizontal X_RUN.  The TRAVEL is the
+total horizontal change -- it is not the length of the vector, it is the
+change in x.  In the special case of vertical vectors, if
+(X_RUN,Y_RISE)=(0,1), then TRAVEL gives the change in y.
 
    For an example see *note picture::.
 
    For elaboration on X_RUN and Y_RISE see *note \line::.  As there, the
-values of X_RUN and Y_RISE are limited.  You must chooses integers
-between -4 and 4, inclusive.  Also, the two you choose must be
+values of X_RUN and Y_RISE are limited.  For '\vector' you must chooses
+integers between -4 and 4, inclusive.  Also, the two you choose must be
 relatively prime.  Thus, '\vector(2,1){4}' is acceptable but
 '\vector(4,2){4}' is not (if you use the latter then you get a sequence
 of arrowheads).
@@ -5351,22 +5388,22 @@
 @-expression, although its synonym vertical bar '|' is more common.
 This command is rarely used in the body of a table; typically a table's
 vertical lines are specified in 'tabular''s COLS argument and overridden
-as needed with '\multicolumn'.
+as needed with '\multicolumn' (*note tabular::).
 
-   This example illustrates some pitfalls.  In the first line's second
-entry the '\hfill' moves the '\vline' to the left edge of the cell.  But
-that is different than putting it halfway between the two columns, so in
-that row between the first and second columns there are two vertical
+   The example below illustrates some pitfalls.  In the first row's
+second entry the '\hfill' moves the '\vline' to the left edge of the
+cell.  But that is different than putting it halfway between the two
+columns, so between the first and second columns there are two vertical
 rules, with the one from the '{c|cc}' specifier coming before the one
-produced by the '\vline\hfill'.  In contrast, the first line's third
+produced by the '\vline\hfill'.  In contrast, the first row's third
 entry shows the usual way to put a vertical bar between two columns.  In
-the second line, the 'ghi' is the widest entry in its column so in the
+the second row, the 'ghi' is the widest entry in its column so in the
 '\vline\hfill' the '\hfill' has no effect and the vertical line in that
 entry appears immediately next to the 'g', with no whitespace.
 
      \begin{tabular}{c|cc}
-       x   &\vline\hfill y   &\multicolumn{1}{|r}{z} \\
-       abc &def &\vline\hfill ghi
+       x   &\vline\hfill y   &\multicolumn{1}{|r}{z} \\ % row 1
+       abc &def &\vline\hfill ghi                       % row 2
      \end{tabular}
 
 
@@ -5800,15 +5837,8 @@
      \verb* CHAR LITERAL-TEXT CHAR
 
    Typeset LITERAL-TEXT as it is input, including special characters and
-spaces, using the typewriter ('\tt') font.  The '*'-form differs only in
-that spaces are printed with a visible space character.
+spaces, using the typewriter ('\tt') font.
 
-   The single-character delimiter CHAR surrounds LITERAL-TEXT; it is the
-same character before and after.  No spaces come between '\verb' or
-'\verb*' and CHAR, or between CHAR and LITERAL-TEXT, or between
-LITERAL-TEXT and the second occurrence of CHAR.  The delimiter must not
-appear in LITERAL-TEXT.  The LITERAL-TEXT cannot include a line break.
-
    This example shows two different invocations of '\verb'.
 
      This is \verb!literally! the biggest pumpkin ever.
@@ -5818,10 +5848,28 @@
 point, '!'.  The second instead uses plus, '+', because the exclamation
 point is part of 'literal-text'.
 
+   The single-character delimiter CHAR surrounds LITERAL-TEXT -- it must
+be the same character before and after.  No spaces come between '\verb'
+or '\verb*' and CHAR, or between CHAR and LITERAL-TEXT, or between
+LITERAL-TEXT and the second occurrence of CHAR (the synopsis shows a
+space only to distinguish one component from the other).  The delimiter
+must not appear in LITERAL-TEXT.  The LITERAL-TEXT cannot include a line
+break.
+
+   The '*'-form differs only in that spaces are printed with a visible
+space character.
+
+   The output from this will include a character showing the spaces.
+
+     The commands's first argument is \verb*!filename with extension! and ...
+
    For typesetting Internet addresses, urls, the package 'url' provides
 an option that is better than the '\verb' command, since it allows line
 breaks.
 
+   For computer code there are many packages with advantages over
+'\verb'.  One is 'listings', another is 'minted'.
+
    You cannot use '\verb' in the argument to a macro, for instance in
 the argument to a '\section'.  It is not a question of '\verb' being
 fragile (*note \protect::), instead it just cannot appear there.  (But
@@ -7496,12 +7544,12 @@
 
      \usecounter{COUNTER}
 
-   Used in the second argument of the 'list' environment (*note list::).
-It sets up COUNTER to number the list items.  It initializes COUNTER to
-zero, and arranges that when '\item' is called without its optional
-argument then COUNTER is incremented by '\refstepcounter', making its
-value be the current 'ref' value (*note \ref::).  This command is
-fragile (*note \protect::).
+   Used in the second argument of the 'list' environment (*note list::),
+this declares that list items will be numbered by COUNTER.  It
+initializes COUNTER to zero, and arranges that when '\item' is called
+without its optional argument then COUNTER is incremented by
+'\refstepcounter', making its value be the current 'ref' value (*note
+\ref::).  This command is fragile (*note \protect::).
 
    Put in the document preamble, this example makes a new list
 environment enumerated with TESTCOUNTER:
@@ -7525,13 +7573,9 @@
 
      \value{COUNTER}
 
-   Expands to the value of COUNTER.  It is often used in '\setcounter'
-or '\addtocounter' but '\value' can be used anywhere that LaTeX expects
-a number.  It must not be preceded by '\protect' (*note \protect::).
+   Expands to the value of the counter COUNTER.  (Note that the name of
+a counter does not begin with a backslash.)
 
-   The '\value' command is not used for typesetting the value of the
-counter.  *Note \alph \Alph \arabic \roman \Roman \fnsymbol::.
-
    This example outputs 'Test counter is 6. Other counter is 5.'.
 
      \newcounter{test} \setcounter{test}{5}
@@ -7541,6 +7585,15 @@
      Test counter is \arabic{test}.
      Other counter is \arabic{other}.
 
+   The '\value' command is not used for typesetting the value of the
+counter.  For that, see *note \alph \Alph \arabic \roman \Roman
+\fnsymbol::.
+
+   It is often used in '\setcounter' or '\addtocounter' but '\value' can
+be used anywhere that LaTeX expects a number, such as in
+'\hspace{\value{foo}\parindent}'.  It must not be preceded by '\protect'
+(*note \protect::).
+
    This example inserts '\hspace{4\parindent}'.
 
      \setcounter{myctr}{3} \addtocounter{myctr}{1}
@@ -8128,35 +8181,33 @@
 15.4 Marginal notes
 ===================
 
-Synopsis:
+Synopsis, one of:
 
+     \marginpar{RIGHT}
      \marginpar[LEFT]{RIGHT}
 
    Create a note in the margin.  The first line of the note will have
 the same baseline as the line in the text where the '\marginpar' occurs.
 
-   When you only specify the mandatory argument RIGHT, the text will be
-placed
+   The margin that LaTeX uses for the note depends on the current layout
+(*note Document class options::) and also on '\reversemarginpar' (see
+below).  If you are using one-sided layout (document option 'oneside')
+then it goes in the right margin.  If you are using two-sided layout
+(document option 'twoside') then it goes in the outside margin.  If you
+are in two-column layout (document option 'twocolumn') then it goes in
+the nearest margin.
 
-   * in the right margin for one-sided layout (option 'oneside', see
-     *note Document class options::);
+   If you declare '\reversemarginpar' then LaTeX will place subsequent
+marginal notes in the opposite margin to that given in the prior
+paragraph.  Revert that to the default position with '\normalmarginpar'.
 
-   * in the outside margin for two-sided layout (option 'twoside', see
-     *note Document class options::);
+   When you specify the optional argument LEFT then it is used for a
+note in the left margin, while the mandatory argument RIGHT is used for
+a note in the the right margin.
 
-   * in the nearest margin for two-column layout (option 'twocolumn',
-     see *note Document class options::).
+   Normally, a note's first word will not be hyphenated.  You can enable
+hyphenation there by beginning LEFT or RIGHT with '\hspace{0pt}'.
 
-   The command '\reversemarginpar' places subsequent marginal notes in
-the opposite (inside) margin.  '\normalmarginpar' places them in the
-default position.
-
-   When you specify both arguments, LEFT is used for the left margin,
-and RIGHT is used for the right margin.
-
-   The first word will normally not be hyphenated; you can enable
-hyphenation there by beginning the node with '\hspace{0pt}'.
-
    These parameters affect the formatting of the note:
 
 '\marginparpush'
@@ -8191,38 +8242,32 @@
      \end{displaymath}
      where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.
 
-   Math mode is for inline mathematics.  It is invoked by the starting
-'\(' and finished by the matching ending '\)'.  Display math mode is for
-displayed equations and here is invoked by the 'displaymath'
-environment.  Note that any mathematical text whatever, including that
-consisting of single characters, is handled in math mode.
+Math mode is for inline mathematics.  In the above example it is invoked
+by the starting '\(' and finished by the matching ending '\)'.  Display
+math mode is for displayed equations and here is invoked by the
+'displaymath' environment.  Note that any mathematical text whatever,
+including mathematical text consisting of just one character, is handled
+in math mode.
 
-   The American Mathematical Society has made freely available a set of
-packages that greatly expand your options for writing mathematics,
-'amsmath' and 'amssymb' (also be aware of the 'mathtools' package that
-is an extension to, and loads, 'amsmath').  New documents that will have
-mathematical text should use these packages.  Descriptions of these
-packages is outside the scope of this document; see their documentation
-on CTAN.
-
    When in math mode or display math mode, LaTeX handles many aspects of
 your input text differently than in other text modes.  For example,
 
-     contrast x+y with \( x+y \).
+     contrast x+y with \( x+y \)
 
 in math mode the letters are in italics and the spacing around the plus
 sign is different.
 
-   To make inline formulas, put LaTeX in math mode with one of these
-three.
+   There are three ways to make inline formulas, to put LaTeX in math
+mode.
 
      \( MATHEMATICAL MATERIAL \)
      $ MATHEMATICAL MATERIAL $
      \begin{math} MATHEMATICAL MATERIAL \end{math}
 
-The first form is preferred, and the third form is very rarely used.
-You can mix them, sometimes using one and sometimes another.  These can
-be used in paragraph mode or in LR mode (*note Modes::).
+The first form is preferred and the second is quite common, but the
+third form is rarely used.  You can sometimes use one and sometimes
+another, as in '\(x\) and $y$'.  You can use these in paragraph mode or
+in LR mode (*note Modes::).
 
    To make displayed formulas, put LaTeX into display math mode with
 either:
@@ -8237,9 +8282,9 @@
        MATHEMATICAL MATERIAL
      \end{equation}
 
-The only difference is that with the 'equation' environment, LaTeX puts
-a formula number alongside the formula, which by default has the form
-'(ARABIC NUMBER)'.  The construct '\[ MATH \]' is equivalent to
+(*note displaymath::, *note equation::).  The only difference is that
+with the 'equation' environment, LaTeX puts a formula number alongside
+the formula.  The construct '\[ MATH \]' is equivalent to
 '\begin{displaymath} MATH \end{displaymath}'.  These environments can
 only be used in paragraph mode (*note Modes::).
 
@@ -8248,11 +8293,12 @@
 in display math mode they are further apart and in inline math mode they
 are closer together.
 
-   Sometimes you want the display math treatment to happen in the inline
-math mode.  For this, the '\displaystyle' declaration forces the size
-and style of the formula to be that of 'displaymath'.  Thus
-'\(\displaystyle \sum_{n=0}^\infty x_n\)' will have the limits above and
-below the summation sign, not next to it.  Another example is that
+   Sometimes you want the display math typographical treatment to happen
+in the inline math mode.  For this, the '\displaystyle' declaration
+forces the size and style of the formula to be that of 'displaymath'.
+Thus '\(\displaystyle \sum_{n=0}^\infty x_n\)' will have the limits
+above and below the summation sign, not next to it.  Another example is
+that
 
      \begin{tabular}{r|cc}
        \textsc{Name}  &\textsc{Series}  &\textsc{Sum}  \\  \hline
@@ -8267,6 +8313,14 @@
 line's fraction will be easy to read, with characters the same size as
 in the rest of the line.
 
+   The American Mathematical Society has made freely available a set of
+packages that greatly expand your options for writing mathematics,
+'amsmath' and 'amssymb' (also be aware of the 'mathtools' package that
+is an extension to, and loads, 'amsmath').  New documents that will have
+mathematical text should use these packages.  Descriptions of these
+packages is outside the scope of this document; see their documentation
+on CTAN.
+
 * Menu:
 
 * Subscripts & superscripts::   Also known as exponent or index.
@@ -9235,7 +9289,7 @@
 * Blackboard bold::            Doublestruck characters.
 * Calligraphic::               Cursive characters.
 * \boldmath & \unboldmath::    Symbols in boldface.
-* Ellipses::                   Dots.
+* Dots::                       Ellipses, etc.
 
 
 File: latex2e.info,  Node: Blackboard bold,  Next: Calligraphic,  Up: Math symbols
@@ -9288,7 +9342,7 @@
 outputs a plus sign.
 
 
-File: latex2e.info,  Node: \boldmath & \unboldmath,  Next: Ellipses,  Prev: Calligraphic,  Up: Math symbols
+File: latex2e.info,  Node: \boldmath & \unboldmath,  Next: Dots,  Prev: Calligraphic,  Up: Math symbols
 
 16.2.3 '\boldmath' & '\unboldmath'
 ----------------------------------
@@ -9331,10 +9385,10 @@
 shows that it is an improvement over '\boldmath'.
 
 
-File: latex2e.info,  Node: Ellipses,  Prev: \boldmath & \unboldmath,  Up: Math symbols
+File: latex2e.info,  Node: Dots,  Prev: \boldmath & \unboldmath,  Up: Math symbols
 
-16.2.4 Ellipses
----------------
+16.2.4 Dots, horizontal or vertical
+-----------------------------------
 
 Ellipses are the three dots (usually three) indicating that a pattern
 continues.
@@ -9352,19 +9406,20 @@
      as in U+22EF. Used as: '\( a_0\cdot a_1\cdots a_{n-1} \)'.
 
 '\ddots'
-     Diagonal ellipsis, U+22F1.  See the above example for a usage.
+     Diagonal ellipsis, U+22F1.  See the above array example for a
+     usage.
 
 '\ldots'
      Ellipsis on the baseline, U+2026.  Used as: '\( x_0,\ldots x_{n-1}
-     \)'.  A synonym is '\mathellipsis'.  A synonym from the 'amsmath'
-     package is '\hdots'.
+     \)'.  Another example is the above array example.  A synonym is
+     '\mathellipsis'.  A synonym from the 'amsmath' package is '\hdots'.
 
      You can also use this command outside of mathematical text, as in
-     'The gears, brakes, \ldots{} are all broken'.  (In a text mode a
-     synonym for '\ldots' is '\dots'.)
+     'The gears, brakes, \ldots{} are all broken'.  (In a paragraph mode
+     or LR mode a synonym for '\ldots' is '\dots'.)
 
 '\vdots'
-     Vertical ellipsis, U+22EE. See the above example for a usage.
+     Vertical ellipsis, U+22EE. See the above array example for a usage.
 
    The 'amsmath' package has the command '\dots' to semantically mark up
 ellipses.  This example produces two different-looking outputs for the
@@ -9830,14 +9885,15 @@
      a box with an '\mbox' command.  As in paragraph mode, LaTeX's
      output is a string of words with spaces between them.  Unlike in
      paragraph mode, in LR mode LaTeX never starts a new line, it just
-     keeps going from left to right.  (When it tries to put that box
-     into a line, most likely LaTeX will complain because the box is too
-     wide to fit.)
+     keeps going from left to right.  (Although LaTeX will not complain
+     that the LR box is too long, when it is finished and next tries to
+     put that box into a line, it could very well complain that the
+     finished LR box won't fit there.)
 
-   * "Math mode" happens when LaTeX is generating an inline mathematical
+   * "Math mode" is when LaTeX is generating an inline mathematical
      formula.
 
-     "Display math mode" happens when LaTeX is generating a displayed
+     "Display math mode" is when LaTeX is generating a displayed
      mathematical formula.  (Displayed formulas differ somewhat from
      inline ones.  One example is that the placement of the subscript on
      '\int' differs in the two situations.)
@@ -9850,17 +9906,16 @@
      '\vbox'.  This is the vertical analogue of LR mode.
 
 For instance, if you begin a LaTeX article with 'Let \( x \) be ...'
-then these are the modes.  First, LaTeX starts every document in
-vertical mode.  It reads the 'L' and switches to paragraph mode.  The
-next switch happens at the '\(', where LaTeX changes to math mode.
-Then, when it leaves the formula, it resets itself to paragraph mode.
+then these are the modes: first LaTeX starts every document in vertical
+mode, then it reads the 'L' and switches to paragraph mode, then the
+next switch happens at the '\(' where LaTeX changes to math mode, and
+then when it leaves the formula it pops back to paragraph mode.
 
    Paragraph mode has two subcases.  If you use a '\parbox' command or
-'minipage' environment then LaTeX is put into paragraph mode; it is
-dividing string of words into lines.  But it will not put a page break
-here.  Inside one of these boxes, called a "parbox", LaTeX is in "inner
-paragraph mode".  Its more usual situation, where it can put page
-breaks, is "outer paragraph mode" (*note Page breaking::).
+or a 'minipage' then LaTeX is put into paragraph mode.  But it will not
+put a page break here.  Inside one of these boxes, called a "parbox",
+LaTeX is in "inner paragraph mode".  Its more usual situation, where it
+can put page breaks, is "outer paragraph mode" (*note Page breaking::).
 
 * Menu:
 
@@ -10927,9 +10982,9 @@
 between the questions.
 
    If you use '\vspace' in the middle of a paragraph (i.e., in
-horizontal mode) then the space is inserted after the line with the
-'\vspace' command; it does not start a new paragraph at the '\vspace'
-command.
+horizontal mode) then the space is inserted after the line containing
+the '\vspace' command; it does not start a new paragraph at the
+'\vspace' command.
 
    In this example the two questions will be evenly spaced vertically on
 the page, with at least one inch of space below each.
@@ -10960,16 +11015,16 @@
 '\vfill' ends the current paragraph whereas '\vspace{\fill}' adds the
 infinite vertical space below its line, irrespective of the paragraph
 structure.  In both cases that space will disappear at a page boundary;
-to circumvent this see *note \vspace::.
+to circumvent this see the starred option in *note \vspace::.
 
    In this example the page is filled, so the top and bottom lines
-contain the text 'Lost Dog!' and the third 'Lost Dog!' is exactly
+contain the text 'Lost Dog!' and the second 'Lost Dog!' is exactly
 halfway between them.
 
      \begin{document}
      Lost Dog!
      \vfill
-     Lost Dog!
+     Lost Dog!  % perfectly in the middle
      \vfill
      Lost Dog!
      \end{document}
@@ -11433,9 +11488,10 @@
 
      \usebox{BOX-CMD}
 
-   Produce the box most recently saved in the bin BOX-CMD by '\sbox', or
-'\savebox', or 'lrbox'.  *Note \sbox & \savebox:: for more information
-and examples.  This command is robust (*note \protect::).
+   Produce the box most recently saved in the bin BOX-CMD by the
+commands '\sbox' or '\savebox', or the 'lrbox' environment.  *Note \sbox
+& \savebox:: for more information and examples.  (Note that BOX-CMD
+starts with a backslash.)  This command is robust (*note \protect::).
 
 
 File: latex2e.info,  Node: Color,  Next: Graphics,  Prev: Boxes,  Up: Top
@@ -14061,7 +14117,7 @@
        LETTER BODY
      \closing{CLOSING TEXT}
      \end{letter}
-     ...  more letters ...
+        ...
      \end{document}
 
    Produce one or more letters.
@@ -14071,7 +14127,7 @@
 backslash, ('\\').  For example, you might have:
 
       \begin{letter}{Ninon de l'Enclos \\
-        l'h\^otel Sagonne}
+                     l'h\^otel Sagonne}
         ...
       \end{letter}
 
@@ -14083,7 +14139,7 @@
 with the recipient address, often SENDER ADDRESS contains multiple lines
 separated by a double backslash ('\\').  LaTeX will put the SENDER NAME
 under the closing, after a vertical space for the traditional
-hand-written signature; it also can contain multiple lines.
+hand-written signature.
 
    Each 'letter' environment body begins with a required '\opening'
 command such as '\opening{Dear Madam or Sir:}'.  The LETTER BODY text is
@@ -14097,13 +14153,13 @@
 the Boss's Boss}'.  There's a similar '\encl' command for a list of
 enclosures.  And, you can add a postscript with '\ps'.
 
-   LaTeX's default is to indent the signature and the '\closing' above
-it by a length of '\longindentation'.  By default this is
-'0.5\textwidth'.  To make them flush left, put
-'\setlength{\longindentation}{0em}' in your preamble.
+   LaTeX's default is to indent the sender name and the closing above it
+by a length of '\longindentation'.  By default this is '0.5\textwidth'.
+To make them flush left, put '\setlength{\longindentation}{0em}' in your
+preamble.
 
    To set a fixed date use something like
-'\renewcommand{\today}{2015-Oct-12}'.  If put in your preamble then it
+'\renewcommand{\today}{1958-Oct-12}'.  If put in your preamble then it
 will apply to all the letters.
 
    This example shows only one 'letter' environment.  The three lines
@@ -15057,11 +15113,11 @@
                                                               (line  27)
 * \> (tabbing):                          tabbing.             (line  72)
 * \@:                                    \@.                  (line   6)
-* \@beginparpenalty:                     list.                (line 236)
-* \@endparpenalty:                       list.                (line 244)
+* \@beginparpenalty:                     list.                (line 241)
+* \@endparpenalty:                       list.                (line 249)
 * \@fnsymbol:                            \footnote.           (line  24)
 * \@ifstar:                              \@ifstar.            (line   6)
-* \@itempenalty:                         list.                (line 240)
+* \@itempenalty:                         list.                (line 245)
 * \@startsection:                        \@startsection.      (line   6)
 * \a (tabbing):                          tabbing.             (line 102)
 * \a' (acute accent in tabbing):         tabbing.             (line 103)
@@ -15100,7 +15156,7 @@
 * \arcsin:                               Math functions.      (line  12)
 * \arctan:                               Math functions.      (line  15)
 * \arg:                                  Math functions.      (line  18)
-* \arraycolsep:                          array.               (line  39)
+* \arraycolsep:                          array.               (line  51)
 * \arrayrulewidth:                       tabular.             (line 156)
 * \arraystretch:                         tabular.             (line 162)
 * \ast:                                  Math symbols.        (line  38)
@@ -15177,11 +15233,11 @@
 * \capitalring:                          Accents.             (line  75)
 * \capitaltie:                           Accents.             (line  81)
 * \capitaltilde:                         Accents.             (line  46)
-* \caption:                              figure.              (line  42)
+* \caption:                              figure.              (line  44)
 * \caption <1>:                          table.               (line  47)
 * \cc:                                   \cc.                 (line   6)
 * \cdot:                                 Math symbols.        (line 120)
-* \cdots:                                Ellipses.            (line  17)
+* \cdots:                                Dots.                (line  17)
 * \centering:                            \centering.          (line   6)
 * \chapter:                              Sectioning.          (line   6)
 * \chapter <1>:                          \chapter.            (line   6)
@@ -15257,7 +15313,7 @@
 * \ddag:                                 Text symbols.        (line  18)
 * \ddagger:                              Math symbols.        (line 158)
 * \ddot:                                 Math accents.        (line  22)
-* \ddots:                                Ellipses.            (line  21)
+* \ddots:                                Dots.                (line  21)
 * \DeclareGraphicsExtensions:            \DeclareGraphicsExtensions.
                                                               (line   6)
 * \DeclareGraphicsRule:                  \DeclareGraphicsRule.
@@ -15282,7 +15338,7 @@
 * \diamond:                              Math symbols.        (line 171)
 * \diamondsuit:                          Math symbols.        (line 175)
 * \dim:                                  Math functions.      (line  45)
-* \displaystyle:                         Math formulas.       (line  67)
+* \displaystyle:                         Math formulas.       (line  61)
 * \div:                                  Math symbols.        (line 178)
 * \dj:                                   Additional Latin letters.
                                                               (line  26)
@@ -15449,12 +15505,12 @@
 * \intextsep <1>:                        Floats.              (line 119)
 * \iota:                                 Math symbols.        (line 279)
 * \it:                                   Font styles.         (line  76)
-* \item:                                 description.         (line  29)
+* \item:                                 description.         (line  31)
 * \item <1>:                             enumerate.           (line  29)
 * \item <2>:                             itemize.             (line   6)
-* \item <3>:                             itemize.             (line  27)
-* \itemindent:                           list.                (line  78)
-* \itemsep:                              list.                (line  82)
+* \item <3>:                             itemize.             (line  28)
+* \itemindent:                           list.                (line  83)
+* \itemsep:                              list.                (line  87)
 * \itshape:                              Font styles.         (line  33)
 * \j (dotless j):                        Accents.             (line  17)
 * \jmath:                                Math symbols.        (line 286)
@@ -15472,12 +15528,12 @@
 * \labelenumii:                          enumerate.           (line  56)
 * \labelenumiii:                         enumerate.           (line  56)
 * \labelenumiv:                          enumerate.           (line  56)
-* \labelitemi:                           itemize.             (line  34)
-* \labelitemii:                          itemize.             (line  34)
-* \labelitemiii:                         itemize.             (line  34)
-* \labelitemiv:                          itemize.             (line  34)
-* \labelsep:                             list.                (line  94)
-* \labelwidth:                           list.                (line  99)
+* \labelitemi:                           itemize.             (line  35)
+* \labelitemii:                          itemize.             (line  35)
+* \labelitemiii:                         itemize.             (line  35)
+* \labelitemiv:                          itemize.             (line  35)
+* \labelsep:                             list.                (line  99)
+* \labelwidth:                           list.                (line 104)
 * \Lambda:                               Math symbols.        (line 293)
 * \lambda:                               Math symbols.        (line 296)
 * \land:                                 Math symbols.        (line 299)
@@ -15490,7 +15546,7 @@
 * \lbrace:                               Math symbols.        (line 309)
 * \lbrack:                               Math symbols.        (line 313)
 * \lceil:                                Math symbols.        (line 317)
-* \ldots:                                Ellipses.            (line  24)
+* \ldots:                                Dots.                (line  25)
 * \ldots <1>:                            Text symbols.        (line  34)
 * \le:                                   Math symbols.        (line 321)
 * \leadsto:                              Math symbols.        (line 325)
@@ -15500,14 +15556,14 @@
 * \lefteqn:                              eqnarray.            (line  46)
 * \leftharpoondown:                      Math symbols.        (line 341)
 * \leftharpoonup:                        Math symbols.        (line 344)
-* \leftmargin:                           itemize.             (line  53)
-* \leftmargin <1>:                       list.                (line 119)
-* \leftmargini:                          itemize.             (line  53)
-* \leftmarginii:                         itemize.             (line  53)
-* \leftmarginiii:                        itemize.             (line  53)
-* \leftmarginiv:                         itemize.             (line  53)
-* \leftmarginv:                          itemize.             (line  53)
-* \leftmarginvi:                         itemize.             (line  53)
+* \leftmargin:                           itemize.             (line  54)
+* \leftmargin <1>:                       list.                (line 124)
+* \leftmargini:                          itemize.             (line  54)
+* \leftmarginii:                         itemize.             (line  54)
+* \leftmarginiii:                        itemize.             (line  54)
+* \leftmarginiv:                         itemize.             (line  54)
+* \leftmarginv:                          itemize.             (line  54)
+* \leftmarginvi:                         itemize.             (line  54)
 * \Leftrightarrow:                       Math symbols.        (line 347)
 * \leftrightarrow:                       Math symbols.        (line 352)
 * \leq:                                  Math symbols.        (line 357)
@@ -15531,7 +15587,7 @@
                                                               (line   6)
 * \listoftables:                         Table of contents etc..
                                                               (line   6)
-* \listparindent:                        list.                (line 136)
+* \listparindent:                        list.                (line 141)
 * \ll:                                   Math symbols.        (line 372)
 * \ln:                                   Math functions.      (line  75)
 * \lnot:                                 Math symbols.        (line 376)
@@ -15554,7 +15610,7 @@
 * \makeglossary:                         Glossaries.          (line   6)
 * \makeglossary <1>:                     Glossaries.          (line  43)
 * \makeindex:                            Indexes.             (line   6)
-* \makelabel:                            list.                (line  55)
+* \makelabel:                            list.                (line  60)
 * \makelabels:                           \makelabels.         (line   6)
 * \maketitle:                            \maketitle.          (line   6)
 * \mapsto:                               Math symbols.        (line 401)
@@ -15563,13 +15619,13 @@
                                                               (line  40)
 * \marginparpush <1>:                    Page layout parameters.
                                                               (line  43)
-* \marginparpush <2>:                    Marginal notes.      (line  37)
-* \marginparsep:                         Marginal notes.      (line  41)
+* \marginparpush <2>:                    Marginal notes.      (line  35)
+* \marginparsep:                         Marginal notes.      (line  39)
 * \marginparwidth:                       Page layout parameters.
                                                               (line  42)
 * \marginparwidth <1>:                   Page layout parameters.
                                                               (line  43)
-* \marginparwidth <2>:                   Marginal notes.      (line  45)
+* \marginparwidth <2>:                   Marginal notes.      (line  43)
 * \marginsep:                            Page layout parameters.
                                                               (line  41)
 * \marginsep <1>:                        Page layout parameters.
@@ -15652,7 +15708,7 @@
 * \nopagebreak:                          \pagebreak & \nopagebreak.
                                                               (line   6)
 * \normalfont:                           Font styles.         (line  57)
-* \normalmarginpar:                      Marginal notes.      (line  25)
+* \normalmarginpar:                      Marginal notes.      (line  22)
 * \normalsfcodes:                        \normalsfcodes.      (line   6)
 * \normalsize:                           Font sizes.          (line  11)
 * \not:                                  Math symbols.        (line 455)
@@ -15724,18 +15780,18 @@
                                                               (line   6)
 * \parallel:                             Math symbols.        (line 508)
 * \parbox:                               \parbox.             (line   6)
-* \parindent:                            minipage.            (line 108)
+* \parindent:                            minipage.            (line 104)
 * \parindent <1>:                        \indent & \noindent. (line   6)
 * \parindent <2>:                        \parindent & \parskip.
                                                               (line   6)
-* \parsep:                               list.                (line 142)
+* \parsep:                               list.                (line 147)
 * \parskip:                              \parindent & \parskip.
                                                               (line   6)
-* \parskip example:                      itemize.             (line  72)
+* \parskip example:                      itemize.             (line  73)
 * \part:                                 Sectioning.          (line   6)
 * \part <1>:                             \part.               (line   6)
 * \partial:                              Math symbols.        (line 511)
-* \partopsep:                            list.                (line 151)
+* \partopsep:                            list.                (line 156)
 * \PassOptionsToClass:                   Class and package commands.
                                                               (line 206)
 * \PassOptionsToPackage:                 Class and package commands.
@@ -15815,7 +15871,7 @@
                                                               (line   6)
 * \restriction:                          Math symbols.        (line 583)
 * \revemptyset:                          Math symbols.        (line 588)
-* \reversemarginpar:                     Marginal notes.      (line  25)
+* \reversemarginpar:                     Marginal notes.      (line  22)
 * \rfloor:                               Math symbols.        (line 593)
 * \rhd:                                  Math symbols.        (line 597)
 * \rho:                                  Math symbols.        (line 604)
@@ -15825,7 +15881,7 @@
 * \rightharpoondown:                     Math symbols.        (line 617)
 * \rightharpoonup:                       Math symbols.        (line 620)
 * \rightleftharpoons:                    Math symbols.        (line 623)
-* \rightmargin:                          list.                (line 166)
+* \rightmargin:                          list.                (line 171)
 * \rm:                                   Font styles.         (line  79)
 * \rmfamily:                             Font styles.         (line  30)
 * \roman{COUNTER}:                       \alph \Alph \arabic \roman \Roman \fnsymbol.
@@ -16023,7 +16079,7 @@
 * \topfraction <1>:                      Floats.              (line 108)
 * \topmargin:                            Page layout parameters.
                                                               (line 124)
-* \topsep:                               list.                (line 171)
+* \topsep:                               list.                (line 176)
 * \topskip:                              Page layout parameters.
                                                               (line 131)
 * \topskip <1>:                          Page layout parameters.
@@ -16073,7 +16129,7 @@
 * \varsigma:                             Math symbols.        (line 837)
 * \vartheta:                             Math symbols.        (line 841)
 * \vdash:                                Math symbols.        (line 845)
-* \vdots:                                Ellipses.            (line  33)
+* \vdots:                                Dots.                (line  34)
 * \vec:                                  Math accents.        (line  40)
 * \vector:                               \vector.             (line   6)
 * \vee:                                  Math symbols.        (line 849)
@@ -16093,7 +16149,7 @@
 * \year:                                 \day & \month & \year.
                                                               (line   6)
 * \zeta:                                 Math symbols.        (line 904)
-* \\ (for center):                       center.              (line  22)
+* \\ (for center):                       center.              (line  16)
 * \\ (for eqnarray):                     eqnarray.            (line  29)
 * \\ (for flushright):                   flushright.          (line  12)
 * \\ (for \shortstack objects):          \shortstack.         (line  32)
@@ -16144,16 +16200,18 @@
 * align environment, from amsmath:       eqnarray.            (line   6)
 * aligning equations:                    eqnarray.            (line   6)
 * alignment via tabbing:                 tabbing.             (line   6)
-* amsfonts package:                      Math formulas.       (line  21)
-* amsmath package:                       array.               (line  42)
-* amsmath package <1>:                   displaymath.         (line  22)
-* amsmath package <2>:                   theorem.             (line  28)
-* amsmath package <3>:                   Math formulas.       (line  21)
-* amsmath package <4>:                   Ellipses.            (line  36)
-* amsmath package <5>:                   Math functions.      (line 111)
-* amsmath package <6>:                   Colon character & \colon.
+* amsfonts package:                      Math formulas.       (line  86)
+* amsmath package:                       array.               (line  55)
+* amsmath package <1>:                   array.               (line  66)
+* amsmath package <2>:                   displaymath.         (line  22)
+* amsmath package <3>:                   equation.            (line  20)
+* amsmath package <4>:                   theorem.             (line  28)
+* amsmath package <5>:                   Math formulas.       (line  86)
+* amsmath package <6>:                   Dots.                (line  37)
+* amsmath package <7>:                   Math functions.      (line 111)
+* amsmath package <8>:                   Colon character & \colon.
                                                               (line  15)
-* amsmath package <7>:                   Colon character & \colon.
+* amsmath package <9>:                   Colon character & \colon.
                                                               (line  19)
 * amsmath package, replacing eqnarray:   eqnarray.            (line   6)
 * amsthm package:                        theorem.             (line  28)
@@ -16163,6 +16221,7 @@
 * appendix package:                      \appendix.           (line  29)
 * aring:                                 Additional Latin letters.
                                                               (line  12)
+* array (package) package:               array.               (line  77)
 * array environment:                     array.               (line   6)
 * arrays, math:                          array.               (line   6)
 * arrow, left, in text:                  Text symbols.        (line 140)
@@ -16172,7 +16231,7 @@
 * ASCII circumflex, in text:             Text symbols.        (line  66)
 * ASCII tilde, in text:                  Text symbols.        (line  69)
 * asterisk, centered, in text:           Text symbols.        (line  72)
-* Asymptote package:                     \line.               (line  35)
+* Asymptote package:                     \line.               (line  36)
 * Asymptote package <1>:                 \strut.              (line  62)
 * Asymptote package <2>:                 \mbox & \makebox.    (line  73)
 * at clause, in font definitions:        \newfont.            (line  19)
@@ -16214,7 +16273,7 @@
                                                               (line  32)
 * bold font:                             Font styles.         (line  71)
 * bold math:                             Font styles.         (line 130)
-* bold typewriter, avoiding:             description.         (line  34)
+* bold typewriter, avoiding:             description.         (line  36)
 * boldface mathematics:                  \boldmath & \unboldmath.
                                                               (line   6)
 * book class:                            Document classes.    (line  11)
@@ -16243,6 +16302,7 @@
 * breve accent:                          Accents.             (line  85)
 * breve accent, math:                    Math accents.        (line  17)
 * bug reporting:                         About this document. (line  21)
+* bullet lists:                          itemize.             (line   6)
 * bullet symbol:                         Math symbols.        (line 113)
 * bullet, in text:                       Text symbols.        (line  93)
 * bulleted lists:                        itemize.             (line   6)
@@ -16356,7 +16416,7 @@
                                                               (line   6)
 * counters, setting:                     \setcounter.         (line   6)
 * cprotect package:                      verbatim.            (line  26)
-* cprotect package <1>:                  \verb.               (line  34)
+* cprotect package <1>:                  \verb.               (line  45)
 * creating pictures:                     picture.             (line   6)
 * creating tables:                       table.               (line   6)
 * credit footnote:                       \maketitle.          (line  57)
@@ -16374,6 +16434,7 @@
 * datetime package:                      \today.              (line  27)
 * dbltopnumber:                          Floats.              (line 134)
 * dbltopnumber <1>:                      Floats.              (line 135)
+* dcolumn package:                       array.               (line  77)
 * dd:                                    Units of length.     (line  30)
 * define color:                          Define colors.       (line   6)
 * defining a new command:                \newcommand & \renewcommand.
@@ -16400,7 +16461,7 @@
                                                               (line  15)
 * discretionary breaks, multiplication:  \*.                  (line   6)
 * discretionary hyphenation:             \discretionary.      (line   6)
-* display math mode:                     Modes.               (line  28)
+* display math mode:                     Modes.               (line  29)
 * displaying quoted text with paragraph indentation: quotation & quote.
                                                               (line   6)
 * displaying quoted text without paragraph indentation: quotation & quote.
@@ -16424,7 +16485,7 @@
 * dotless i, math:                       Math symbols.        (line 265)
 * dotless j:                             Accents.             (line  17)
 * dotless j, math:                       Math symbols.        (line 287)
-* dots:                                  Ellipses.            (line   6)
+* dots:                                  Dots.                (line   6)
 * double angle quotation marks:          Text symbols.        (line  31)
 * double dagger, in text:                Text symbols.        (line  19)
 * double dagger, in text <1>:            Text symbols.        (line 111)
@@ -16445,7 +16506,7 @@
 * dvitype command:                       Output files.        (line  10)
 * e-dash:                                Text symbols.        (line 122)
 * e-TeX:                                 TeX engines.         (line  13)
-* ellipses:                              Ellipses.            (line   6)
+* ellipses:                              Dots.                (line   6)
 * ellipsis:                              Text symbols.        (line  37)
 * em:                                    Units of length.     (line  38)
 * em <1>:                                Units of length.     (line  38)
@@ -16459,7 +16520,7 @@
 * engines, TeX:                          TeX engines.         (line   6)
 * enlarge current page:                  \enlargethispage.    (line   6)
 * enumerate environment:                 enumerate.           (line   6)
-* enumitem package:                      list.                (line 248)
+* enumitem package:                      list.                (line 253)
 * environment:                           Starting and ending. (line  22)
 * environment, abstract:                 abstract.            (line   6)
 * environment, array:                    array.               (line   6)
@@ -16541,7 +16602,7 @@
 * feminine ordinal symbol:               Text symbols.        (line 144)
 * figure environment:                    figure.              (line   6)
 * figure number, cross referencing:      \ref.                (line   6)
-* figures, footnotes in:                 minipage.            (line 112)
+* figures, footnotes in:                 minipage.            (line 108)
 * figures, inserting:                    figure.              (line   6)
 * file, root:                            Splitting the input. (line  10)
 * filecontents environment:              filecontents.        (line   6)
@@ -16585,7 +16646,7 @@
                                                               (line   6)
 * footnote, of a footnote:               Footnotes of footnotes.
                                                               (line   6)
-* footnotes in figures:                  minipage.            (line 112)
+* footnotes in figures:                  minipage.            (line 108)
 * footnotes, creating:                   Footnotes.           (line   6)
 * Footnotes, in a minipage:              \footnote.           (line  62)
 * footnotes, symbols instead of numbers: \footnote.           (line  24)
@@ -16624,7 +16685,7 @@
                                                               (line   6)
 * graphics package options:              Graphics package options.
                                                               (line   6)
-* graphics packages:                     \line.               (line  35)
+* graphics packages:                     \line.               (line  36)
 * graphics, resizing:                    \scalebox.           (line   6)
 * graphics, resizing <1>:                \resizebox.          (line   6)
 * graphics, scaling:                     \scalebox.           (line   6)
@@ -16671,7 +16732,7 @@
 * inch:                                  Units of length.     (line  17)
 * including graphics:                    \includegraphics.    (line   6)
 * indent, forcing:                       \indent & \noindent. (line   6)
-* indentation of paragraphs, in minipage: minipage.           (line 108)
+* indentation of paragraphs, in minipage: minipage.           (line 104)
 * indentfirst package:                   \part.               (line  50)
 * indentfirst package <1>:               \chapter.            (line  58)
 * indentfirst package <2>:               \section.            (line  60)
@@ -16691,14 +16752,14 @@
 * indexes:                               Indexes.             (line   6)
 * infinite horizontal stretch:           \hfill.              (line   6)
 * infinite vertical stretch:             \vfill.              (line   6)
-* inner paragraph mode:                  Modes.               (line  46)
+* inner paragraph mode:                  Modes.               (line  47)
 * input file:                            Splitting the input. (line   6)
 * input, on command line:                Command line input.  (line   6)
 * input/output, to terminal:             Terminal input/output.
                                                               (line   6)
 * inserting figures:                     figure.              (line   6)
 * insertions of special characters:      Special insertions.  (line   6)
-* internal vertical mode:                Modes.               (line  37)
+* internal vertical mode:                Modes.               (line  38)
 * italic correction:                     \/.                  (line   6)
 * italic font:                           Font styles.         (line  77)
 * itemize environment:                   itemize.             (line   6)
@@ -16791,6 +16852,7 @@
 * list of tables file:                   Output files.        (line  43)
 * listings package:                      tabbing.             (line 146)
 * listings package <1>:                  verbatim.            (line  31)
+* listings package <2>:                  \verb.               (line  42)
 * lists of items:                        itemize.             (line   6)
 * lists of items, generic:               list.                (line   6)
 * lists of items, numbered:              enumerate.           (line   6)
@@ -16836,16 +16898,16 @@
 * math formulas:                         Math formulas.       (line   6)
 * math functions:                        Math functions.      (line   6)
 * math miscellany:                       Math miscellany.     (line   6)
-* math mode:                             Modes.               (line  25)
+* math mode:                             Modes.               (line  26)
 * math mode, entering:                   Math formulas.       (line   6)
 * math mode, spacing:                    Spacing in math mode.
                                                               (line   6)
 * math symbols:                          Math symbols.        (line   6)
 * math, bold:                            Font styles.         (line 130)
-* mathtools package:                     Math formulas.       (line  21)
+* mathtools package:                     Math formulas.       (line  86)
 * mathtools package <1>:                 Over- and Underlining.
                                                               (line  45)
-* MetaPost package:                      \line.               (line  35)
+* MetaPost package:                      \line.               (line  36)
 * mfirstuc package:                      Upper and lower case.
                                                               (line  45)
 * mhchem package:                        Subscripts & superscripts.
@@ -16855,6 +16917,7 @@
 * minipage, creating a:                  minipage.            (line   6)
 * minted package:                        tabbing.             (line 146)
 * minted package <1>:                    verbatim.            (line  31)
+* minted package <2>:                    \verb.               (line  42)
 * mm:                                    Units of length.     (line  27)
 * modes:                                 Modes.               (line   6)
 * monospace font:                        Font styles.         (line  92)
@@ -16930,7 +16993,7 @@
 * ordinals, feminine and masculine:      Text symbols.        (line 144)
 * oslash:                                Additional Latin letters.
                                                               (line  44)
-* outer paragraph mode:                  Modes.               (line  46)
+* outer paragraph mode:                  Modes.               (line  47)
 * overbar accent:                        Accents.             (line  34)
 * overdot accent, math:                  Math accents.        (line  26)
 * overlining:                            Over- and Underlining.
@@ -16943,21 +17006,24 @@
 * package options <1>:                   Class and package commands.
                                                               (line  66)
 * package, algorithm2e:                  tabbing.             (line 146)
-* package, amsfonts:                     Math formulas.       (line  21)
-* package, amsmath:                      array.               (line  42)
-* package, amsmath <1>:                  displaymath.         (line  22)
-* package, amsmath <2>:                  theorem.             (line  28)
-* package, amsmath <3>:                  Math formulas.       (line  21)
-* package, amsmath <4>:                  Ellipses.            (line  36)
-* package, amsmath <5>:                  Math functions.      (line 111)
-* package, amsmath <6>:                  Colon character & \colon.
+* package, amsfonts:                     Math formulas.       (line  86)
+* package, amsmath:                      array.               (line  55)
+* package, amsmath <1>:                  array.               (line  66)
+* package, amsmath <2>:                  displaymath.         (line  22)
+* package, amsmath <3>:                  equation.            (line  20)
+* package, amsmath <4>:                  theorem.             (line  28)
+* package, amsmath <5>:                  Math formulas.       (line  86)
+* package, amsmath <6>:                  Dots.                (line  37)
+* package, amsmath <7>:                  Math functions.      (line 111)
+* package, amsmath <8>:                  Colon character & \colon.
                                                               (line  15)
-* package, amsmath <7>:                  Colon character & \colon.
+* package, amsmath <9>:                  Colon character & \colon.
                                                               (line  19)
 * package, amsthm:                       theorem.             (line  28)
 * package, amsthm <1>:                   \rule.               (line  18)
 * package, appendix:                     \appendix.           (line  29)
-* package, Asymptote:                    \line.               (line  35)
+* package, array (package):              array.               (line  77)
+* package, Asymptote:                    \line.               (line  36)
 * package, Asymptote <1>:                \strut.              (line  62)
 * package, Asymptote <2>:                \mbox & \makebox.    (line  73)
 * package, babel:                        \chapter.            (line  71)
@@ -16975,9 +17041,10 @@
 * package, cleveref <1>:                 \ref.                (line  29)
 * package, cleveref <2>:                 \footnotemark.       (line  48)
 * package, cprotect:                     verbatim.            (line  26)
-* package, cprotect <1>:                 \verb.               (line  34)
+* package, cprotect <1>:                 \verb.               (line  45)
 * package, datetime:                     \today.              (line  27)
-* package, enumitem:                     list.                (line 248)
+* package, dcolumn:                      array.               (line  77)
+* package, enumitem:                     list.                (line 253)
 * package, envlab:                       \makelabels.         (line  55)
 * package, etoolbox:                     Class and package commands.
                                                               (line 110)
@@ -17006,26 +17073,28 @@
 * package, index:                        \index.              (line 101)
 * package, listings:                     tabbing.             (line 146)
 * package, listings <1>:                 verbatim.            (line  31)
+* package, listings <2>:                 \verb.               (line  42)
 * package, macros2e:                     \makeatletter & \makeatother.
                                                               (line  39)
-* package, mathtools:                    Math formulas.       (line  21)
+* package, mathtools:                    Math formulas.       (line  86)
 * package, mathtools <1>:                Over- and Underlining.
                                                               (line  45)
-* package, MetaPost:                     \line.               (line  35)
+* package, MetaPost:                     \line.               (line  36)
 * package, mfirstuc:                     Upper and lower case.
                                                               (line  45)
 * package, mhchem:                       Subscripts & superscripts.
                                                               (line  60)
 * package, minted:                       tabbing.             (line 146)
 * package, minted <1>:                   verbatim.            (line  31)
+* package, minted <2>:                   \verb.               (line  42)
 * package, multind:                      Indexes.             (line  32)
-* package, pict2e:                       \line.               (line  35)
+* package, pict2e:                       \line.               (line  36)
 * package, polyglossia:                  Accents.             (line   6)
 * package, polyglossia <1>:              \today.              (line  13)
 * package, polyglossia <2>:              Table of contents etc..
                                                               (line  80)
 * package, polyglossia <3>:              \index.              (line  56)
-* package, PSTricks:                     \line.               (line  35)
+* package, PSTricks:                     \line.               (line  36)
 * package, sagetex:                      Command line options.
                                                               (line  62)
 * package, setspace:                     Low-level font commands.
@@ -17036,7 +17105,7 @@
 * package, textcase:                     Upper and lower case.
                                                               (line  42)
 * package, textcomp:                     Font styles.         (line 134)
-* package, TikZ:                         \line.               (line  35)
+* package, TikZ:                         \line.               (line  36)
 * package, TikZ <1>:                     \strut.              (line  62)
 * package, TikZ <2>:                     \mbox & \makebox.    (line  72)
 * package, titlesec:                     \part.               (line  54)
@@ -17051,7 +17120,7 @@
                                                               (line  91)
 * package, ulem:                         Over- and Underlining.
                                                               (line  15)
-* package, url:                          \verb.               (line  30)
+* package, url:                          \verb.               (line  38)
 * package, verbatimbox:                  verbatim.            (line  37)
 * packages, loading additional:          Additional packages. (line   6)
 * page break, forcing:                   \pagebreak & \nopagebreak.
@@ -17073,7 +17142,7 @@
                                                               (line   6)
 * paragraph indentation:                 \parindent & \parskip.
                                                               (line   6)
-* paragraph indentation, in minipage:    minipage.            (line 108)
+* paragraph indentation, in minipage:    minipage.            (line 104)
 * paragraph indentations in quoted text: quotation & quote.   (line   6)
 * paragraph indentations in quoted text, omitting: quotation & quote.
                                                               (line   6)
@@ -17100,8 +17169,8 @@
 * period, sentence-ending:               \@.                  (line   6)
 * period, spacing after:                 \@.                  (line   6)
 * pica:                                  Units of length.     (line  14)
-* pict2e package:                        \line.               (line  35)
-* pict2e package <1>:                    \line.               (line  35)
+* pict2e package:                        \line.               (line  36)
+* pict2e package <1>:                    \line.               (line  36)
 * picture environment:                   picture.             (line   6)
 * pictures, creating:                    picture.             (line   6)
 * pilcrow:                               Text symbols.        (line  45)
@@ -17132,7 +17201,7 @@
 * prompt, *:                             Recovering from errors.
                                                               (line  23)
 * pronunciation:                         Overview.            (line  24)
-* PSTricks package:                      \line.               (line  35)
+* PSTricks package:                      \line.               (line  36)
 * pt:                                    Units of length.     (line  10)
 * quad:                                  Spacing in math mode.
                                                               (line  50)
@@ -17343,7 +17412,7 @@
 * three-quarters em-dash:                Text symbols.        (line 178)
 * tie:                                   ~.                   (line   6)
 * tie-after accent:                      Accents.             (line  81)
-* TikZ package:                          \line.               (line  35)
+* TikZ package:                          \line.               (line  36)
 * TikZ package <1>:                      \strut.              (line  62)
 * TikZ package <2>:                      \mbox & \makebox.    (line  72)
 * tilde accent:                          Accents.             (line  46)
@@ -17392,7 +17461,7 @@
 * typeface sizes:                        Font sizes.          (line   6)
 * typefaces:                             Fonts.               (line   6)
 * typewriter font:                       Font styles.         (line  92)
-* typewriter labels in lists:            description.         (line  34)
+* typewriter labels in lists:            description.         (line  36)
 * ulem package:                          Over- and Underlining.
                                                               (line  15)
 * umlaut accent:                         Accents.             (line  23)
@@ -17406,7 +17475,7 @@
 * unordered lists:                       itemize.             (line   6)
 * uppercase:                             Upper and lower case.
                                                               (line   6)
-* url package:                           \verb.               (line  30)
+* url package:                           \verb.               (line  38)
 * using BibTeX:                          Using BibTeX.        (line   6)
 * usrguide official documentation:       About this document. (line  36)
 * UTF-8:                                 TeX engines.         (line   6)
@@ -17419,12 +17488,12 @@
 * verse environment:                     verse.               (line   6)
 * vertical bar, double, in text:         Text symbols.        (line  81)
 * vertical bar, in text:                 Text symbols.        (line  78)
-* vertical mode:                         Modes.               (line  33)
+* vertical mode:                         Modes.               (line  34)
 * vertical space:                        \vspace.             (line   6)
 * vertical space <1>:                    \addvspace.          (line   6)
 * vertical space before paragraphs:      \parindent & \parskip.
                                                               (line   6)
-* visible space:                         \verb.               (line  12)
+* visible space:                         \verb.               (line  31)
 * visible space symbol, in text:         Text symbols.        (line 190)
 * weights, of fonts:                     Low-level font commands.
                                                               (line  58)
@@ -17567,382 +17636,382 @@
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 Node: abstract116333
 Node: array117922
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-Ref: enumerate labelenumii131459
-Ref: enumerate labelenumiii131459
-Ref: enumerate labelenumiv131459
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-Node: equation133993
-Node: figure134621
-Node: filecontents136696
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-Node: \hss375674
-Node: \spacefactor376368
-Node: \@379755
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-Node: \normalsfcodes382630
-Node: \(SPACE)382877
-Node: ~384512
-Node: \thinspace & \negthinspace386982
-Node: \/387925
-Node: \hrulefill & \dotfill389231
-Node: \bigskip & \medskip & \smallskip390587
-Ref: bigskip391405
-Ref: medskip391609
-Ref: smallskip391818
-Node: \bigbreak & \medbreak & \smallbreak392479
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-Node: \vfill398216
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-Node: \mbox & \makebox401798
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-Ref: mbox makebox height403013
-Ref: mbox makebox width403013
-Ref: mbox makebox totalheight403013
-Node: \fbox & \framebox405107
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-Ref: raisebox height410966
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-Node: lrbox414646
-Node: \usebox415468
-Node: Color415800
-Node: Color package options416644
-Node: Color models418290
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-Ref: color models rgb419599
-Ref: color models RGB419936
-Ref: color models named420311
-Node: Commands for color420599
-Node: Define colors421014
-Node: Colored text421739
-Node: Colored boxes424137
-Node: Colored pages425526
-Node: Graphics426219
-Node: Graphics package options428346
-Node: Graphics package configuration431099
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-Node: \DeclareGraphicsExtensions434792
-Node: \DeclareGraphicsRule436560
-Node: Commands for graphics439746
-Node: \includegraphics440251
-Ref: includegraphics width445301
-Ref: includegraphics height445832
-Ref: includegraphics totalheght446238
-Ref: includegraphics keepaspectratio446502
-Ref: includegraphics viewport448188
-Ref: includegraphics trim448558
-Ref: includegraphics clip449014
-Ref: includegraphics page449274
-Ref: includegraphics pagebox449365
-Ref: includegraphics interpolate450230
-Ref: includegraphics quiet450435
-Ref: includegraphics draft450596
-Ref: includegraphics bb451401
-Ref: includegraphics bbllx451799
-Ref: includegraphics bblly451799
-Ref: includegraphics bburx451799
-Ref: includegraphics bbury451799
-Ref: includegraphics natwidth451941
-Ref: includegraphics natheight451941
-Ref: includegraphics hiresbb452127
-Ref: includegraphics type452889
-Ref: includegraphics ext452929
-Ref: includegraphics read453032
-Ref: includegraphics command453149
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-Node: \scalebox456225
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-Node: Special insertions458473
-Node: Reserved characters459275
-Node: Upper and lower case460473
-Node: Symbols by font position462388
-Node: Text symbols463008
-Node: Accents467009
-Node: Additional Latin letters469024
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-Node: Splitting the input472320
-Node: \endinput473854
-Node: \include & \includeonly475121
-Node: \input479343
-Node: Front/back matter480558
-Node: Table of contents etc.480891
-Node: \addcontentsline484627
-Node: \addtocontents487469
-Node: \nofiles489060
-Node: Indexes489792
-Node: \index491420
-Node: makeindex496535
-Ref: makeindex preamble498203
-Ref: makeindex postamble498343
-Ref: makeindex group skip498428
-Ref: makeindex letheadflag498748
-Ref: makeindex lethead prefix499212
-Ref: makeindex lethead suffix499364
-Ref: makeindex item 0499512
-Ref: makeindex item 1499592
-Ref: makeindex item 2499667
-Ref: makeindex item 01499745
-Ref: makeindex item x1499850
-Ref: makeindex item 12500055
-Ref: makeindex item x2500163
-Ref: makeindex delim 0500323
-Ref: makeindex delim 1500453
-Ref: makeindex delim 2500583
-Ref: makeindex delim n500709
-Ref: makeindex delim r500844
-Ref: makeindex line max500952
-Ref: makeindex indent space501087
-Ref: makeindex indent length501182
-Ref: makeindex page precedence501367
-Node: \printindex502241
-Node: Glossaries502713
-Node: \newglossaryentry504680
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-Node: Letters506943
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-Node: \closing511863
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-Node: \location512591
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-Node: \ps515694
-Node: \signature515983
-Node: \telephone517211
-Node: Terminal input/output517576
-Node: \typein517841
-Node: \typeout519090
-Node: Command line520134
-Node: Command line options522192
-Node: Command line input525734
-Node: Recovering from errors527598
-Node: Document templates528932
-Node: beamer template529377
-Node: article template530031
-Node: book template530458
-Node: Larger book template530939
-Node: tugboat template532425
-Node: Index534796
-Ref: Command Index534882
+Node: center120814
+Node: \centering122566
+Node: description124063
+Node: displaymath126278
+Node: document128065
+Node: \AtBeginDocument128495
+Node: \AtEndDocument129119
+Node: enumerate129763
+Ref: enumerate enumi131626
+Ref: enumerate enumii131626
+Ref: enumerate enumiii131626
+Ref: enumerate enumiv131626
+Ref: enumerate labelenumi132024
+Ref: enumerate labelenumii132024
+Ref: enumerate labelenumiii132024
+Ref: enumerate labelenumiv132024
+Node: eqnarray132563
+Node: equation134558
+Node: figure135226
+Node: filecontents137380
+Node: flushleft139127
+Node: \raggedright140144
+Node: flushright141342
+Node: \raggedleft142078
+Node: itemize142868
+Ref: itemize labelitemi144090
+Ref: itemize labelitemii144090
+Ref: itemize labelitemiii144090
+Ref: itemize labelitemiv144090
+Ref: itemize leftmargin144932
+Ref: itemize leftmargini144932
+Ref: itemize leftmarginii144932
+Ref: itemize leftmarginiii144932
+Ref: itemize leftmarginiv144932
+Ref: itemize leftmarginv144932
+Ref: itemize leftmarginvi144932
+Node: letter146336
+Node: list146574
+Ref: list makelabel149019
+Ref: list itemindent150403
+Ref: list itemsep150540
+Ref: list labelsep151192
+Ref: list labelwidth151355
+Ref: list leftmargin152366
+Ref: list listparindent153219
+Ref: list parsep153450
+Ref: list partopsep153953
+Ref: list rightmargin154751
+Ref: list topsep154936
+Ref: list beginparpenalty158511
+Ref: list itempenalty158610
+Ref: list endparpenalty158714
+Node: \item159586
+Node: trivlist160837
+Node: math162365
+Node: minipage162671
+Node: picture167949
+Node: \put174365
+Node: \multiput174843
+Node: \qbezier175582
+Node: \graphpaper176507
+Node: \line177301
+Node: \linethickness179265
+Node: \thinlines179714
+Node: \thicklines180125
+Node: \circle180509
+Node: \oval181049
+Node: \shortstack182025
+Node: \vector183422
+Node: \makebox (picture)184338
+Node: \framebox (picture)185520
+Node: \frame186993
+Node: \dashbox187432
+Node: quotation & quote188567
+Node: tabbing189463
+Node: table195456
+Node: tabular197481
+Ref: tabular arrayrulewidth203573
+Ref: tabular arraystrech203813
+Ref: tabular doublerulesep204034
+Ref: tabular tabcolsep204170
+Node: \multicolumn204691
+Node: \vline208550
+Node: \cline209941
+Node: \hline210651
+Node: thebibliography211333
+Node: \bibitem213743
+Node: \cite216018
+Node: \nocite217668
+Node: Using BibTeX218152
+Node: theorem220307
+Node: titlepage221229
+Node: verbatim222512
+Node: \verb224022
+Node: verse225842
+Node: Line breaking227069
+Node: \\228435
+Node: \obeycr & \restorecr230868
+Node: \newline231662
+Node: \- (hyphenation)232691
+Node: \discretionary234329
+Node: \fussy & \sloppy235217
+Node: sloppypar236000
+Node: \hyphenation237146
+Node: \linebreak & \nolinebreak237740
+Node: Page breaking238887
+Node: \clearpage & \cleardoublepage240916
+Node: \newpage242436
+Node: \enlargethispage243734
+Node: \pagebreak & \nopagebreak244690
+Node: Footnotes246357
+Node: \footnote247503
+Ref: footnote footnoterule248771
+Ref: footnote footnotesep249382
+Node: \footnotemark250448
+Node: \footnotetext252787
+Node: Footnotes in section headings253388
+Node: Footnotes in a table254221
+Node: Footnotes of footnotes257143
+Node: Definitions257847
+Node: \newcommand & \renewcommand258724
+Node: \providecommand263954
+Node: \newcounter265100
+Node: \newlength266827
+Node: \newsavebox267649
+Node: \newenvironment & \renewenvironment268565
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+Node: \newfont277453
+Node: \protect278689
+Node: \ignorespaces & \ignorespacesafterend281075
+Node: Counters283813
+Node: \alph \Alph \arabic \roman \Roman \fnsymbol285514
+Node: \usecounter288168
+Node: \value289027
+Node: \setcounter290080
+Node: \addtocounter290676
+Node: \refstepcounter291130
+Node: \stepcounter291799
+Node: \day & \month & \year292345
+Node: Lengths293156
+Node: Units of length297509
+Ref: units of length pt297712
+Ref: units of length pc297834
+Ref: units of length in297857
+Ref: units of length bp297883
+Ref: units of length cm298014
+Ref: units of length mm298036
+Ref: units of length dd298058
+Ref: units of length cc298090
+Ref: units of length sp298115
+Ref: Lengths/em298146
+Ref: Lengths/en298146
+Ref: Lengths/ex298146
+Ref: units of length em298146
+Ref: units of length en298146
+Ref: units of length ex298146
+Node: \setlength299002
+Node: \addtolength299779
+Node: \settodepth300741
+Node: \settoheight301531
+Node: \settowidth302325
+Node: Making paragraphs303104
+Node: \par304753
+Node: \indent & \noindent306598
+Node: \parindent & \parskip308132
+Node: Marginal notes309167
+Ref: marginal notes marginparpush310567
+Ref: marginal notes marginparsep310680
+Ref: marginal notes marginparwidth310812
+Node: Math formulas311161
+Node: Subscripts & superscripts315329
+Node: Math symbols317438
+Node: Blackboard bold343605
+Node: Calligraphic344377
+Node: \boldmath & \unboldmath344949
+Node: Dots346463
+Ref: ellipses cdots346885
+Ref: ellipses ddots347032
+Ref: ellipses ldots347121
+Ref: ellipses vdots347542
+Node: Math functions348728
+Node: Math accents350372
+Node: Over- and Underlining351271
+Node: Spacing in math mode353098
+Ref: spacing in math mode thickspace353916
+Ref: spacing in math mode medspace354008
+Ref: Spacing in math mode/\thinspace354104
+Ref: spacing in math mode thinspace354104
+Ref: spacing in math mode negthinspace354585
+Ref: spacing in math mode quad354783
+Ref: spacing in math mode qquad355039
+Node: Math miscellany355137
+Node: Colon character & \colon355696
+Node: \*356389
+Node: \frac356973
+Node: \left & \right357353
+Node: \sqrt358527
+Node: \stackrel359122
+Node: Modes359395
+Ref: modes paragraph mode359845
+Ref: modes lr mode360041
+Ref: modes math mode360647
+Ref: modes vertical mode360982
+Ref: modes internal vertical mode361153
+Ref: modes inner paragraph mode361626
+Ref: modes outer paragraph mode361626
+Node: \ensuremath362042
+Node: Page styles362747
+Node: \maketitle363510
+Node: \pagenumbering366520
+Node: \pagestyle368508
+Node: \thispagestyle372010
+Node: Spaces372967
+Node: \enspace & \quad & \qquad374408
+Node: \hspace375322
+Node: \hfill377160
+Node: \hss378224
+Node: \spacefactor378918
+Node: \@382305
+Ref: \AT382405
+Node: \frenchspacing384345
+Node: \normalsfcodes385180
+Node: \(SPACE)385427
+Node: ~387062
+Node: \thinspace & \negthinspace389532
+Node: \/390475
+Node: \hrulefill & \dotfill391781
+Node: \bigskip & \medskip & \smallskip393137
+Ref: bigskip393955
+Ref: medskip394159
+Ref: smallskip394368
+Node: \bigbreak & \medbreak & \smallbreak395029
+Node: \strut396015
+Node: \vspace399209
+Node: \vfill400772
+Node: \addvspace401700
+Node: Boxes403698
+Node: \mbox & \makebox404404
+Ref: mbox makebox depth405619
+Ref: mbox makebox height405619
+Ref: mbox makebox width405619
+Ref: mbox makebox totalheight405619
+Node: \fbox & \framebox407713
+Ref: fbox framebox fboxrule409026
+Ref: fbox framebox fboxsep409216
+Node: \parbox410305
+Node: \raisebox412609
+Ref: raisebox depth413572
+Ref: raisebox height413572
+Ref: raisebox width413572
+Ref: raisebox totalheight413572
+Node: \sbox & \savebox414286
+Node: lrbox417252
+Node: \usebox418074
+Node: Color418480
+Node: Color package options419324
+Node: Color models420970
+Ref: color models cmyk421767
+Ref: color models gray422130
+Ref: color models rgb422279
+Ref: color models RGB422616
+Ref: color models named422991
+Node: Commands for color423279
+Node: Define colors423694
+Node: Colored text424419
+Node: Colored boxes426817
+Node: Colored pages428206
+Node: Graphics428899
+Node: Graphics package options431026
+Node: Graphics package configuration433779
+Node: \graphicspath434581
+Node: \DeclareGraphicsExtensions437472
+Node: \DeclareGraphicsRule439240
+Node: Commands for graphics442426
+Node: \includegraphics442931
+Ref: includegraphics width447981
+Ref: includegraphics height448512
+Ref: includegraphics totalheght448918
+Ref: includegraphics keepaspectratio449182
+Ref: includegraphics viewport450868
+Ref: includegraphics trim451238
+Ref: includegraphics clip451694
+Ref: includegraphics page451954
+Ref: includegraphics pagebox452045
+Ref: includegraphics interpolate452910
+Ref: includegraphics quiet453115
+Ref: includegraphics draft453276
+Ref: includegraphics bb454081
+Ref: includegraphics bbllx454479
+Ref: includegraphics bblly454479
+Ref: includegraphics bburx454479
+Ref: includegraphics bbury454479
+Ref: includegraphics natwidth454621
+Ref: includegraphics natheight454621
+Ref: includegraphics hiresbb454807
+Ref: includegraphics type455569
+Ref: includegraphics ext455609
+Ref: includegraphics read455712
+Ref: includegraphics command455829
+Node: \rotatebox456074
+Node: \scalebox458905
+Node: \resizebox459961
+Node: Special insertions461153
+Node: Reserved characters461955
+Node: Upper and lower case463153
+Node: Symbols by font position465068
+Node: Text symbols465688
+Node: Accents469689
+Node: Additional Latin letters471704
+Ref: Non-English characters471875
+Node: \rule472892
+Node: \today474064
+Node: Splitting the input475000
+Node: \endinput476534
+Node: \include & \includeonly477801
+Node: \input482023
+Node: Front/back matter483238
+Node: Table of contents etc.483571
+Node: \addcontentsline487307
+Node: \addtocontents490149
+Node: \nofiles491740
+Node: Indexes492472
+Node: \index494100
+Node: makeindex499215
+Ref: makeindex preamble500883
+Ref: makeindex postamble501023
+Ref: makeindex group skip501108
+Ref: makeindex letheadflag501428
+Ref: makeindex lethead prefix501892
+Ref: makeindex lethead suffix502044
+Ref: makeindex item 0502192
+Ref: makeindex item 1502272
+Ref: makeindex item 2502347
+Ref: makeindex item 01502425
+Ref: makeindex item x1502530
+Ref: makeindex item 12502735
+Ref: makeindex item x2502843
+Ref: makeindex delim 0503003
+Ref: makeindex delim 1503133
+Ref: makeindex delim 2503263
+Ref: makeindex delim n503389
+Ref: makeindex delim r503524
+Ref: makeindex line max503632
+Ref: makeindex indent space503767
+Ref: makeindex indent length503862
+Ref: makeindex page precedence504047
+Node: \printindex504921
+Node: Glossaries505393
+Node: \newglossaryentry507360
+Node: \gls508829
+Node: Letters509623
+Node: \address513250
+Node: \cc514061
+Node: \closing514503
+Node: \encl514817
+Node: \location515231
+Node: \makelabels515495
+Node: \name517812
+Node: \opening518053
+Node: \ps518334
+Node: \signature518623
+Node: \telephone519851
+Node: Terminal input/output520216
+Node: \typein520481
+Node: \typeout521730
+Node: Command line522774
+Node: Command line options524832
+Node: Command line input528374
+Node: Recovering from errors530238
+Node: Document templates531572
+Node: beamer template532017
+Node: article template532671
+Node: book template533098
+Node: Larger book template533579
+Node: tugboat template535065
+Node: Index537436
+Ref: Command Index537522
 
 End Tag Table

Modified: trunk/latex2e.pdf
===================================================================
(Binary files differ)

Modified: trunk/latex2e.texi
===================================================================
--- trunk/latex2e.texi	2018-07-01 20:07:33 UTC (rev 675)
+++ trunk/latex2e.texi	2018-07-02 15:52:35 UTC (rev 676)
@@ -3828,7 +3828,7 @@
 @end example
 
 @noindent
-or
+or:
 
 @example
 \begin@{array@}[@var{pos}]@{@var{cols}@}
@@ -3839,10 +3839,25 @@
 
 Produce a mathematical array.  This environment can only be used in math
 mode, and normally appears within a displayed mathematics environment
-such as @code{equation} (@pxref{equation}).  Column entries are
-separated by an ampersand at tie{}(@code{&}).  Rows are terminated with
-double-backslashes (@pxref{\\}).  
+such as @code{equation} (@pxref{equation}).  Inside of each row the
+column entries are separated by an ampersand, (@code{&}).  Rows are
+terminated with double-backslashes (@pxref{\\}).
 
+This example shows a three by three array.
+
+ at example
+\begin@{equation*@}
+  \chi(x) =
+  \left|              % vertical bar fence
+    \begin@{array@}@{ccc@}
+      x-a  &-b  &-c  \\
+      -d   &x-e &-f  \\
+      -g   &-h  &x-i
+    \end@{array@}
+ \right|
+\end@{equation*@}
+ at end example
+
 The required argument @var{cols} describes the number of columns, their
 alignment, and the formatting of the intercolumn regions.  For instance,
 @code{\begin@{array@}@{rcl@}...\end@{array@}} gives three columns: the
@@ -3853,14 +3868,15 @@
 
 There are two ways that @code{array} diverges from @code{tabular}.  The
 first is that @code{array} entries are typeset in math mode, in
-textstyle (except if the @var{cols} definition specifies the column with
- at code{p@{...@}}, which causes the entry to be typeset in text mode).
-The second is that, instead of @code{tabular}'s parameter
- at code{\tabcolsep}, @LaTeX{}'s intercolumn space in an @code{array} is governed
-by
+textstyle (@pxref{Modes}) except if the @var{cols} definition specifies
+the column with @code{p@{...@}}, which causes the entry to be typeset in
+text mode.  The second is that, instead of @code{tabular}'s parameter
+ at code{\tabcolsep}, @LaTeX{}'s intercolumn space in an @code{array} is
+governed by
 @findex \arraycolsep
 @code{\arraycolsep}, which gives half the width between columns. The
-default for this is @samp{5pt}.
+default for this is @samp{5pt} so that between two columns comes
+10 at dmn{pt} of space.
 
 @PkgIndex{amsmath}
 To obtain arrays with braces the standard is to use the @file{amsmath}
@@ -3872,30 +3888,28 @@
 @code{Vmatrix} for an array surrounded by double vertical
 bars at tie{}@code{||...||}, along with a number of other array constructs.
 
-Here is an example of an array:
+ at PkgIndex{amsmath}
+The next example uses the @file{amsmath} package.
 
 @example
-\begin@{equation@}
-  \begin@{array@}@{cr@}
-    \sqrt@{y@}  &12.3 \\
-    x^2       &3.4       
-  \end@{array@}
-\end@{equation@}
- at end example
+\usepackage@{amsmath@}  % in preamble
 
-The next example works if @code{\usepackage@{amsmath@}} is in the
-preamble:
-
- at example
-\begin@{equation@}
-  \begin@{vmatrix@}@{cc@}
+\begin@{equation@}    
+  \begin@{vmatrix@}@{cc@}  % array with vert lines
     a  &b \\
     c  &d       
   \end@{vmatrix@}=ad-bc
 \end@{equation@}
 @end example
 
+ at PkgIndex{array (package)}
+ at PkgIndex{dcolumn}
+There are many packages concerning arrays.  The @file{array} package has
+many useful extensions, including more column types.  The @file{dcolumn}
+package adds a column type to center on a decimal point.  For both see
+the documentation on CTAN.
 
+
 @node center
 @section @code{center}
 
@@ -3906,23 +3920,14 @@
 
 @example
 \begin@{center@}
-  ... text ...
-\end@{center@}
- at end example
-
- at noindent
-or
-
- at example
-\begin@{center@}
-  text on first line \\
-  text on second line \\
+  @var{line1} \\
+  @var{line2} \\
   ...
 \end@{center@}
 @end example
 
 Create a new paragraph consisting of a sequence of lines that are
-centered within the left and right margins on the current page.  Use
+centered within the left and right margins.  Use
 double-backslash, @code{\\}, to get a line break (@pxref{\\}).
 @findex \\ @r{(for @code{center})}
 If some text is too long to fit on a line then @LaTeX{} will insert line
@@ -3958,8 +3963,12 @@
 \end@{center@}
 @end example
 
-A double backslash after the final line is optional.
+A double backslash after the final line is optional.  If present it
+doesn't add any vertical space.
 
+In a two-column document the text is centered in a column, not in the
+entire page.
+
 @menu
 * \centering::          Declaration form of the @code{center} environment.
 @end menu
@@ -4032,9 +4041,9 @@
 
 @example
 \begin@{description@}
-\item[@var{label of first item}] @var{text of first item}
-\item[@var{label of second item}] @var{text of second item}
-  ...
+  \item[@var{label of first item}] @var{text of first item}
+  \item[@var{label of second item}] @var{text of second item}
+   ...
 \end@{description@}
 @end example
 
@@ -4045,8 +4054,6 @@
 missing \item}.
 
 This example shows the environment used for a sequence of definitions.
-The labels @samp{lama} and @samp{llama} come out in boldface with their
-left edges aligned on the left margin.
 
 @example
 \begin@{definition@}
@@ -4055,6 +4062,10 @@
 \end@{definition@}
 @end example
 
+ at noindent
+The labels @samp{lama} and @samp{llama} are output in boldface, with the
+left edge on the left margin.
+
 @findex \item
 Start list items with the @code{\item} command (@pxref{\item}).  Use the
 optional labels, as in @code{\item[Main point]}, because there is
@@ -4067,10 +4078,10 @@
 change given in argument style (see @ref{Font styles}) then it will come
 out bold.  For instance, if the label text calls for typewriter with
 @code{\item[\texttt@{label text@}]} then it will appear in bold
-typewriter, if that is available. The simplest way to get non-bold
-typewriter is to use declarative style: @code{\item[@{\tt label
-text@}]}.  Similarly, get the standard roman font with @code{\item[@{\rm
-label text@}]}.
+typewriter, if that is available. The simplest way around this, in this
+example to get non-bold typewriter, is to use declarative style:
+ at code{\item[@{\tt label text@}]}.  Similarly, get the standard roman
+font with @code{\item[@{\rm label text@}]}.
 
 For other major @LaTeX{} labelled list environments, see @ref{itemize}
 and @ref{enumerate}.  Unlike those environments, nesting
@@ -4100,7 +4111,7 @@
 
 @example
 \begin@{displaymath@}
- at var{math text}
+  @var{mathematical text}
 \end@{displaymath@}
 @end example
 
@@ -4214,9 +4225,9 @@
 
 @example
 \begin@{enumerate@}
-\item[@var{optional label of first item}] text of first item
-\item[@var{optional label of second item}] text of second item
-...
+  \item[@var{optional label of first item}] @var{text of first item}
+  \item[@var{optional label of second item}] @var{text of second item}
+  ...
 \end@{enumerate@}
 @end example
 
@@ -4389,18 +4400,19 @@
 
 @example
 \begin@{equation@}
-  math text
+  @var{mathematical text}
 \end@{equation@}
 @end example
 
-Make a @code{displaymath} environment (@pxref{displaymath}) with an
-equation number in the right margin.  The equation number is generated
-using the @code{equation} counter.
+The same as a @code{displaymath} environment (@pxref{displaymath})
+except that @LaTeX{} puts an equation number flush to the right margin.
+The equation number is generated using the @code{equation} counter.
 
 You should have no blank lines between @code{\begin@{equation@}} and
- at code{\begin@{equation@}} or @LaTeX{} will tell you that there is a
+ at code{\begin@{equation@}}, or @LaTeX{} will tell you that there is a
 missing dollar sign.
 
+ at PkgIndex{amsmath}
 The package @file{amsmath} package has extensive displayed equation
 facilities.  New documents should include this package.
 
@@ -4416,31 +4428,32 @@
 
 @example
 \begin@{figure@}[@var{placement}]
-  figure body
+  @var{figure body}
   \caption[@var{loftitle}]@{@var{title}@}  % optional
   \label@{@var{label@}}              % optional
 \end@{figure@}
 @end example
 
 @noindent
-or
+or:
 
 @example
 \begin@{figure*@}[@var{placement}]
-  figure body
+  @var{figure body}
   \caption[@var{loftitle}]@{@var{title}@}  % optional
   \label@{@var{label@}}              % optional  
 \end@{figure*@}
 @end example
 
-The figure body is made up of imported graphics, or text, LaTeX
-commands, etc.  It is typeset in a @code{parbox} of width
- at code{\textwidth}.
+Figures are for material that is not part of the normal text.  An
+example is material that you cannot have split between two pages, such
+as a graphic.  Because of this, @LaTeX{} does not typeset figures in
+sequence with normal text but instead ``floats'' them to a convenient
+place, such as the top of a following page (@pxref{Floats}).
 
-Figures are not part of the normal text.  A long figure will not be
-split between two pages.  Because of this, they are not typeset in
-sequence with the normal text but instead are ``floated'' to a
-convenient place, such as the top of a following page (@pxref{Floats}).
+The @var{figure body} can consist of imported graphics
+(@pxref{Graphics}), or text, @LaTeX{} commands, etc.  It is typeset in a
+ at code{parbox} of width @code{\textwidth}.
 
 The possible values of @var{placement} are @code{h} for @samp{here},
 @code{t} for @samp{top}, @code{b} for @samp{bottom}, and @code{p} for
@@ -4461,12 +4474,13 @@
 used in the list of figures instead of @var{title} (@pxref{Table of
 contents etc.}).
 
-This example makes a figure out of a graphic.  It requires one of the
-packages @file{graphics} or @file{graphicx}.  The graphic, with its
-caption, will be placed at the top of a page or, if it is pushed to the
+This example makes a figure out of a graphic.  @LaTeX{} will place that
+graphic and its caption at the top of a page or, if it is pushed to the
 end of the document, on a page of floats.
 
 @example
+\usepackage@{graphicx@}  % in preamble
+  ...
 \begin@{figure@}[t]
   \centering
   \includegraphics[width=0.5\textwidth]@{CTANlion.png@}
@@ -4561,9 +4575,10 @@
 
 @findex \\ @r{for @code{flushleft}}
 An environment that creates a paragraph whose lines are flush to the
-left-hand margin and ragged right. @LaTeX{} will break long lines to
-avoid hyphenation and stretching or shrinking spaces.  Force a new line
-with a double backslash @code{\\}.  For the declaration form
+left-hand margin, and ragged right. If you have lines that are too long
+then @LaTeX{} will linebreak them in a way that avoids hyphenation and
+stretching or shrinking spaces.  To force a new line use a double
+backslash, @code{\\}.  For the declaration form
 see at tie{}@ref{\raggedright}.
 
 This creates a box of text that is at most 3 inches wide, with the text
@@ -4650,9 +4665,10 @@
 
 @findex \\ (for @code{flushright})
 An environment that creates a paragraph whose lines are flush to the
-right-hand margin and ragged left. @LaTeX{} will break long lines to
-avoid hyphenation and stretching or shrinking spaces.  Force a new line
-with a double backslash @code{\\}.  For the declaration form
+right-hand margin and ragged left. If you have lines that are too long
+to fit the margins then @LaTeX{} will linebreak them in a way that
+avoids hyphenation and stretching or shrinking spaces.  To force a new
+line use a double backslash, @code{\\}.  For the declaration form
 see at tie{}@ref{\raggedleft}.
 
 For an example related to this environment, see at tie{}@ref{flushleft}.
@@ -4707,24 +4723,23 @@
 @cindex lists of items
 @cindex unordered lists
 @cindex bulleted lists
+ at cindex bullet lists
 
 Synopsis:
 
 @example
 \begin@{itemize@}
-\item[@var{optional label of first item}] text of first item
-\item[@var{optional label of second item}] text of second item
-...
+  \item[@var{optional label of first item}] @var{text of first item}
+  \item[@var{optional label of second item}] @var{text of second item}
+  ...
 \end@{itemize@}
 @end example
 
-Produces an ``unordered,'' or ``bulleted,'' list.  The format of the
-labelling depends on the nesting level; see below.  Each @code{itemize}
-list environment must have at least one item; having none causes the
+Produce a list that is unordered, sometimes called a bullet list.  The
+environment must have at least one @code{\item}; having none causes the
 @LaTeX{} error @samp{Something's wrong--perhaps a missing \item}.
 
-This example gives a two-item list.  As a top-level list each label
-would come out as a bullet, @bullet{}.
+This gives a two-item list.
 
 @example
 \begin@{itemize@}
@@ -4733,6 +4748,10 @@
 \end@{itemize@}
 @end example
 
+ at noindent
+As a top-level list each label would come out as a bullet, @bullet{}.
+The format of the labeling depends on the nesting level; see below.
+
 @findex \item
 Start list items with the @code{\item} command (@pxref{\item}).  If you
 give @code{\item} an optional argument by following it with square
@@ -4848,21 +4867,25 @@
 
 @example
 \begin@{list@}@{@var{labeling}@}@{@var{spacing}@}
-\item[@var{optional label of first item}] text of first item
-\item[@var{optional label of second item}] text of second item
-...
+  \item[@var{optional label of first item}] @var{text of first item}
+  \item[@var{optional label of second item}] @var{text of second item}
+  ...
 \end@{list@}
 @end example
 
-A generic environment for constructing more specialized lists.  It is
-most often used to create lists via the @code{description},
- at code{enumerate}, and @code{itemize} environments (@pxref{description},
- at ref{enumerate}, and @ref{itemize}).  Also, many standard @LaTeX{}
-environments that are not visually lists are constructed using
- at code{list}, including @code{quotation}, @code{quote}, @code{center},
- at code{verbatim}, and plenty more (@pxref{quotation & quote},
- at pxref{center}, @pxref{flushright}).
+An environment for constructing lists.
 
+Note that this environment does not typically appear in the document
+body.  Most lists created by @LaTeX{} authors are the ones that come
+standard: the @code{description}, @code{enumerate}, and @code{itemize}
+environments (@pxref{description}, @ref{enumerate}, and @ref{itemize}).
+
+Instead, the @code{list} environment is most often used in macros.  For
+example, many standard @LaTeX{} environments that do not immediately
+appear to be lists are in fact constructed using @code{list}, including
+ at code{quotation}, @code{quote}, and @code{center} (@pxref{quotation &
+quote}, @pxref{center}).
+
 This uses the @code{list} environment to define a new custom
 environment.
 
@@ -4870,9 +4893,9 @@
 \newcounter@{namedlistcounter@}  % number the items
 \newenvironment@{named@}
   @{\begin@{list@}
-     @{Item~\Roman@{namedlistcounter@}.@} % labeling argument
-     @{\usecounter@{namedlistcounter@}   % spacing argument
-      \setlength@{\leftmargin@}@{3.5em@}@} % still spacing arg
+     @{Item~\Roman@{namedlistcounter@}.@} % labeling 
+     @{\usecounter@{namedlistcounter@}   % set counter
+      \setlength@{\leftmargin@}@{3.5em@}@} % set spacing 
   @}
   @{\end@{list@}@}
 
@@ -4893,20 +4916,21 @@
 optional argument by including square braces and the text, as in the
 above @code{\item[Special label.]}; @pxref{\item}.
 
-The mandatory second argument @var{spacing} has a list of commands.  One
-that goes in here is @code{\usecounter@{@var{countername}@}}
-(@pxref{\usecounter}).  Use this to tell @LaTeX{} to number the items
-using the given counter.  The counter will be reset to zero each time
- at LaTeX{} enters the environment, and the counter is incremented by one
-each time @LaTeX{} encounters an @code{\item}.
+The mandatory second argument @var{spacing} has a list of commands.
+This list can be empty.  A command that can go in here is
+ at code{\usecounter@{@var{countername}@}} (@pxref{\usecounter}).  Use this
+to tell @LaTeX{} to number the items using the given counter.  The
+counter will be reset to zero each time @LaTeX{} enters the environment,
+and the counter is incremented by one each time @LaTeX{} encounters an
+ at code{\item} that does not have an optional argument.
 
 @findex \makelabel
- at anchor{list makelabel}
-Another command that can go in @var{spacing} is @code{\makelabel}, which
-constructs the label box.  By default it puts the contents flush
-right.  Its only argument is the label, which it typesets in
-LR mode. One example of changing its definition is that to the above
- at code{named} example before the definition of the environment add
+ at anchor{list makelabel} Another command that can go in @var{spacing} is
+ at code{\makelabel}, which constructs the label box.  By default it puts
+the contents flush right.  Its only argument is the label, which it
+typesets in LR mode (@pxref{Modes}). One example of changing its
+definition is that to the above @code{named} example, before the
+definition of the environment add
 @code{\newcommand@{\namedmakelabel@}[1]@{\textsc@{#1@}@}}, and between
 the @code{\setlength} command and the parenthesis that closes the
 @var{spacing} argument also add @code{\let\makelabel\namedmakelabel}.
@@ -5297,24 +5321,22 @@
 is similar to @code{\parbox} (@pxref{\parbox}) but here you can have
 paragraphs.
 
-This puts the footnote at the bottom of the table, not the bottom of the
-page.
+This example will be 3 at tie{}inches wide, and has two paragraphs.
 
 @example
-\begin@{center@}           % center the minipage on the line
-\begin@{minipage@}@{2.5in@}
-  \begin@{center@}         % center the table inside the minipage
-    \begin@{tabular@}@{ll@}
-      \textsc@{Monarch@}  &\textsc@{Reign@}             \\ \hline
-      Elizabeth II      &63 years\footnote@{to date@} \\
-      Victoria          &63 years                   \\
-      George III        &59 years
-    \end@{tabular@}
-  \end@{center@}  
+\begin@{minipage@}@{3in@}
+  Stephen Kleene was a founder of the Theory of Computation.
+
+  He was a student of Church, wrote three influential texts,
+  was President of the Association for Symbolic Logic,
+  and won the National Medal of Science.
 \end@{minipage@}
-\end@{center@}
 @end example
 
+ at noindent
+See below for a discussion of the paragraph indent inside a
+ at code{minipage}.
+
 The required argument @var{width} is a rigid length (@pxref{Lengths}).
 It gives the width of the box into which @var{contents} are typeset.
 
@@ -5410,6 +5432,24 @@
 uses the @code{\mpfootnote} counter instead of the ordinary
 @code{footnote} counter (@pxref{Counters}).
 
+This puts the footnote at the bottom of the table, not the bottom of the
+page.
+
+ at example
+\begin@{center@}           % center the minipage on the line
+\begin@{minipage@}@{2.5in@}
+  \begin@{center@}         % center the table inside the minipage
+    \begin@{tabular@}@{ll@}
+      \textsc@{Monarch@}  &\textsc@{Reign@}             \\ \hline
+      Elizabeth II      &63 years\footnote@{to date@} \\
+      Victoria          &63 years                   \\
+      George III        &59 years
+    \end@{tabular@}
+  \end@{center@}  
+\end@{minipage@}
+\end@{center@}
+ at end example
+
 If you nest minipages then there is an oddness when using footnotes.
 Footnotes appear at the bottom of the text ended by the next
 @code{\end@{minipage@}} which may not be their logical place.
@@ -5763,8 +5803,9 @@
 @end example
 
 Draw a line.  It slopes such that it vertically rises @var{y_rise} for
-every horizontal @var{x_run}, and such that the total horizontal change
-is @var{travel}.  In the special case of vertical lines, where
+every horizontal @var{x_run}.  The @var{travel} is the total horizontal
+change at tie{}--- it is not the length of the vector, it is the change in
+ at math{x}.  In the special case of vertical lines, where
 (@var{x_run}, at var{y_rise})=(0,1), the @var{travel} gives the change in
 @math{y}.
 
@@ -5989,20 +6030,21 @@
 \vector(@var{x_run}, at var{y_rise})@{@var{travel}@}
 @end example
 
-Draw a line ending in an arrow.  It slopes such that it vertically rises
- at var{y_rise} for every horizontal @var{x_run}, and such that the total
-horizontal change is @var{travel}.  In the special case of vertical
-vectors, if (@var{x_run}, at var{y_rise})=(0,1), then @var{travel} gives
-the change in @math{y}.
+Draw a line ending in an arrow.  The slope of that line is: it
+vertically rises @var{y_rise} for every horizontal @var{x_run}.  The
+ at var{travel} is the total horizontal change at tie{}--- it is not the
+length of the vector, it is the change in @math{x}.  In the special case
+of vertical vectors, if (@var{x_run}, at var{y_rise})=(0,1), then
+ at var{travel} gives the change in @math{y}.
 
 For an example see @ref{picture}.
 
 For elaboration on @var{x_run} and @var{y_rise} see @ref{\line}.  As
-there, the values of @var{x_run} and @var{y_rise} are limited.  You must
-chooses integers between @minus{}4 and 4, inclusive.  Also, the two you
-choose must be relatively prime.  Thus, @code{\vector(2,1)@{4@}} is
-acceptable but @code{\vector(4,2)@{4@}} is not (if you use the latter
-then you get a sequence of arrowheads).
+there, the values of @var{x_run} and @var{y_rise} are limited.  For
+ at code{\vector} you must chooses integers between @minus{}4 and 4,
+inclusive.  Also, the two you choose must be relatively prime.  Thus,
+ at code{\vector(2,1)@{4@}} is acceptable but @code{\vector(4,2)@{4@}} is
+not (if you use the latter then you get a sequence of arrowheads).
 
 
 @node \makebox (picture)
@@ -6786,24 +6828,24 @@
 bar at tie{}@code{|} is more common.  This command is rarely used in the
 body of a table; typically a table's vertical lines are specified in
 @code{tabular}'s @var{cols} argument and overridden as needed with
- at code{\multicolumn}.
+ at code{\multicolumn} (@pxref{tabular}).
 
-This example illustrates some pitfalls.  In the first line's second
+The example below illustrates some pitfalls.  In the first row's second
 entry the @code{\hfill} moves the @code{\vline} to the left edge of the
 cell.  But that is different than putting it halfway between the two
-columns, so in that row between the first and second columns there are
-two vertical rules, with the one from the @code{@{c|cc@}} specifier
-coming before the one produced by the @code{\vline\hfill}.  In contrast,
-the first line's third entry shows the usual way to put a vertical bar
-between two columns.  In the second line, the @code{ghi} is the widest
-entry in its column so in the @code{\vline\hfill} the @code{\hfill} has
-no effect and the vertical line in that entry appears immediately next
-to the @code{g}, with no whitespace.
+columns, so between the first and second columns there are two vertical
+rules, with the one from the @code{@{c|cc@}} specifier coming before the
+one produced by the @code{\vline\hfill}.  In contrast, the first row's
+third entry shows the usual way to put a vertical bar between two
+columns.  In the second row, the @code{ghi} is the widest entry in its
+column so in the @code{\vline\hfill} the @code{\hfill} has no effect and
+the vertical line in that entry appears immediately next to the
+ at code{g}, with no whitespace.
 
 @example
 \begin@{tabular@}@{c|cc@}
-  x   &\vline\hfill y   &\multicolumn@{1@}@{|r@}@{z@} \\  
-  abc &def &\vline\hfill ghi 
+  x   &\vline\hfill y   &\multicolumn@{1@}@{|r@}@{z@} \\ % row 1  
+  abc &def &\vline\hfill ghi                       % row 2  
 \end@{tabular@}
 @end example
 
@@ -7321,20 +7363,7 @@
 
 Typeset @var{literal-text} as it is input, including special characters
 and spaces, using the typewriter (@code{\tt}) font.
- at cindex visible space
-The @code{*}-form differs only in that spaces are printed with a visible
-space character.
- at tex
-(Namely, {\tt\char`\ }.)
- at end tex
 
-The single-character delimiter @var{char} surrounds @var{literal-text};
-it is the same character before and after.  No spaces come between
- at code{\verb} or @code{\verb*} and @var{char}, or between @var{char} and
- at var{literal-text}, or between @var{literal-text} and the second
-occurrence of @var{char}.  The delimiter must not appear in
- at var{literal-text}. The @var{literal-text} cannot include a line break.
-
 This example shows two different invocations of @code{\verb}.
 
 @example
@@ -7347,11 +7376,38 @@
 exclamation point, @code{!}.  The second instead uses plus, @code{+},
 because the exclamation point is part of @code{literal-text}.
 
+The single-character delimiter @var{char} surrounds
+ at var{literal-text}@tie{}--- it must be the same character before and
+after.  No spaces come between @code{\verb} or @code{\verb*} and
+ at var{char}, or between @var{char} and @var{literal-text}, or between
+ at var{literal-text} and the second occurrence of @var{char} (the synopsis
+shows a space only to distinguish one component from the other).  The
+delimiter must not appear in @var{literal-text}. The @var{literal-text}
+cannot include a line break.
+
+ at cindex visible space
+The @code{*}-form differs only in that spaces are printed with a visible
+space character.
+ at tex
+(Namely, {\tt\char`\ }.)
+ at end tex
+
+The output from this will include a character showing the spaces.
+
+ at example
+The commands's first argument is \verb*!filename with extension! and ...
+ at end example
+
 @PkgIndex{url}
 For typesetting Internet addresses, urls, the package @code{url}
 provides an option that is better than the @code{\verb} command, since
 it allows line breaks.
 
+ at PkgIndex{listings}
+ at PkgIndex{minted}
+For computer code there are many packages with advantages over
+ at code{\verb}.  One is @file{listings}, another is @file{minted}.
+
 @PkgIndex{cprotect}
 You cannot use @code{\verb} in the argument to a macro, for instance in
 the argument to a @code{\section}.  It is not a question of @code{\verb}
@@ -9377,11 +9433,11 @@
 @end example
 
 Used in the second argument of the @code{list} environment
-(@pxref{list}).  It sets up @var{counter} to number the list items.  It
-initializes @var{counter} to zero, and arranges that when @code{\item}
-is called without its optional argument then @var{counter} is
-incremented by @code{\refstepcounter}, making its value be the current
- at code{ref} value (@pxref{\ref}).  This command is fragile
+(@pxref{list}), this declares that list items will be numbered by
+ at var{counter}.  It initializes @var{counter} to zero, and arranges that
+when @code{\item} is called without its optional argument then
+ at var{counter} is incremented by @code{\refstepcounter}, making its value
+be the current @code{ref} value (@pxref{\ref}).  This command is fragile
 (@pxref{\protect}).
 
 Put in the document preamble, this example makes a new list environment
@@ -9411,14 +9467,9 @@
 \value@{@var{counter}@}
 @end example
 
-Expands to the value of @var{counter}.  It is often used in
- at code{\setcounter} or @code{\addtocounter} but @code{\value} can be used
-anywhere that @LaTeX{} expects a number.  It must not be preceded by
- at code{\protect} (@pxref{\protect}).
+Expands to the value of the counter @var{counter}. (Note that the name
+of a counter does not begin with a backslash.)
 
-The @code{\value} command is not used for typesetting the value of the
-counter.  @xref{\alph \Alph \arabic \roman \Roman \fnsymbol}.
-
 This example outputs @samp{Test counter is at tie{}6. Other counter
 is at tie{}5.}.
 
@@ -9431,6 +9482,14 @@
 Other counter is \arabic@{other@}.
 @end example
 
+The @code{\value} command is not used for typesetting the value of the
+counter.  For that, see @ref{\alph \Alph \arabic \roman \Roman \fnsymbol}.
+
+It is often used in @code{\setcounter} or @code{\addtocounter} but
+ at code{\value} can be used anywhere that @LaTeX{} expects a number, such
+as in @code{\hspace@{\value@{foo@}\parindent@}}.  It must not be
+preceded by @code{\protect} (@pxref{\protect}).
+
 This example inserts @code{\hspace@{4\parindent@}}.
 
 @example
@@ -10203,9 +10262,10 @@
 @cindex remarks in the margin
 @findex \marginpar
 
-Synopsis:
+Synopsis, one of:
 
 @example
+\marginpar@{@var{right}@}
 \marginpar[@var{left}]@{@var{right}@}
 @end example
 
@@ -10213,34 +10273,28 @@
 same baseline as the line in the text where the @code{\marginpar}
 occurs.
 
-When you only specify the mandatory argument @var{right}, the text
-will be placed
+The margin that @LaTeX{} uses for the note depends on the current layout
+(@pxref{Document class options}) and also on @code{\reversemarginpar}
+(see below).  If you are using one-sided layout (document option
+ at code{oneside}) then it goes in the right margin.  If you are using
+two-sided layout (document option @code{twoside}) then it goes in the
+outside margin.  If you are in two-column layout (document option
+ at code{twocolumn}) then it goes in the nearest margin.
 
- at itemize @bullet
- at item
-in the right margin for one-sided layout (option @code{oneside}, see
- at ref{Document class options});
-
- at item
-in the outside margin for two-sided layout (option @code{twoside}, see
- at ref{Document class options});
-
- at item
-in the nearest margin for two-column layout (option @code{twocolumn},
-see @ref{Document class options}).
- at end itemize
-
 @findex \reversemarginpar
 @findex \normalmarginpar
-The command @code{\reversemarginpar} places subsequent marginal notes
-in the opposite (inside) margin.  @code{\normalmarginpar} places them
-in the default position.
+If you declare @code{\reversemarginpar} then @LaTeX{} will place
+subsequent marginal notes in the opposite margin to that given in the
+prior paragraph.  Revert that to the default position with
+ at code{\normalmarginpar}.
 
-When you specify both arguments, @var{left} is used for the left
-margin, and @var{right} is used for the right margin.
+When you specify the optional argument @var{left} then it is used for a
+note in the left margin, while the mandatory argument @var{right} is
+used for a note in the the right margin.
 
-The first word will normally not be hyphenated; you can enable
-hyphenation there by beginning the node with @code{\hspace@{0pt@}}.
+Normally, a note's first word will not be hyphenated.  You can enable
+hyphenation there by beginning @var{left} or @var{right} with
+ at code{\hspace@{0pt@}}.
 
 These parameters affect the formatting of the note:
 
@@ -10292,35 +10346,27 @@
 where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.
 @end example
 
-Math mode is for inline mathematics.  It is invoked by the starting
- at code{\(} and finished by the matching ending @code{\)}.  Display math
-mode is for displayed equations and here is invoked by the
+ at noindent
+Math mode is for inline mathematics.  In the above example it is invoked
+by the starting @code{\(} and finished by the matching ending @code{\)}.
+Display math mode is for displayed equations and here is invoked by the
 @code{displaymath} environment.  Note that any mathematical text
-whatever, including that consisting of single characters, is handled in
-math mode.
+whatever, including mathematical text consisting of just one character,
+is handled in math mode.
 
- at PkgIndex{amsmath} @PkgIndex{amsfonts} @PkgIndex{mathtools}
-The American Mathematical Society has made freely available a set of
-packages that greatly expand your options for writing mathematics,
- at file{amsmath} and @file{amssymb} (also be aware of the
- at file{mathtools} package that is an extension to, and loads,
- at file{amsmath}).  New documents that will have mathematical text should
-use these packages.  Descriptions of these packages is outside the scope
-of this document; see their documentation on CTAN.
-
 When in math mode or display math mode, @LaTeX{} handles many aspects of
 your input text differently than in other text modes.  For example,
 
 @example
-contrast x+y with \( x+y \).
+contrast x+y with \( x+y \)
 @end example
 
 @noindent
 in math mode the letters are in italics and the spacing around the plus
 sign is different.
 
-To make inline formulas, put @LaTeX{} in math mode with one of these
-three.
+There are three ways to make inline formulas, to put @LaTeX{} in math
+mode.
 
 @example
 \( @var{mathematical material} \)
@@ -10329,9 +10375,10 @@
 @end example
 
 @noindent
-The first form is preferred, and the third form is very rarely used.
-You can mix them, sometimes using one and sometimes another.  These can
-be used in paragraph mode or in LR mode (@pxref{Modes}).
+The first form is preferred and the second is quite common, but the
+third form is rarely used.  You can sometimes use one and sometimes
+another, as in @code{\(x\) and $y$}.  You can use these in paragraph
+mode or in LR mode (@pxref{Modes}).
 
 To make displayed formulas, put @LaTeX{} into display math mode with
 either:
@@ -10352,10 +10399,10 @@
 @end example
 
 @noindent
-The only difference is that with the @code{equation} environment,
- at LaTeX{} puts a formula number alongside the formula, which by default
-has the form @samp{(@var{arabic number})}.  The construct @code{\[
- at var{math} \]} is equivalent to @code{\begin@{displaymath@} @var{math}
+(@pxref{displaymath}, @pxref{equation}).  The only difference is that
+with the @code{equation} environment, @LaTeX{} puts a formula number
+alongside the formula.  The construct @code{\[ @var{math} \]} is
+equivalent to @code{\begin@{displaymath@} @var{math}
 \end@{displaymath@}}.  These environments can only be used in paragraph
 mode (@pxref{Modes}).
 
@@ -10365,12 +10412,12 @@
 math mode they are further apart and in inline math mode they are closer
 together.
 
-Sometimes you want the display math treatment to happen in the inline
-math mode.  For this, the @code{\displaystyle} declaration forces the
-size and style of the formula to be that of @code{displaymath}.  Thus
- at code{\(\displaystyle \sum_@{n=0@}^\infty x_n\)} will have the limits
-above and below the summation sign, not next to it.  Another example is
-that
+Sometimes you want the display math typographical treatment to happen in
+the inline math mode.  For this, the @code{\displaystyle} declaration
+forces the size and style of the formula to be that of
+ at code{displaymath}.  Thus @code{\(\displaystyle \sum_@{n=0@}^\infty
+x_n\)} will have the limits above and below the summation sign, not next
+to it.  Another example is that
 
 @example
 \begin@{tabular@}@{r|cc@}
@@ -10388,6 +10435,17 @@
 the @samp{Geometric} line's fraction will be easy to read, with
 characters the same size as in the rest of the line.
 
+ at PkgIndex{amsmath}
+ at PkgIndex{amsfonts}
+ at PkgIndex{mathtools}
+The American Mathematical Society has made freely available a set of
+packages that greatly expand your options for writing mathematics,
+ at file{amsmath} and @file{amssymb} (also be aware of the @file{mathtools}
+package that is an extension to, and loads, @file{amsmath}).  New
+documents that will have mathematical text should use these packages.
+Descriptions of these packages is outside the scope of this document;
+see their documentation on CTAN.
+
 @menu
 * Subscripts & superscripts::   Also known as exponent or index.
 * Math symbols::                Various mathematical squiggles.
@@ -11408,7 +11466,7 @@
 * Blackboard bold::            Doublestruck characters.
 * Calligraphic::               Cursive characters.
 * \boldmath & \unboldmath::    Symbols in boldface.
-* Ellipses::                   Dots.
+* Dots::                       Ellipses, etc.
 @end menu
 
 
@@ -11537,8 +11595,8 @@
 shows that it is an improvement over @code{\boldmath}.
 
 
- at node Ellipses
- at subsection Ellipses
+ at node Dots
+ at subsection Dots, horizontal or vertical
 
 @cindex ellipses
 @cindex dots
@@ -11565,22 +11623,23 @@
 
 @anchor{ellipses ddots}
 @item \ddots
-Diagonal ellipsis, @BES{22F1,\ddots}.  See the above example for a
+Diagonal ellipsis, @BES{22F1,\ddots}.  See the above array example for a
 usage.
 
 @anchor{ellipses ldots}
 @item \ldots
 Ellipsis on the baseline, @BES{2026,\ldots}.  Used as: @code{\(
-x_0,\ldots x_@{n-1@} \)}.  A synonym is @code{\mathellipsis}.  A synonym
-from the @file{amsmath} package is @code{\hdots}.
+x_0,\ldots x_@{n-1@} \)}.  Another example is the above array example. A
+synonym is @code{\mathellipsis}.  A synonym from the @file{amsmath}
+package is @code{\hdots}.
 
 You can also use this command outside of mathematical text, as in
- at code{The gears, brakes, \ldots@{@} are all broken}.  (In a text mode a
-synonym for @code{\ldots} is @code{\dots}.)
+ at code{The gears, brakes, \ldots@{@} are all broken}.  (In a paragraph
+mode or LR mode a synonym for @code{\ldots} is @code{\dots}.)
 
 @anchor{ellipses vdots}
 @item \vdots
-Vertical ellipsis, @BES{22EE,\vdots}.  See the above example for a
+Vertical ellipsis, @BES{22EE,\vdots}.  See the above array example for a
 usage.
 
 @end ftable
@@ -12315,9 +12374,9 @@
 in one mode or another (in particular, many commands only work in one of
 the math modes), and error messages will refer to these.
 
- at itemize @bullet
+ at itemize
+ at item
 @anchor{modes paragraph mode}
- at item
 @cindex paragraph mode
 @dfn{Paragraph mode} is what @LaTeX{} is in when processing ordinary
 text.  It breaks the input text into lines and breaks the lines into
@@ -12331,18 +12390,18 @@
 making a box with an @code{\mbox} command.  As in paragraph mode,
 @LaTeX{}'s output is a string of words with spaces between them.  Unlike
 in paragraph mode, in LR mode @LaTeX{} never starts a new line, it just
-keeps going from left to right.  (When it tries to put that box into a
-line, most likely @LaTeX{} will complain because the box is too wide to
-fit.)
+keeps going from left to right.  (Although @LaTeX{} will not complain
+that the LR box is too long, when it is finished and next tries to put
+that box into a line, it could very well complain that the finished LR
+box won't fit there.)
 
 @item
 @cindex math mode
- at anchor{modes math mode}
- at dfn{Math mode} happens when @LaTeX{} is generating an inline
-mathematical formula.
+ at anchor{modes math mode} @dfn{Math mode} is when @LaTeX{} is generating
+an inline mathematical formula.
 
 @cindex display math mode
- at dfn{Display math mode} happens when @LaTeX{} is generating a displayed
+ at dfn{Display math mode} is when @LaTeX{} is generating a displayed
 mathematical formula.  (Displayed formulas differ somewhat from inline
 ones.  One example is that the placement of the subscript on @code{\int}
 differs in the two situations.)
@@ -12361,23 +12420,24 @@
 
 @end itemize
 
- at noindent For instance, if you begin a @LaTeX{} article with
- at samp{Let \( x \) be ...} then these are the modes.  First, @LaTeX{}
-starts every document in vertical mode.  It reads the @samp{L} and
-switches to paragraph mode.  The next switch happens at the @samp{\(},
-where @LaTeX{} changes to math mode.  Then, when it leaves the formula,
-it resets itself to paragraph mode.
+ at noindent
+For instance, if you begin a @LaTeX{} article with @samp{Let \( x \) be
+...} then these are the modes: first @LaTeX{} starts every document in
+vertical mode, then it reads the @samp{L} and switches to paragraph
+mode, then the next switch happens at the @samp{\(} where @LaTeX{}
+changes to math mode, and then when it leaves the formula it pops
+back to paragraph mode.
 
 @cindex inner paragraph mode
 @cindex outer paragraph mode
 @anchor{modes inner paragraph mode}
 @anchor{modes outer paragraph mode}
 Paragraph mode has two subcases.  If you use a @code{\parbox} command or
- at code{minipage} environment then @LaTeX{} is put into paragraph mode; it
-is dividing string of words into lines.  But it will not put a page
-break here.  Inside one of these boxes, called a @dfn{parbox}, @LaTeX{}
-is in @dfn{inner paragraph mode}.  Its more usual situation, where it
-can put page breaks, is @dfn{outer paragraph mode} (@pxref{Page breaking}).
+or a @code{minipage} then @LaTeX{} is put into paragraph mode.  But it
+will not put a page break here.  Inside one of these boxes, called a
+ at dfn{parbox}, @LaTeX{} is in @dfn{inner paragraph mode}.  Its more usual
+situation, where it can put page breaks, is @dfn{outer paragraph mode}
+(@pxref{Page breaking}).
 
 @menu
 * \ensuremath:: Ensure that math mode is active
@@ -13661,8 +13721,8 @@
 between the questions.
 
 If you use @code{\vspace} in the middle of a paragraph (i.e., in
-horizontal mode) then the space is inserted after the line with the
- at code{\vspace} command; it does not start a new paragraph at the
+horizontal mode) then the space is inserted after the line containing
+the @code{\vspace} command; it does not start a new paragraph at the
 @code{\vspace} command.
 
 In this example the two questions will be evenly spaced vertically on
@@ -13701,17 +13761,18 @@
 @code{\vfill} ends the current paragraph whereas @code{\vspace@{\fill@}}
 adds the infinite vertical space below its line, irrespective of the
 paragraph structure.  In both cases that space will disappear at a page
-boundary; to circumvent this see at tie{}@ref{\vspace}.
+boundary; to circumvent this see the starred option
+in at tie{}@ref{\vspace}.
 
 In this example the page is filled, so the top and bottom lines contain
-the text @samp{Lost Dog!} and the third @samp{Lost Dog!} is exactly
+the text @samp{Lost Dog!} and the second @samp{Lost Dog!} is exactly
 halfway between them.
  
 @example
 \begin@{document@}
 Lost Dog!
 \vfill
-Lost Dog!
+Lost Dog!  % perfectly in the middle
 \vfill
 Lost Dog!
 \end@{document@}
@@ -14286,10 +14347,11 @@
 \usebox@{@var{box-cmd}@}
 @end example
 
-Produce the box most recently saved in the bin @var{box-cmd} by
- at code{\sbox}, or @code{\savebox}, or @code{lrbox}. @xref{\sbox &
-\savebox} for more information and examples.  This command is robust
-(@pxref{\protect}).
+Produce the box most recently saved in the bin @var{box-cmd} by the
+commands @code{\sbox} or @code{\savebox}, or the @code{lrbox}
+environment. @xref{\sbox & \savebox} for more information and examples.
+(Note that @var{box-cmd} starts with a backslash.)  This command is
+robust (@pxref{\protect}).
 
 
 @node Color
@@ -17674,7 +17736,7 @@
   @var{letter body}
 \closing@{@var{closing text}@}
 \end@{letter@}
-...  more letters ...
+   ...
 \end@{document@}
 @end example
 
@@ -17686,7 +17748,7 @@
 
 @example
  \begin@{letter@}@{Ninon de l'Enclos \\
-   l'h\^otel Sagonne@}
+                l'h\^otel Sagonne@}
    ...
  \end@{letter@}
 @end example
@@ -17700,7 +17762,7 @@
 contains multiple lines separated by a double
 backslash at tie{}(@code{\\}).  @LaTeX{} will put the @var{sender name}
 under the closing, after a vertical space for the traditional
-hand-written signature; it also can contain multiple lines.
+hand-written signature.
 
 Each @code{letter} environment body begins with a required
 @code{\opening} command such as @code{\opening@{Dear Madam or Sir:@}}.
@@ -17716,13 +17778,13 @@
 Boss \\ the Boss's Boss@}}.  There's a similar @code{\encl} command for
 a list of enclosures.  And, you can add a postscript with @code{\ps}.
 
- at LaTeX{}'s default is to indent the signature and the @code{\closing}
-above it by a length of @code{\longindentation}.  By default this is
+ at LaTeX{}'s default is to indent the sender name and the closing above it
+by a length of @code{\longindentation}.  By default this is
 @code{0.5\textwidth}. To make them flush left, put
 @code{\setlength@{\longindentation@}@{0em@}} in your preamble.
 
 To set a fixed date use something like
- at code{\renewcommand@{\today@}@{2015-Oct-12@}}.  If put in your preamble
+ at code{\renewcommand@{\today@}@{1958-Oct-12@}}.  If put in your preamble
 then it will apply to all the letters.
 
 This example shows only one @code{letter} environment.  The three lines



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