euclideangeometry (15feb20)

git-svn-id: svn://tug.org/texlive/trunk@53794 c570f23f-e606-0410-a88d-b1316a301751

4 files changed, 210 insertions, 190 deletions

diff --git a/Master/texmf-dist/doc/latex/euclideangeometry/README.txt b/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
index 300e9c9f936..6402a6e9ff3 100644
--- a/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
+++ b/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
@@ -10,7 +10,7 @@
 %%   License information appended
 %% 
 File README.txt for package euclideangeometry
-        [2020-02-11 v.0.1.4 Extension package for curve2e]
+        [2020-02-12 v.0.1.5 Extension package for curve2e]
 
 The package bundle euclideangeometry is composed of the following files
 
diff --git a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf
index 593310a47f5..d36d79326ed 100644
--- a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf
+++ b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf
diff --git a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex
index 01ee2978b3f..4c09bb60256 100644
--- a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex
+++ b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex
@@ -1,7 +1,7 @@
 % !TEX encoding = UTF-8 Unicode
 % !TEX TS-program = pdflatex
 
-\documentclass[11pt,titlepage]{article}\errorcontextlines=100
+\documentclass[11pt,titlepage,a4paper]{article}\errorcontextlines=100
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
 \usepackage[english]{babel}
@@ -101,9 +101,30 @@ g\raisebox{-0.715ex}{\kern-0.26em u}\kern-0.13em\I\kern-0.14em t}\xspace}
 \newwrite\example@out
 \newlength\Wboxu \newlength\Wboxd
 
-\DeclareDocumentEnvironment{Esempio}{ O{\normalsize} D(){0.40}}
+% Attention!
+%
+% This is the latest version of the Esempio/Example environment
+% It differs from the previous versions because it accepts an optional
+% first argument asterisk; if the asterisk is not specified, the
+% environment produces the code and the typeset result side by side.
+% If the asterisk is specified, the code is typeset first, and its typeset
+% result is shown below the code.
+% Very handy when the typeset result cannot be shrunk too much and/or
+% when the code is really lengthy possibly with lines that are quite long.
+% With reasonably short codes and lines that can be folded, the code font
+% size can be specified even with a fractional size; obviously, the
+% default value is \normalsize, but, if necessary, it can be specified with
+% something such as [\setfontsize{8,25}] (if the unit of measure is not
+% specified, pt is assumed; otherwise it is possible to specify something
+% such as 2.33mm).
+% When the asterisk is NOT specified, the \textwidth fraction for the
+% code may be specified: default is (0.40); the remaining fraction minus
+% \columnsep is used for the code typeset result.
+%
+\newwrite\example@out
+\DeclareDocumentEnvironment{Esempio}{s O{\normalsize} D(){0.40}}
 {\par\addvspace{3.0ex plus 0.8ex minus 0.5ex}\vskip -\parskip
-\Wboxu=#2\textwidth\relax
+\Wboxu=#3\textwidth\relax
 \Wboxd=\dimexpr\linewidth-\columnsep-\Wboxu\relax
 \begingroup
 \@bsphack
@@ -113,23 +134,19 @@ g\raisebox{-0.715ex}{\kern-0.26em u}\kern-0.13em\I\kern-0.14em t}\xspace}
   \immediate\write\example@out{\the\verbatim@line}}%
 \verbatim@start\relax}%
 {\immediate\closeout\example@out\@esphack\endgroup
-\begin{lrbox}{0}%
 \begin{minipage}{\textwidth}%
-\begin{minipage}{\Wboxu}%
-#1\relax
+\IfBooleanTF{#1}{\begin{minipage}{\textwidth}}{\begin{minipage}{\Wboxu}}%
+#2\relax
 \verbatiminput{\jobname-temp.tex}
 \end{minipage}%
-\hfill
-\begin{minipage}{\Wboxd}\raggedleft
-\input{\jobname-temp}%
+\IfBooleanTF{#1}{\par\bigskip}{\hfill}%
+\IfBooleanTF{#1}{\begin{minipage}{\textwidth}}{\begin{minipage}{\Wboxd}}%
+\raggedleft
+\input{\jobname-temp}
 \end{minipage}
-\end{minipage}%
-\end{lrbox}%
-
-\medskip
-\noindent\makebox[\textwidth]{\box0}%
-\par\addvspace{3.0ex plus 0.8ex minus 0.5ex}\vskip -\parskip
+\end{minipage}\par
 }
+
 \makeatother
 
 \newenvironment{ttsintassi}{\begin{lrbox}{0}
@@ -173,22 +190,21 @@ Version \fileversion\ of \filedate
  kernel source file.
 
  The \pack{curve2e} package was upgraded a the beginning of 2020; the 
- material
- of this new package, might have been included in the former one, but is
- is sospecific, that we preferred defining a standalone one; this package 
- takes care of requesting the packages it depends from.
+ material of this new package, might have been included in the former one, 
+ but it is so specific, that we preferred defining a standalone one; this 
+ package takes care of requesting the packages it depends from.
 
  The purpose is to provide the tools to draw most of the geometrical
  constructions that a high school instructor or bachelor degree professor
- might need to teach geometry. The connection to Euclide depends on the
- fact that in its times calculations were made with ruler, compass, and,
- apparently, also with ellipsograph,
+ might need in order to teach geometry. The connection to Euclide depends 
+ on the fact that in its times calculations were made with ruler, compass, 
+ and, apparently, also with ellipsograph.
 
  The user of this package has available all the machinery provided by
- the \pack{pict2e} and \pack{curve2e} packages, in order to define new functionalities
- and build macros that draw the necessary lines, circles, and other such
- objects, as they would have done in the ancient times. Actually just one 
- macro is programmed to solve a linear system of equations
+ the \pack{pict2e} and \pack{curve2e} packages, in order to define new 
+ functionalities and build macros that draw the necessary lines, circles, 
+ and other such objects, as they would have done in the ancient times. 
+ Actually just one macro is programmed to solve a linear system of equations
  \end{abstract}
  
  \tableofcontents
@@ -207,36 +223,36 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  that allowed to draw very simple line graphics with many limitations.
  When \LaTeX was upgraded from \LaTeX\!2.09 to \LaTeXe in 1994, Leslie
  Lamport announced an upgrade that eventually became available in 2003
- with package \pack{pict2e}; in 2006 I wrote the \pack{curve2e} package that added
- many more functionalities; both packages were upgraded during these
- years; and now line graphics with the \env{picture} environment can perform
- pretty well. The package \pack{euclideangeometry} adds even more specific
- functionalities in order to produce geometric drawings as they were
- possible in the old times, when calculus and analytic geometry were
- not available.
+ with package \pack{pict2e}; in 2006 I wrote the \pack{curve2e} package 
+ that added many more functionalities; both packages were upgraded during 
+ these years; and now line graphics with the \env{picture} environment 
+ can perform pretty well. The package \pack{euclideangeometry} adds even 
+ more specific functionalities in order to produce geometric drawings as 
+ they were possible in the old times, when calculus and analytic geometry 
+ were not available.
  
  In these years other drawing programs were made available to the \TeX 
- community; \pack{PSTricks} and \pack{TikZ} are the most known ones, but there are 
- other less known packages, that perform very well; among the latter 
- I would like to mention \pack{xpicture}, that relies on \pack{pict2e} and 
- \pack{curve2e}, but extends the functionalities with a very smart handling 
- of coordinate systems, that allow to draw many line drawings suitable 
- for teaching geometry in high schools and introductory courses in the 
- university bachelor degree programs.
+ community; \pack{PSTricks} and \pack{TikZ} are the most known ones, but 
+ there are other less known packages, that perform very well; among the 
+ latter I would like to mention \pack{xpicture}, that relies on 
+ \pack{pict2e} and \pack{curve2e}, but extends the functionalities with a 
+ very smart handling of coordinate systems, that allow to draw many line 
+ drawings suitable for teaching geometry in high schools and introductory 
+ courses in the university bachelor degree programs.
  
- This package \pack{euclideangeomery} in a certain way follows the same
- path of \pack{xpicture} but it avoids defining a new user language
+ This package \pack{euclideangeomery} apparently follows the same
+ path of \pack{xpicture}, but it avoids defining a new user language
  interface; rather it builds new macros by using the same philosophy of
  the recent \pack{curve2e} package.
  
  It is worth mentioning that now \pack{curve2e} accepts coordinates in both 
  cartesian and  polar form; it allows to identify specific points of the 
  drawing with macros, so the same macro can be used over and over again to 
- address the same points.The package can draw lines, vectors, arcs 
+ address the same points. The package can draw lines, vectors, arcs 
  with no arrow tips, or with one arrow tip, or with arrow tips at both ends,
  arcs included. The macros for drawing poly lines, polygons, circles,
  generic curves (by means of Bézier cubic or quadratic splines) are
- already available; such facilities are well documented and exemplified
+ already available; such facilities are documented and exemplified
  in the user manual of \pack{curve2e} package. 
 
  In what follows there will be several figures drawn with this package;
@@ -245,7 +261,7 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  understand the position of the various drawings on the picture canvas.
  This grid is useful also to the end user, while s/he is working on a 
  particular drawing, but when the drawing is finished, the user can 
- delete the grid command or comment ot that line of code.
+ delete the grid command or comment out that line of code.
  For what regards the commands used to render the images, their codes can
  be found in the documented code file \pack{euclideangeometry.pdf}.
  
@@ -257,18 +273,20 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  installation, otherwise this package won't work; this means that
  you have done your updating after 2020-01-18. And this package is already
  present in any modern updated complete installation of the \TeX system.
- Nevertheless the package will load \pack{curve2e} with the wrong version
- and file date, but this package will abort its own loading.
+ Otherwise the package will load \pack{curve2e} with an old version
+ and file date, and this package will abort its own loading, besides
+  aborting the whole job.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \section{Loading \pack{euclideangeometry}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- If you want to use the \pack{euclideangeometry} package, we suggest you load it with the following command:
+ If you want to use the \pack{euclideangeometry} package, we suggest you 
+ load it with the following command:
 \begin{flushleft}\obeylines
 \cs{usepackage}\oarg{options}\Marg{euclideangeomery}
 \end{flushleft}
  The package will take care of managing the possible \meta{options}
- and to call \pack{curve2e} with the specified options; on turn
+ and to call \pack{curve2e} with the such specified options; on turn
  \pack{curve2e} calls \pack{pict2e} passing on the \meta{options}; such
  \meta{options} are only those usable by \pack{pict2e} because neither
  \pack{curve2e} nor \pack{euclideangeometry} use any option. If the
@@ -341,31 +359,31 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  command to put the segment in place; nevertheless it can be shifted
  somewhere else with \cs{put} if it becomes necessary.
 
-\item the new command \cs{polyline} draws a sequence of connected
+\item The new command \cs{polyline} draws a sequence of connected
  segments that form a piecewise linear “curve”; the way segments are
  joined to one another depend from the “join” specifiers that
  \pack{pict2e} has introduced; they will be described further on.
 
 \item \cs{polygon} and \cs{polygon*} produce closed paths as it would
  be possible when using \cs{polyline} and specifying the last point
- coincident with the first point of that curve. The closed path is
- filled with the default color if the asterisk is used.
+ coincident with the first point of that curve. If the asterisk is used 
+ the closed path is filled with the default color.
 \end{enumerate}
 
  There were also the low level commands user interfaces to the various 
  drivers; these drivers really exist, but \pack{pict2e}
  knows how to detect the correct language of the necessary drive;
  the user is therefore allowed to pretend to ignore the existence
- of such drivers; s/he can simply use these commands; their names are
- almost self explanatory.
+ of such drivers, and s/he can simply use these low level commands; their 
+ names are almost self explanatory.
 \begin{enumerate}[noitemsep]
-\item \cs{moveto} Sets the start of a line tracing to an initial point.
+\item \cs{moveto} Sets the start of a line to an initial point.
 
 \item \cs{lineto} traces a segment up to a specified point.
 
-\item \cs{curveto} traces a third degree Bézier up to the third specified
- point, while using the other two ones as control points.\footnote{If
- these terms are unfamiliar, please read the \pack{pict2e} documentation.}
+\item \cs{curveto} traces a third degree Bézier spline  up to the third 
+ specified point, while using the other two ones as control 
+ points.\footnote{If these terms are unfamiliar, please read the \pack{pict2e} documentation.}
 
  \item \cs{circlearc} traces a circumference arc from the last line
  point to a specified destination; its center, its angle amplitude, its
@@ -375,8 +393,8 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
 \item[]\mbox{\bfseries Attention!} Notice that these commands produce
  just information to trace lines, but by themselves they do not trace 
  anything; in order to actually trace the curve or do other operations 
- with what has been done after the user finished describing the line to 
- trace, the following low level commands must be used.
+ with what has been done after the user finished describing the line to be 
+ traced, the following low level commands must be used.
 
 \item A \cs{closepath} is necessary if it is desired to
  join the last position to the initial one. But if the last point
@@ -385,7 +403,7 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
 
 \item If a \cs{strokepath} command is used the line is drawn.
 
-\item If a \cs{fillpath} command is used, the line loop is filled by
+\item If a \cs{fillpath} command is used, the line loop is filled with
  the current color. Notice, if the described line is not a closed loop,
  this filling command acts as if the line first point and last point were
  joined by a straight line.
@@ -405,7 +423,7 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
 
 \item \cs{roundcap} adds a semicircle to the very end of each line.
 
-\item \cs{squarecap} adds the half square to the very end of each line.
+\item \cs{squarecap} adds a half square to the very end of each line.
 
 \item \cs{miterjoin} joins two (generally straight) lines with a miter
  (or mitre) joint; this means that the borders of the line are prolonged
@@ -414,7 +432,7 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  type of joint is the default.
 
 \item \cs{roundjoin} joins each (generally straight) line with
- a \cs{roundcap}; it is good in most circumstances.
+ an arc on the external part of the bend; it is good in most circumstances.
 
 \item \cs{beveljoin} joins two (generally straight) lines with a miter
  joint truncated with a sharp cut perpendicular to the bisector of the
@@ -430,7 +448,8 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  drawing and the \pack{pic2e} extensions can consult that package
  documentation. Actually all commands have been redefined or modified
  by \pack{curve2e} in order to render them at least compatible with
- both the cartesian and polar coordinates. In oder to have a better understanding of these details, see figure~\ref{fig:joins}\footnote{The \cs{polyline} macro has the default join of type bevel; remember to specify a different join type if you want a different one.}.
+ both the cartesian and polar coordinates. In oder to have a better 
+ understanding of these details, see figure~\ref{fig:joins}\footnote{The \cs{polyline} macro has the default join of type bevel; remember to specify a different join type if you want a different one.}.
  
  \begin{figure}[!htb] \centering
  \makebox[\textwidth]{\unitlength=0.009\textwidth
@@ -498,10 +517,10 @@ z_1 z_2 &=( m_1 m_2) \eu^{\iu(\phi_1 + \phi_2)} \\
 z_1/z_2 &=( m_1/m_2) \eu^{\iu(\phi_1 - \phi_2)}
 \end{align*}
  Squares and square roots\footnote{The square root of a complex number 
- has two values; here we do not go into the details on how \pack{curve2e} 
- choses one or the other value. In practice, the \pack{curve2e} macros 
- that use square roots, work mostly on scalars to find magnitudes that 
- are always positive.} are simply done with:
+ has two complex values; here we do not go into the details on how 
+ \pack{curve2e} choses one or the other value. In practice, the 
+ \pack{curve2e} macros that use square roots, work mostly on scalars to 
+ find magnitudes that are always positive.} are simply done with:
 \begin{align*}
 z^2      &= m^2\eu^{\iu 2\phi}\\
 \sqrt{z} &= \sqrt{m}\eu^{\iu\phi/2}
@@ -519,7 +538,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  generally be introduced with point macros, as well as numerical
  coordinates (no matter if cartesian and polar ones) while
  the output(s) should always be in form of point macro(s). Parentheses
- for delimiting the ordered couples or the point macros are seldom
+ for delimiting the ordered pairs or the point macros are seldom
  required. On the other side, the variety of multiple optional
  arguments, sometimes requires the use of different delimiters,
  most often than not the signs~\texttt{<~>}, in addition to the
@@ -533,10 +552,10 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 %
 \item Cartesian and polar coordinates; they are distinguished by
  their separator; cartesian coordinates are the usual comma separated
- couple \meta{$x,y$}; polar coordinates are specified with a colon
- separated couple \meta{$\theta{:}\,\rho$}. In general they are
+ pair \meta{$x,y$}; polar coordinates are specified with a colon
+ separated pair \meta{$\theta{:}\,\rho$}. In general they are
  specified within parentheses, but some commands require them without
- any parentheses. In what follows a generic math symbol, such as for
+ any parenthesis. In what follows a generic math symbol, such as for
  example $P_1$, is used to indicate a complex number that addresses
  a particular point, irrespective of the chosen coordinate type,
  or a macro  defined to contain those coordinates.
@@ -545,45 +564,45 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  \pack{curve2e} are the following; we specify “macro” because in general
  macros are used, instead of explicit numerical values, but for input
  vector macros it is possible to use the comma or colon separated ordered
- couple; “versor” means “unit vector”; angles are always expressed in
+ pair; “versor” means “unit vector”; angles are always expressed in
  degrees; output quantities are everything follows the key word
  \texttt{to}; output quantities are alway supposed to be in the form
  of control sequences.
 \begin{itemize}\small
 \item \cs{MakeVectorFrom}\meta{number,number}\meta{numeric macro} to\meta{vector macro}
-\item \cs{CopyVect}\meta{vector macro} to\meta{vector macro}
-\item \cs{ModOfVect}\meta{vector macro} to\meta{modulus macro}
-\item \cs{DirOfVect}\meta{vector macro} to\meta{versor macro}
-\item \cs{ModAndDirOfVect}\meta{vector macro} to\meta{modulus macro}
-    and\meta{versor macro}
-\item \cs{ModAndAngleOfVect}\meta{vector macro} to \meta{modulus macro}
+\item \cs{CopyVect}\meta{vector macro} \texttt{to}\meta{vector macro}
+\item \cs{ModOfVect}\meta{vector macro} \texttt{to}\meta{modulus macro}
+\item \cs{DirOfVect}\meta{vector macro} \texttt{to}\meta{versor macro}
+\item \cs{ModAndDirOfVect}\meta{vector macro} \texttt{to}\meta{modulus macro}
+    \texttt{and}\meta{versor macro}
+\item \cs{ModAndAngleOfVect}\meta{vector macro} \texttt{to}\meta{modulus macro}
  and\meta{angle macro}
 \item \cs{DistanceAndDirOfVect}\meta{1st vector macro}
-    minus\meta{2nd vector macro} to\meta{distance macro}
-    and\meta{versor macro}
-\item \cs{XpartOfVect}\meta{vector macro} to\meta{numerical macro}
-\item \cs{YpartOfVect}\meta{vector macro} to\meta{numerical macro}
-\item \cs{DirFromAngle}\meta{angle macro} to\meta{versor macro}
-\item \cs{ArgOfVect}\meta{vector macro} to\meta{angle macro}
-\item \cs{ScaleVect}\meta{vector macro} by\meta{scale factor}
-    to\meta{vector macro}
+    \texttt{minus}\meta{2nd vector macro} \texttt{to}\meta{distance macro}
+    \texttt{and}\meta{versor macro}
+\item \cs{XpartOfVect}\meta{vector macro} \texttt{to}\meta{numerical macro}
+\item \cs{YpartOfVect}\meta{vector macro} \texttt{to}\meta{numerical macro}
+\item \cs{DirFromAngle}\meta{angle macro} \texttt{to}\meta{versor macro}
+\item \cs{ArgOfVect}\meta{vector macro} \texttt{to}\meta{angle macro}
+\item \cs{ScaleVect}\meta{vector macro} \texttt{by}\meta{scale factor}
+    \texttt{to}\meta{vector macro}
 \item \cs{ConjVect}\meta{vector macro} to\meta{conjugate vector macro}
-\item \cs{SubVect}\meta{subtrahend vector} from\meta{minuend vector}
-    to\meta{vector macro}
-\item \cs{AddVect}\meta{1st vector} and\meta{2nd vector}
-    to\meta{vector macro}
+\item \cs{SubVect}\meta{subtrahend vector} \texttt{from}\meta{minuend vector}
+    \texttt{to}\meta{vector macro}
+\item \cs{AddVect}\meta{1st vector} \texttt{and}\meta{2nd vector}
+    \texttt{to}\meta{vector macro}
 \item \cs{Multvect}\marg{1st vector}\meta{$\star$}\marg{2nd vector}\meta{$
     \star$}\meta{output vector macro}\newline the asterisks are optional;
     either one changes the \meta{2nd vector} into its complex conjugate
 \item \cs{MultVect}\meta{1st vector}\meta{$\star$}\meta{2nd vector}
-    to\meta{vector macro}\newline discouraged; maintained for backward
+    \texttt{to}\meta{vector macro}\newline discouraged; maintained for backward
     compatibility; the only optional asterisk changes the \meta{2nd vector}
     into its complex conjugate
 \item \cs{Divvect}\marg{dividend vector}\marg{divisor vector}\marg{output
     vector macro}
-\item \cs{DivVect}\meta{dividend vector}\meta{divisor vector}
-    to\meta{vector macro}\newline maintained for backwards
-    compatibility
+\item \cs{DivVect}\meta{dividend vector} \texttt{by}\meta{divisor vector}
+    \texttt{to}\meta{vector macro}\newline maintained for backwards
+    compatibility.
 \end{itemize}
 
 \item A new command \cs{segment}\parg{$P_1$}\parg{$P_2$} draws a line that
@@ -592,7 +611,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 \item Command \cs{Dashline}\parg{$P_1$}\parg{$P_2$}\marg{dash length}
  draws a dashed line between the specified points; the
  \meta{dash length} is specified as a coefficient of
- \cs{unitlenth} so they are proportioned  to the diagram scale. The gap
+ \cs{unitlenth} so it is a proportioned  to the diagram scale. The gap
  between dashes is just as wide as the dashes; they are recomputed by
  the command in order to slightly adjust the \meta{dash length} so
  that the line starts at point $P_1$ with a dash, and ends at $P_2$
@@ -614,7 +633,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 
 \item New commands \cs{Arc}\parg{center}\parg{start}\marg{angle} and,
  with the same syntax, \cs{VectorArc} and \cs{VectorARC} draw 
- arcs without or with arrow tip(s), with the specified \meta{center},
+ arcs with the specified \meta{center},
  starting at point \meta{start}, with an aperture of \meta{angle}
  degrees (not radians). \cs{Arc} draws the arc without arrow tips;
  \cs{VectorArc} draws the arc with one arrow tip at the end point;
@@ -703,7 +722,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 \item The new command \cs{Curve} joins a sequence of third order
  splines by simply specifying the node-direction coordinates; i.e. at the
  junction of two consecutive splines, in a certain interpolation node the
- final previous spline tangent has the same direction of the tangent
+ final previous spline tangent has the same direction as that 
  at the second spline first node; if a change of direction is required, an
  optional new direction can be specified. Therefore this triplet of
  information has the following syntax:
@@ -718,17 +737,17 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 \end{flushleft}
  where \meta{start} is the spline starting “looseness” and \meta{end}
  is the spline ending one. These (generally different) values
- are an index of how far is the control point from the adjacent node.
+ are an index of how far the control point is from the adjacent node.
  With this functionality the user has a very good control on the curve
  shape and curvature.
 
 \item A similar command \cs{Qurve} works almost the same way, but it
  traces a quadratic Bézier spline; this one is specified only with two
  nodes an a single control point, therefore is less configurable than
- cubic splines; the same final line requires several quadratic splines
+ cubic splines; the same final line may require several quadratic splines
  when just a single cubic spline might do the same job. Notice also that
- quadratic splines are just parabolic arcs, therefore without inflections,
- while a cubic spline can have one inflexion. 
+ quadratic splines are just parabolic arcs, therefore without inflection 
+ points, while a cubic spline can have one inflexion point. 
 
 \item A further advanced variation is obtained with the new
  \cs{CurveBetween} command that creates a single cubic spline between two
@@ -757,8 +776,8 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  that kind of geometry that was used in the ancient times when
  mathematicians did not have available the sophisticated means they
  have today; they did not even have a positional numerical notation, that
- arrived in the “west” of the world we are familiar with, just by
- the XI-XII century; before replacing the roman numbering system another
+ arrived in the “western world” we are familiar with, just by
+ the XI-XII century; before replacing the roman numbering system, another
  couple of centuries passed by; real numbers with the notation we use
  today with a decimal separator, had to wait till the XVI century (at
  least); many things that naw are taught in elementary school were
@@ -789,7 +808,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  one the \emph{golden section}. 
 
  Luca Pacioli, by the turn of centuries XV–XVI, was the tutor of
- Guidubaldo, the heir of Federico di Montefeltro, Duke of
+ Guidubaldo, the son and heir of Federico di Montefeltro, Duke of
  Urbino\footnote{If you never visited this Renaissance city and its Ducal
  Palace, consider visiting it; it is one of the many UNESCO Heritage
  places.}; he wrote the famous book \emph{De Diuina Proportione} that
@@ -836,7 +855,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  Mathematicians in the classical times B.C. up to the artists in the
  Renaissance, had no other means but to use geometrical constructions with
  ruler and compass. Even today in schools where calculus is not yet
- taught as a normal subject, possibly not  in certainly high school degree
+ taught as a normal subject, possibly not in certainly high school degree
  courses, but certainly not in elementary and junior high schools, the
  instructors have to recourse to geometrical constructions. Sometimes, as
  in Italy, access to public universities is open with no restrictions to
@@ -847,7 +866,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  education.
 
  The instructors nowadays very often prepare some booklets with their
- lessons; such documents, especially in electronic form, are a nice help
+ lessons; such documents, especially in electronic form, are a good help
  for many students. And \LaTeX is used to write such documents.
  Therefore this extension module is mostly dedicated to such instructors.
 
@@ -861,9 +880,10 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 \begin{enumerate}[noitemsep]
 \item Command \cs{IntersectionOfLines} is a fundamental one; its syntax is
  the following:
-\begin{ttsintassi}
-\cs{IntersecionOfLines}\parg{point1}\parg{dir1} and\parg{point2}\parg{dir2} to\meta{vector}
-\end{ttsintassi}
+\begin{ttsyntax}
+\cs{IntersecionOfLines}\parg{point1}\parg{dir1} and\parg{point2}\parg{dir2}
+\qquad to\meta{vector}
+\end{ttsyntax}
  were each line is identified with its \meta{point} and its direction
  \meta{dir}; the intersection coordinates go to the output \meta{vector}.
 
@@ -871,44 +891,44 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  work, but the coordinates of a segment define also its direction,
  which is the argument of the difference of the terminal nodes of each
  segment; the syntax therefore is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{IntersectionOfSegments}\parg{point11}\parg{point12} 
- and\parg{point21}\parg{point22}to\meta{vector}
-\end{ttsintassi}
+\qquad and\parg{point21}\parg{point22}to\meta{vector}
+\end{ttsyntax}
  Again the intersection point coordinates go to the output \meta{vector}.
  The first segment is between points 11 and 12, and, similarly, the second
  segment is between points 21 and 22.
 
 \item Command \cs{ThreePointCircle} draws a circle that goes through three
  given points; the syntax is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
  \cs{ThreePointCircle}\meta{$\star$}\parg{point1}\parg{point2}\parg{point3}
-\end{ttsintassi}
+\end{ttsyntax}
  A sub product of this macro is formed by the vector \cs{C} that contains
  the coordinates of the center of the circle, that might be useful even
  if the circle is not drawn; the optional asterisk, if present, does not
  draw the circle, but the center is available.
 
 \item Alternatively
-\begin{ttsintassi}
+\begin{ttsyntax}\setfontsize{10.5}
  \cs{ThreePointCircleCenter}\parg{point1}\parg{point2}\parg{point3}to\meta{vector}
-\end{ttsintassi}
+\end{ttsyntax}
  computes the three point circle center assigning its coordinates to
  \meta{vector}.
 
 \item Command \cs{CircleWithCenter} draws a circle given its center and it
  radius; in facts the syntax is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{CircleWithCenter}\meta{center} Radius\meta{Radius}
-\end{ttsintassi}
+\end{ttsyntax}
  This macro does not require the \cs{put} command to put the circle
  in place.
 
 \item A similar macro \cs{Circlewithcenter} does almost the same; its
  syntax is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{Circlewithcenter}\meta{center} radius\meta{radius}
-\end{ttsintassi}
+\end{ttsyntax}
  Apparently these two commands do the same, but, no, they behave
  differently: in the former command the \meta{Radius} is a vector the
  modulus of which si computed and used as the radius; in the latter
@@ -916,19 +936,19 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  used.
 
 \item Command with syntax:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{AxisOf}\meta{point1} and\meta{point2} to \meta{point3} and\meta{point4}
-\end{ttsintassi}
+\end{ttsyntax}
  is used to determine the axis of a segment; the given
  segment is specified with its end points \meta{point1} and \meta{point2}
  and the axis is determined by point \meta{point3} and \meta{point4};
  actually \meta{point3} is the middle point of the given segment.
 
 \item These two commands with syntax:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{SegmentCenter}\parg{point1}\parg{point2}to\meta{center}
 \cs{MiddlePointOf}\parg{point1}\parg{point2}to\meta{center}
-\end{ttsintassi}
+\end{ttsyntax}
  determine just the middle point between two given points. They are
  totally equivalent, aliases to one another; sometimes it is more
  convenient to use a name, sometimes the other; it helps reading the
@@ -938,53 +958,53 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  the middle point of the opposite side; it is not very difficult, but it
  is very handy to have all the necessary elements to draw the median line.
  The simple syntax is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{TriangleMedianBase}\meta{vertex} on\meta{base1} and\meta{base2}
 \qquad to\meta{base middle point}
-\end{ttsintassi}
+\end{ttsyntax}
 
 \item A similar command \cs{TriangleHeightBase} is used to determine the
  intersection of the height segment from one vertex to the opposite base;
  with triangles that have an obtuse angle, the height base might lay
  externally to one of the bases adjacent to such an angle. The syntax is
  the following
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{TriangleHeigthtBase}\meta{vertex} on\meta{base1} and\meta{base2} to\meta{height base}
-\end{ttsintassi}
+\end{ttsyntax}
 
 \item Similarly there is the \cs{TriangleBisectorBase} macro with
  a similar syntax:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{TriangleBisectorBase}\meta{vertex} on\meta{base1} and\meta{base2}
 \qquad to\meta{bisector base}
-\end{ttsintassi}
+\end{ttsyntax}
 
 \item A triangle \emph{barycenter} is the point where its median lines
  intersect; command \cs{TriangleBarycenter} determines its coordinates
  with the following syntax.
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{TriangleBarycenter}\parg{vertex1}\parg{vertex2}\parg{vertex3} to\meta{barycenter}
-\end{ttsintassi}
+\end{ttsyntax}
 
 \item A triangle \emph{orthocenter} is the point where its height lines
  intersect; command \cs{TriangleOrthocenter} determines its coordinates
  with the following syntax:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{TriangleOrthocenter}\parg{vertex1}\parg{vertex2}\parg{vertex3} to\meta{orthocenter}
-\end{ttsintassi}
+\end{ttsyntax}
 
 \item A triangle \emph{incenter} is the point where its bisector lines
  intersect; command \cs{TriangleIncenter} determines its coordinates
  with the following syntax:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{TriangleIncenter}\parg{vertex1}\parg{vertex2}\parg{vertex3} to\meta{incenter}
-\end{ttsintassi}
+\end{ttsyntax}
 
 \item The distance of a specified point from a given segment or line is
  computed with the following command
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{DistanceOfPoint}\meta{point} from\parg{point1}\parg{point2} to\meta{distance}
-\end{ttsintassi}
+\end{ttsyntax}
  where \meta{point} specifies the point and \meta{point1} and \meta{point2}
  identify two points on a segment or a line; \meta{distance} is a scalar
  value.
@@ -999,10 +1019,10 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  otherwise the user should pay attention to use as the first entry the
  smaller among $b$ and $c$, so as to compute a Pitagorean sum. The command
  is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{AxisFromAxisAndFocus}\meta{axis or focus} and\meta{focus or axis} 
 \qquad to\meta{other axis or focus}
-\end{ttsintassi}
+\end{ttsyntax}
  The word “axis” stands for “semi axis length”; the word “focus" stands
  for “focal semi distance”; actually the macro works equally well with
  full lengths, instead of half lengths; its is important not to mix
@@ -1018,23 +1038,23 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  compute modulus and argument of a vector, but consists in computing such
  quantities from the difference of the vectors pointing to the segment
  end points. These two macros are the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{SegmentLength}\parg{point1}\parg{point2} to\meta{length}
 \cs{SegmentArg}\parg{point1}\parg{point2} to\meta{argument}
-\end{ttsintassi}
+\end{ttsyntax}
  The \meta{argument} is computed in the interval $-180^\circ < \phi \leq
  +180^\circ$; it represents the argument of the vector that goes from
  \meta{point1} to \meta{point2}, therefore the user must pay attention to
- the order s/he enters the end points coordinates.
+ the order s/he enters the end point coordinates.
 
 \item The next command \cs{SymmetricalPointOf} is used to find the
  reflection of a specified point with respect to a fixed point; of course
  the latter is the middle point of the couple, but the unknown to be
  determined is not the center of a segment, but one of its end points.
  The syntax is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{SymmetricalPointOf}\meta{point1} respect\meta{fixed} to\meta{point2}
-\end{ttsintassi}
+\end{ttsyntax}
 
 \item  Command \cs{RegPolygon} draws a regular polygon inscribed within
  a circle of given radius and center, with a specified number of sides;
@@ -1046,11 +1066,11 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  different settings; but it would not be too difficult to arrange a new
  macro or to modify this one in order to get “bicolor” polygons.
  It is not necessary for the purpose of this package, therefore we
- let the user express his/her phantasy with other macros. The actual
+ let the user express his/her phantasy by creating other macros. The actual
  syntax is the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{RegPolygon}\meta{$\star$}\parg{center}\marg{radius}\marg{sides}\oarg{angle}\aarg{settings}
-\end{ttsintassi}
+\end{ttsyntax}
  The initial optional asterisk specifies if the interior has to be
  coloured; if yes, the \meta{settings} refer to the color of the
  interior; if not, the \meta{settings} refer to the thickness and
@@ -1065,11 +1085,11 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  argument is specified, the polygon center is displaced accordingly.
  The number of sides in theory may be very high, but it is not wise
  to exceed a couple of dozen sides; if the number of sides is too
- high, the polygon becomes undistinguishable from a circumference.
+ high, a polygon (completely contained in an A4 page) may become undistinguishable from a circumference.
 
 \item Several macros are dedicated to ellipses; their names are spelled
  in Italian, “ellisse”, because the name “ellipse” is already taken by
- other packages; with Italian user command names there should be no
+ other packages; with an Italian user command names there should be no
  interference with other packages, or the risk is reduced to
  a minimum. The various macros are \cs{ellisse}, \cs{Sellisse},
  \cs{Xellisse}, \cs{XSellisse}, \cs{EllisseConFuoco} \cs{EllisseSteiner};
@@ -1080,17 +1100,16 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  similar and are pronounced almost identically.
 
  {\tolerance=3000 Actually \cs{ellisse} is practically a shorthand for 
- \cs{Sellisse} because
- some optional arguments are already fixed, but the meaning of
- \cs{fillstroke} depends on the presence or absence of an initial
- asterisk; similarly \cs{Xellisse} is a sort of a shorthand for
- \cs{XSellisse}; in facts those commands, that contain
- an ‘S’ in their names, can optionally perform also the affine
- \emph{shear} transformation, while those without the ‘S’ do not execute
- such transformation. Figure~\ref{fig:shear} displays a normal ellipse
- with its bounding rectangle, and the same ellipse to which the shear
- affine transformation is applied; the labeled points represent the
- third order Bézier spline nodes and control points.\par}
+ \cs{Sellisse} because some optional arguments are already fixed, but the 
+ meaning of \cs{fillstroke} depends on the presence or absence of an 
+ initial asterisk; similarly \cs{Xellisse} is a sort of a shorthand for
+ \cs{XSellisse}; in facts those commands, that contain  an ‘S’ in their 
+ names, can optionally perform also the affine \emph{shear} transformation,
+ while those without the ‘S’ do not execute such transformation. 
+ Figure~\ref{fig:shear} displays a normal ellipse  with its bounding 
+ rectangle, and the same ellipse to which the shear affine transformation 
+ is applied; the labeled points represent the third order Bézier spline 
+ nodes and control points.\par}
 \begin{figure}[!htb]
 \dimendef\Wmp=2000 \Wmp=\dimexpr(\textwidth-\columnsep)/2\relax
 \begin{minipage}{\Wmp}\centering
@@ -1110,7 +1129,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 \end{figure}
 
 \item The syntax of those six commands are the following:
-\begin{ttsintassi}
+\begin{ttsyntax}
 \cs{Sellisse}\meta{$\star$}\marg{semiaxis-h}\marg{semiaxis-v}\oarg{shear}
 \cs{ellisse}\meta{$\star$}\marg{semiaxis-h}\marg{semiaxis-v}
 \cs{XSellisse}\meta{$\star$}\parg{center}\oarg{angle}\aarg{shear}\marg{semiaxis-h}\%
@@ -1119,20 +1138,21 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 \qquad\marg{semiaxis-v}\oarg{settings1}\marg{settings2}
 \cs{EllipseWithFocus}\meta{$\star$}\parg{vertex1}\parg{vertex2}\parg{vertex3}\parg{focus}
 \cs{SteinerEllipse}\meta{$\star$}\parg{vertex1}\parg{vertex2}\parg{vertex3}\oarg{diameter}
-\end{ttsintassi}
+\end{ttsyntax}
  All require the semi axis lengths; the \meta{semiaxis-h} and
  \meta{semiaxis-v} refer to the semi axes before possible rotation by
  \meta{angle} degrees, and do not make assumptions on which axis is the
- larger one. The optional parameter \meta{shear} is the angle in degrees
- by which the vertical coordinate lines are rotated by effect of shearing. 
+ bigger one. The optional parameter \meta{shear} is the angle in degrees
+ by which the vertical coordinate lines are slanted by effect of shearing. 
  If \meta{shear}, that by default equals zero, is not set
  to another value, the asterisks of command \cs{Sellisse} and
  \cs{XSellisse} do not have any effect. Otherwise the asterisk of
  \cs{Sellisse} forces to draw the ellipse bounding box (rectangle before
  shearing, parallelogram after shearing) as shown together with some
  marked special points (the vertices, spline nodes and control points
- of the quarter circles or quarter ellipses) in figure~\ref{fig:shear}.
- For \cs{ellipse} the asterisk implies filling, instead of stroking the
+ of the quarter circle or quarter ellipse Bézier splines) in 
+ figure~\ref{fig:shear}.
+ For \cs{ellisse} the asterisk implies filling, instead of stroking the
  ellipse contour.
  The \meta{setting}~1 and~2 refer to the color filling and/or border
  color, and contour thickness, as already explained. For the
@@ -1237,7 +1257,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \subsection{Dashed and dotted lines}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- For dotted lines there is a possibility of specifying the dot size;
+ For dotted lines it is possible to specify the dot size;
  it can be specified with an explicit unit of measure, or, if no unit is
  specified, it is assumed to be “points”. The \cs{Dotline} takes care
  of transforming the implied or the explicit dimension in multiples of
@@ -1245,19 +1265,19 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
  codes.
 
 \begin{figure}[!htb]
-\begin{Esempio}[\setfontsize{10}](0.65)
-\unitlength=1mm
+\begin{Esempio}[\setfontsize{10}](0.45)
+\unitlength=0.02\linewidth
 \begin{picture}(40,40)
 \GraphGrid(40,40)
 \Dashline(0,0)(40,10){4}
-\put(0,0){\circle*{2}}
+\put(0,0){\circle*{1}}
 \Dashline(40,10)(0,25){4}
-\put(40,10){\circle*{2}}
+\put(40,10){\circle*{1}}
 \Dashline(0,25)(20,40){4}
-\put(0,25){\circle*{2}}
-\put(20,40){\circle*{2}}
+\put(0,25){\circle*{1}}
+\put(20,40){\circle*{1}}
 \Dotline(0,0)(40,40){2}[0.75mm]
-\put(40,40){\circle*{2}}
+\put(40,40){\circle*{1}}
 \end{picture}
 \end{Esempio}
 \caption{Dashed and dotted lines}\label{fig:DashDot}
@@ -1267,7 +1287,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Generic curves}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- With the \cs{Curve} macro it is possible to make line art or filled shapes. Figures~\ref{fig:hearts} show the same shape, the first just stroked and the second color filled. 
+With the \cs{Curve} macro it is possible to make line art or filled shapes. Figures~\ref{fig:hearts} show the same shape, the first just stroked and the second color filled. 
 
 \begin{figure}[!htp]
 \begin{Esempio}[\setfontsize{9}](0.65)
@@ -1488,10 +1508,10 @@ y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
  special lines relative to a specific vertex. Thanks to the macros 
  described earlier in this list, this drawing is particularly simple; most
  of the code is dedicated to labelling the various points and to
- assign coordinate values to the macros that are going to use them
+ assign coordinate values to the macros that are going to be use 
  in a symbolic way. The generic triangle (not a regular polygon) requires 
- one line, and the determination of the intersections of the lines with
- the suitable triangle side, and their tracing requires two code lines
+ one line of code, and the determination of the intersections of the lines
+ with the suitable triangle side, and their tracing requires two code lines
  each.
 
 \begin{figure}[!tb]\centering
@@ -1526,7 +1546,7 @@ y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
  \emph{barycenter}, the height lines in the \emph{orthocenter}, the 
  bisectors lines in the \emph{incenter}; these centers may be those of 
  special circles: Figures~\ref{fig:barycenter} to~\ref{fig:circumcenter}; 
- the \emph{incircle}, centered in the incenter,
+ the \emph{incircle}, centred in the incenter,
  has a special name, because it has the property of being tangent to all
  the three triangle sides; there is also the circumcircle that passes
  through the three vertices, its center is the intersection of the
@@ -1631,7 +1651,7 @@ y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
  Although these examples require some new simple macros, described
  in the previous sections; some more more examples can be made that require 
  more complex macros. Even these macros are just examples. For other
- applications it is probably necessary to add more macros.
+ applications it is probably necessary to add even more macros.
 
  Let us proceed with the construction of the Steiner ellipse: given a
  triangle, there exists only one ellipse that is internally tangent to
@@ -1721,7 +1741,7 @@ y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
 
 
  The geometrical construction is rather complicated; the steps to follow
- are the following:
+ are the following:\enlargethispage*{\baselineskip}
 \begin{itemize}[noitemsep]
 
 \item draw the triangle and the given focus $\mathsf{F}$;
@@ -1744,8 +1764,8 @@ y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
 
 \item equation~\eqref{equ:axes-foci} allows to find the second axis
  length; the segment that joins the foci has the required inclination
- of the main axis; therefore all necessary pieces of information to
- draw the ellipse are known.
+ of the main axis; its middle point is the ellipse center; therefore all
+  necessary pieces of information to draw the ellipse are known.
 
 \end{itemize}
  Figures~\ref{fig:ellisse-interna-finale} and~\ref{fig:ellisse-interna}
@@ -1761,7 +1781,7 @@ y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
  code for the initial \env{picture} environment.
  
  The reader can easily understand that this package is far from being
- exhaustive for all geometrical problema]s to be solved with ruler and
+ exhaustive for all geometrical problems to be solved with ruler and
  compass; it shows a way to add more commands to approach further problems;
  if any author, who creates new commands, would like to  contribute more
  macros to this package, I will be happy to integrate his/her contribution
@@ -1769,12 +1789,12 @@ y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
  be very happy to add its author name to this  package author list; for
  simpler contributions each contributor will be duly acknowledged.
 
- Creating new macros to solve more problems is pleasant and more
- difficult is the problem, greater is the satisfaction in solving it.
+ Creating new macros to solve more problems is pleasant; the more
+ difficult the problem, the greater the satisfaction in solving it.
 
 
 \begin{center}
- Have fun with \LaTeX and its potential  applications!
+ Have fun with \LaTeX and its potential applications!
 \end{center}
 
 \end{document}
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf
index 54f15c13550..1665a1b1f00 100644
--- a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf
+++ b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf