euclideangeometry (4oct21)

git-svn-id: svn://tug.org/texlive/trunk@60697 c570f23f-e606-0410-a88d-b1316a301751

6 files changed, 143 insertions, 53 deletions

diff --git a/Master/texmf-dist/doc/latex/euclideangeometry/README.txt b/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
index e2bf9e75dba..0402ef848d0 100644
--- a/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
+++ b/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
@@ -1,5 +1,5 @@
 File README.txt for package euclideangeometry
-        [2021-05-16 v.0.2.0 Extension package for curve2e]
+        [2021-10-04 v.0.2.1 Extension package for curve2e]
 
 
 This work is "maintained"
@@ -13,7 +13,7 @@ This work consists of files:
 
 euclideangeometry.dtx is the documented TeX source file of package
 euclideangeometry.sty obtained by running pdflatex on euclideangeometry.dtx
-euclideangeometry.pdf obtained by running pdflatex on euclideangeometry.dtx.
+euclideangeometry.pdf obtained by running pdflatex on euclideangeometry.dtx
 
 README.txt, this file, contains general information.
 
diff --git a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf
index a441c7fccba..85b35db4369 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 1a640af4627..c59fb6fdda5 100644
--- a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex
+++ b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex
@@ -1,6 +1,10 @@
 % !TEX encoding = UTF-8 Unicode
 % !TEX TS-program = pdflatex
 
+%%%% NON USARE ZBOX IN QUESTA DOCUMENTAZIONE: EUCLIDEANGEOMERY LO 
+%%%% RIDEFINISCE RISPETTO ALLA DEFINIZIONE CONTENUTA IN CURVE2E
+%%%% E LA NUOVA SINTASSI È COMPLETAMENTE DIVERSA.
+
 \documentclass[11pt,titlepage,a4paper]{article}\errorcontextlines=100
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
@@ -106,8 +110,8 @@ g\raisebox{-0.715ex}{\kern-0.26em u}\kern-0.13em\I\kern-0.14em t}\xspace}
 % It differs from the previous ones 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.
+% 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
@@ -140,7 +144,7 @@ g\raisebox{-0.715ex}{\kern-0.26em u}\kern-0.13em\I\kern-0.14em t}\xspace}
 
 \DeclareDocumentEnvironment{Esempio}{ s O{\normalsize} D(){0.40} }%
 {%
-  \par%\addvspace{3.0ex plus 0.8ex minus 0.5ex}\vskip -\parskip
+  \par
   \Wboxu=#3\textwidth
   \Wboxd=\dimexpr\linewidth-\columnsep-\Wboxu\relax
   \VerbatimOut{\jobname-temp.tex}%
@@ -202,21 +206,22 @@ Version \fileversion\ of \filedate
  defined in the \LaTeX\ 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 it is so specific, 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 teacher or bachelor degree professor
  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.
+ 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 old times. 
- Actually just one macro is programmed to solve a linear system of equations
+ Actually just one macro is programmed to solve a linear system of 
+ equations
  \end{abstract}
  
  \tableofcontents
@@ -230,9 +235,10 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \section{Introduction}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- The \pack{picture} environment has been available since the very beginning
- of \LaTeX in 1985. At that time it was a really simple environment
- that allowed to draw very simple line graphics with many limitations.
+ The \pack{picture} environment has been available since the very 
+ beginning of \LaTeX in 1985. At that time it was a really simple 
+ environment 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 
@@ -250,13 +256,10 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  \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. It is worth mentioning
- that an extension of \pack{TikZ}, called \pack{tkz-euclide} is also 
- available in a complete and updated \TeX system installation; at the 
- moment its documentation needs some refinements, at least to 
- consistently use a single language, without switching from English 
- to French and viceversa. It aims at the same readership, but it allows 
- to do many more geometrical constructions, than \pack{euclideangeometry}. 
+ courses in the university bachelor degree programs. 
+ 
+ It is worth  mentioning that an extension of \pack{TikZ}, called \pack{tkz-euclide} is also  available in a complete and updated \TeX 
+ system installation; at the  moment its documentation needs some refinements, at least to  consistently use a single language, without switching from English  to French and viceversa. It aims at the same readership, but it allows to do many more geometrical constructions than \pack{euclideangeometry}. 
  The real difference is that \pack{euclideangemetry} may be easily 
  expanded without the need of knowing the complex machinery and coding  
  of the \pack{tkz-euclide} underlaying \pack{TikZ} package.
@@ -266,14 +269,14 @@ The \pack{euclideangeometry} package requires the advanced functionalities of th
  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 point. 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 documented and exemplified
+ 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 point. 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 documented and exemplified
  in the user manual of \pack{curve2e} package. 
 
  In what follows there will be several figures drawn with this package;
@@ -1280,6 +1283,7 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  Here we can show some examples of the advanced \pack{curve2e} commands
  and of what can be done with this \pack{euclideangeometry} extension.
+ If the user wants to practice by replicating the following examples, remember to load the \pack{pm-isomath} package, very useful to typeset the labels of some drawings. Matter of facts, this very documentation is being typeset by using the following package list, in addition to the usual encoding and language related ones: \pack{lmodern}, \pack{textcomp}, \pack{mflogo}, \pack{amsmath}, \pack{fancyvrb}, \pack{graphicx}, \pack{afterpage}, \pack{etoolbox}, \pack{enumitem}, \pack{xspace}, \pack{xcolor}, \pack{euclideangeometry}, \pack{pm-isomath}.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Straight and curved vectors}
@@ -1396,6 +1400,90 @@ z^2      &= m^2\eu^{\iu 2\phi}\\
 \caption{Dashed and dotted lines}\label{fig:DashDot}
 \end{figure}
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{A simple application: Pitagoras' theorem}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+Everybody know Pitagoras' theorem and its famous final formula: «If a right triangle has arms of lengths $a$ and $b$, and hypothenuse of length $c$, then the squares built on the arms are collectively equivalent to the square built on the hypothenuse: $a^2 + b^2 = c^2$.»Or, in simpler terms the sum of areas of the squares built on the arms is equal to the area of the square built on the hypothenuse.
+
+\subsection{First solution}
+This result may be proved with a simple geometrical construction that is shown in figure~\ref{fig:pitagora}.
+
+\begin{figure}[!tbp]
+\centering
+\begin{Esempio}*[\normalsize](0.40)
+\unitlength=0.0125\linewidth
+\begin{picture}(70,80)(-10,-50)
+\AutoGrid
+\thicklines\polygon(0,0)(50,0)(18,24)
+\thinlines\polyline(0,0)(0,-50)(50,-50)(50,0)
+\Pbox(0,0)[r]{C}[0.75ex]\Pbox(18,0)[tr]{H}[0.75ex]
+\Pbox(50,0)[l]{B}[0.75ex]\Pbox(18,24)[b]{A}[0.75ex]
+\Pbox(0,-50)[br]{E}[0.75ex]\Pbox(50,-50)[bl]{D}[0.75ex]
+\Pbox(18,-50)[br]{F}[0.75ex]\Pbox(10,12)[br]{a}[0]
+\Pbox(33,12)[bl]{b}[0]\Pbox(25,0)[t]{c}[0]
+\Pbox(9,0)[b]{d}[0]\Pbox(30,0)[b]{e}[0]
+\Pbox(50,-25)[r]{c}[0]\Pbox(25,-50)[b]{c}[0]
+\Pbox(0,-25)[l]{c}[0]
+\Dashline(18,24)(18,-50){1.5}
+\end{picture}
+\end{Esempio}
+\caption{Geometrical construction to prove Pitagoras' theorem}
+\label{fig:pitagora}
+\end{figure}
+ 
+The proof is based in the fact the the heigh of the right triangle \textsf{ABC} with respect to the hypotenuse divide the triangle in two smaller and similar ones; so that triangles \textsf{ABC}, \textsf{AHC}, and \textsf{ABH}, are similar to one another. This similatity allows us to write:
+\begin{align*}
+d : a = a : c &\Longrightarrow d = a^2/c\\
+e : b = b : c &\Longrightarrow e = b^2/c
+\end{align*}
+
+The dashed height \textsf{AH} may be continued until the opposite side of the square built on the hypothenuse and dives such square in two rectangles \textsf{CHFE} and \textsf{HBDF}; the former rectangle area equals $ c\cdot a^2/c = a^2$, while the later rectangle area equals $ c\cdot b^2/c= b^2$; therefore the full hypothenuse square, sum of these two rectangles, equals: 
+\[ c^2 = a^2 + b^2\]
+
+Of course Euclid did not have the modern mathematical “language” available, and reading his book \emph{Elements} (in ancient Greek)  is not that simple and requires a deep knowledge of the scientific prose of his time. But substantially his proof was purely geometric and based on equivalence of triangles and rectangles areas (Euclide, \emph{Elements}, book \~I,47). 
+
+\subsection{Second solution}
+Another simple purely geometrical proof is shown in figures~\ref{fig:pitagora2}~$(a)$ and~$(b)$.
+Build a square of side $a+b$ where two grays squares of sides $a$ and $b$ 
+are contained as in figure~\ref{fig:pitagora2}-$(a)$: their total area
+equals $a^2+b^2$. Notice that the white triangles contained in this figure have arms of length $a$ and $b$ and hypothenuse $c$. In figure~\ref{fig:pitagora2}~$(b)$ such four white triangles are moved to the corners of the larger square, so that the gray interior is a square of side $c$. Due to the identity of the four white triangles in both figures, the gray areas are equivalent, therefore the square with side equal to the hypotenuse $c$ is equivalent to the squares built on the triangle arms $a$ and $b$, and this, again, proves Pitagoras' theorem.
+\begin{figure}
+\begin{Esempio}*[\small](0.40)
+\unitlength=0.00675\linewidth
+\begin{picture}(70,70)
+\AutoGrid
+\polygon(0,0)(70,0)(70,70)(0,70)
+{\color{lightgray}
+\polygon*(0,40)(30,40)(30,70)(0,70)
+\polygon*(30,0)(70,0)(70,40)(30,40)}
+\segment(30,70)(70,40)
+\segment(0,0)(30,40)
+\Pbox(15,55)[cc]{a^2}[0]\Pbox(50,20)[cc]{b^2}[0]
+\Pbox(15,40)[t]{a}[0]\Pbox(15,00)[b]{a}[0]
+\Pbox(70,55)[r]{a}[0]\Pbox(30,55)[l]{a}[0]
+\Pbox(00,20)[l]{b}[0]\Pbox(30,20)[r]{b}[0]
+\Pbox(50,40)[b]{b}[0]\Pbox(50,70)[t]{b}[0]
+\Pbox(15,20)[br]{c}[0]\Pbox(50,55)[tr]{c}[0]
+\put(0,-6){\makebox(0,0)[bl]{$(a)$}}
+\end{picture}
+\hfill
+\begin{picture}(70,70)
+\AutoGrid
+\polygon(0,0)(70,0)(70,70)(0,70)
+{\color{lightgray}
+\polygon*(40,0)(70,40)(30,70)(0,30)}
+\put(70,-6){\makebox(0,0)[br]{$(b)$}}
+\Pbox(35,35)[cc]{c^2}[0]
+\Pbox(55,00)[b]{a}[0]\Pbox(70,55)[r]{a}[0]
+\Pbox(00,15)[l]{a}[0]\Pbox(15,70)[t]{a}[0]
+\Pbox(00,55)[l]{b}[0]\Pbox(55,70)[t]{b}[0]
+\Pbox(15,00)[b]{b}[0]\Pbox(70,20)[r]{b}[0]
+\Pbox(15,50)[br]{c}[0]\Pbox(50,55)[bl]{c}[0]
+\Pbox(20,15)[tr]{c}[0]\Pbox(55,20)[tl]{c}[0]
+\end{picture}
+\end{Esempio}
+\caption{Another proof of Pitagoras' theorem}\label{fig:pitagora2}
+\end{figure}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Generic curves}
@@ -1471,7 +1559,7 @@ With the \cs{Curve} macro it is possible to make line art or filled shapes. The
 \end{figure}
 
  Another interesting construction is a clock quadrant; this is shown
- in figure~\ref{fig:orologio}
+ in figure~\ref{fig:orologio}; remember that in order to rotate any object, therefore using the \cs{rotatebox} command, the \pack{graphicx} package is necessary; package \pack{euclideangeomentry} and its partners do no load it. This very manual explicitly loads it together with the other necesssary packages.
 
 \begin{figure}[!htb]
 \begin{Esempio}[\setfontsize{9.5}](0.525)
@@ -1701,10 +1789,10 @@ Th symbols are self explanatory; as usual, input data (those entered before the
 \Circlewithcenter\Kdue radius\RKdue
 \thinlines
 \TwoCirclesIntersections(\Kuno)(\Kdue)withradii\RKuno and\RKdue to\Puno and\Pdue 
-\Pbox(\Kuno)[br]{C_1}[4]         \Pbox(\Kdue)[bl]{C_2}[4]
+\Pbox(\Kuno)[br]{C_1}[4]         \Pbox(\Kdue)[bc]{C_2}[4]
 \Pbox(\Puno)[tl]{P_1}[4]        \Pbox(\Pdue)[bc]{P_2}[4]
 \put(\Kuno){\Vector(-45:\RKuno)}\Pbox(5,-27)[bl]{R_1}[0]
-\put(\Kdue){\Vector(-45:\RKdue)}\Pbox(25, 3)[bl]{R_2}[0]
+\put(\Kdue){\Vector(-45:\RKdue)}\Pbox(26, 2)[bl]{R_2}[0]
                                 \Pbox(\CI)[t]{I}[4]
 %
 \segment(\Kuno)(\Kdue)\segment(\Puno)(\Pdue)
@@ -1752,10 +1840,10 @@ The code for drawing figure~\ref{fig;Intersections-of-two-circles} is the follow
 \thinlines
 \TwoCirclesIntersections(\Kuno)(\Kdue)withradii\RKuno 
    and\RKdue to\Puno and\Pdue 
-\Pbox(\Kuno)[br]{C_1}[4]        \Pbox(\Kdue)[bl]{C_2}[4]
+\Pbox(\Kuno)[br]{C_1}[4]        \Pbox(\Kdue)[bc]{C_2}[4]
 \Pbox(\Puno)[tl]{P_1}[4]        \Pbox(\Pdue)[bc]{P_2}[4]
 \put(\Kuno){\Vector(-45:\RKuno)}\Pbox(5,-27)[bl]{R_1}[0]
-\put(\Kdue){\Vector(-45:\RKdue)}\Pbox(25, 3)[bl]{R_2}[0]
+\put(\Kdue){\Vector(-45:\RKdue)}\Pbox(26, 2)[bl]{R_2}[0]
                                 \Pbox(\CI)[t]{I}[4]
 %
 \segment(\Kuno)(\Kdue)\segment(\Puno)(\Pdue)
@@ -2005,20 +2093,7 @@ Ellipses have many interesting properties. One that I was not able to find anywh
 \url{https://docplayer.com.br/345411-Elipses-inscritas-num-triangulo.html}\end{flushleft} 
 is the \emph{director circumference}, literal translation of the Portuguese definition \emph{circunfência diretriz}.
 
-Consider an ellipse with its foci $F$ en $F'$, and a generic point $P$ on its contour.
-Trace a segment from $F\,P$  and another segment for $P\,F'$; these segments measure the distances from point $P$ to each focus: their sum is the length of the main ellipse axis $2a$, where $a$ is the semi axis. Now lengthen the segment $P\,F'$ to point $S$ by the length of $F\,P$; the length of $S\,F'$ is therefore equal to $2a$; now trace the circumference with center in $F'$ and radius $2a$; this is the \emph{director circumference}, that is labelled with~$\Gamma$.
-
-By construction, then, the circle $\gamma$ centred in $F$ and radius equal to $F\,P$ is tangent to $\Gamma$ in $S$ and passes through $F$. This allows to say that:
-\begin{itemize}[noitemsep]
-\item the ellipse is the locus of the centres of all circles passing through  focus $F$ and internally tangent to the circle $\Gamma$ centred in the other focus $F'$ and with radius $2a$;
-\item the axis of segment $S\,F$ is tangent to the ellipse;
-\item the tangency point is the point $P$;
-\item since this axis  passes through the midpoint $M$ of segment $S\,F$ and it is perpendicular to it, the segment $M\,P$ determines the direction of the tangent to the ellipse;
-\item notice that points $S$ and $F$ are symmetrical with respect to the tangent in point $P$.
-\end{itemize}
-Such properties can be viewed and controlled in figure~\ref{fig:diretriz}.
-
-\begin{figure}[!tbp]\centering
+\begin{figure}[!htbp]\centering
 \begin{Esempio}*[\setfontsize{8.2}](0.40)
 \unitlength=0.005\linewidth
 \begin{picture}(170,160)(-60,-80)
@@ -2032,8 +2107,9 @@ Such properties can be viewed and controlled in figure~\ref{fig:diretriz}.
 \edef\P{\X,\Y}\Pbox(\P)[b]{P}[3]
 % Foci coordinates
 \edef\C{\fpeval{sqrt(\A**2-\B**2)}}
-\CopyVect-\C,0 to\F \CopyVect\C,0 to\Fp\Pbox(\Fp)[t]{F'}[3]
-\Pbox(\F)[t]{F}[3]\Pbox(0,0)[tr]{O}[3]
+\CopyVect-\C,0 to\F \CopyVect\C,0 to\Fp
+\Pbox(\Fp)[t]{F'}[3]\Pbox(\F)[t]{F}[3]\Pbox(0,0)[tr]{O}[3]
+\segment(\P)(\F)
 % Director circumference
 \edef\Raggio{\fpeval{2*\A}}
 \Circlewithcenter\Fp radius\Raggio \Pbox(80,60)[tr]{\ISOGamma{lmss}}[0]
@@ -2053,6 +2129,20 @@ Such properties can be viewed and controlled in figure~\ref{fig:diretriz}.
 \caption{The director circumference}\label{fig:diretriz}
 \end{figure}
 
+
+Consider an ellipse with its foci $F$ en $F'$, and a generic point $P$ on its contour.
+Trace a segment  $FP$  and another segment $PF'$; these segments measure the distances from point $P$ to each focus: their sum is the length of the main ellipse axis $2a$, where $a$ is the semi axis. Now lengthen the segment $P\,F'$ to point $S$ by the length of $F\,P$; the length of $S\,F'$ is therefore equal to $2a$; now trace the circumference with center in $F'$ and radius $2a$; this is the \emph{director circumference}, that is labelled with~$\Gamma$.
+
+By construction, then, the circle $\gamma$ centred in $P$ and radius equal to $F\,P$ is tangent to $\Gamma$ in $S$ and passes through $F$. This allows to say that:
+\begin{itemize}[noitemsep]
+\item the ellipse is the locus of the centres of all circles passing through  focus $F$ and internally tangent to the circle $\Gamma$ with radius $2a$, centred in the other focus $F'$;
+\item the axis of segment $SF$ is tangent to the ellipse;
+\item the tangency point is the point $P$;
+\item since this axis  passes through the midpoint $M$ of segment $S\,F$ and it is perpendicular to it, the segment $M\,P$ determines the direction of the tangent to the ellipse;
+\item notice that points $S$ and $F$ are symmetrical with respect to the tangent in point $P$.
+\end{itemize}
+Such properties can be viewed and controlled in figure~\ref{fig:diretriz} on page~\pageref{fig:diretriz}.
+
 Of course the geometrical construction of figure~\ref{fig:diretriz} can be used also in reverse order; for example it may be given a line to play the role of the tangent, a point on  this line to play the role of tangency, and a point not belonging to the line to play the role of a focus, then it is possible to find the other focus laying on a horizontal line passing through the given focus. It suffices to find the symmetrical point of the first focus with respect with the given line, and to draw a line passing through this symmetrical point and the point of tangency that intersects the  horizontal line through the first focus, concluding that this is the second focus and that the ellipse major axis length is that of the segment joining this second focus with the above mentioned symmetrical point.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf
index 2dec94adc22..1a837c1d5ad 100644
--- a/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf
+++ b/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf
diff --git a/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx b/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx
index f8850eef509..90008b0ac48 100644
--- a/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx
+++ b/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx
@@ -33,7 +33,7 @@
 %<package>\ProvidesPackage{euclideangeometry}%
 %<readme>File README.txt for package euclideangeometry
 %<*package|readme>
-        [2021-05-016 v.0.2.0 Extension package for curve2e]
+        [2021-10-04 v.0.2.1 Extension package for curve2e]
 %</package|readme>
 %<*driver>
 \documentclass{ltxdoc}\errorcontextlines=100
@@ -295,7 +295,7 @@ g\raisebox{-0.715ex}{\kern-0.26em u}\kern-0.13em\I\kern-0.14em t}\xspace}
 % evolution of a command that I have been using for years in several
 % documents of mine. It uses some general text, not necessarily
 % connected to a particular point of the |picture| environment,
-% as a legend; It can draw short text as a simple horizontal box,
+% as a legend; it can draw short text as a simple horizontal box,
 % and longer texts as a vertical box of specified width and height
 %
 % Is syntax is the following:
diff --git a/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty b/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty
index c303ae5f81a..ddc4d17b9ff 100644
--- a/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty
+++ b/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty
@@ -14,7 +14,7 @@
 %% 
 \NeedsTeXFormat{LaTeX2e}[2019/01/01]
 \ProvidesPackage{euclideangeometry}%
-        [2021-05-016 v.0.2.0 Extension package for curve2e]
+        [2021-10-04 v.0.2.1 Extension package for curve2e]
 
 \RequirePackage{curve2e}
 \@ifpackagelater{curve2e}{2020/01/18}{}%