some fixes in layout, including margin pictures

byrne-en-latex.tex

@@ -6,6 +6,7 @@
 \thispagestyle{empty}
 
 \begin{center}
+
 \Large \uppercase{The first six books of}
 
 \LARGE \uppercase{The elements of Euclid}
@@ -102,11 +103,11 @@
 
 \part*{Introduction}
 
-\regularLettrine{T}{he} arts and sciences have become so extensive, that to facilitate their acquirement is of as much importance as to extend their boundaries. Illustration, if it does not shorten the time of study, will at least make it more agreeable. This Work has a greater aim than mere illustration; we do not introduce colors for the purpose of entertainment, or to amuse \emph{by certain combinations of tint and form}, % don't know where this is from
-but to assist the mind in its researches after truth, to increase the facilities of introduction, and to diffuse permanent knowledge. If we wanted authorities to prove the importance and usefulness of geometry, we might quote every philosopher since the day of Plato. Among the Greeks, in ancient, as in the school of Pestalozzi and others in recent times, geometry was adopted as the best gymnastic of the mind. In fact, Euclid's Elements have become, by common consent, the basis of mathematical science all over the civilized globe. But this will not appear extraordinary, if we consider that this sublime science is not only better calculated than any other to call forth the spirit of inquiry, to elevate the mind, and to strengthen the reasoning faculties, but also it forms the best introduction to most of the useful and important vocations of human life. Arithmetic, land-surveying, hydrostatics, pneumatics, optics, physical astronomy, \&c.\ are all dependent on the propositions of geometry.
+\charspacing{-2}{\regularLettrine{T}{he} arts and sciences have become so extensive, that to facilitate their acquirement is of as much importance as to extend their boundaries. Illustration, if it does not shorten the time of study, will at least make it more agreeable. This Work has a greater aim than mere illustration; we do not introduce colors for the purpose of entertainment, or to amuse \emph{by certain combinations of tint and form}, % don't know where this is from
+but to assist the mind in its researches after truth, to increase the facilities of introduction, and to diffuse permanent knowledge. If we wanted authorities to prove the importance and usefulness of geometry, we might quote every philosopher since the day of Plato. Among the Greeks, in ancient, as in the school of Pestalozzi and others in recent times, geometry was adopted as the best gymnastic of the mind. In fact, Euclid's Elements have become, by common consent, the basis of mathematical science all over the civilized globe. But this will not appear extraordinary, if we consider that this sublime science is not only better calculated than any other to call forth the spirit of inquiry, to elevate the mind, and to strengthen the reasoning faculties, but also it forms the best introduction to most of the useful and important vocations of human life. Arithmetic, land-surveying, hydrostatics, pneumatics, optics, physical astronomy, \&c.\ are all dependent on the propositions of geometry.}
 
-Much however depends on the first communication of any science to a learner, though the best and most easy methods are seldom adopted. Propositions are placed before a student, who though having a sufficient understanding, is told just as much about them on entering at the very threshold of the science, as given him a prepossession most unfavorable to his future study of this delightful subject; or \enquote{the formalities and paraphernalia of rigour are so ostentatiously put forward, as almost to hide the reality. Endless and perplexing repetitions, which do not confer greater exactitude on the reasoning, render the demonstrations involved and obscure, and conceal from the view of the student the consecution of evidence.} % quotation seems to be from The First Six Books of the Elements of Euclid by Dionysius Lardner https://books.google.ru/books?id=YnkAAAAAMAAJ
-Thus an aversion is created in the mind of the pupil, and a subject so calculated to improve the reasoning powers, and give the habit of close thinking, is degraded by a dry and rigid course of instruction into an uninteresting exercise of the memory. To rise the curiosity, and to awaken the listless and dormant powers of younger minds should be the aim of every teacher; but where examples of excellence are wanting, the attempts to attain it are but few, while eminence excites attention and produces imitation. The object of this Work is to introduce a method of teaching geometry, which has been much approved of by many scientific men in this country, as well as in France and America. The plan here adopted forcibly appeals to the eye, the most sensitive and the most comprehensive of our external organs, and its pre-eminence to imprint its subject on the mind is supported by the incontrovertible maxim expressed in the well known words of Horace:—
+\charspacing{-1}{Much however depends on the first communication of any science to a learner, though the best and most easy methods are seldom adopted. Propositions are placed before a student, who though having a sufficient understanding, is told just as much about them on entering at the very threshold of the science, as given him a prepossession most unfavorable to his future study of this delightful subject; or \enquote{the formalities and paraphernalia of rigour are so ostentatiously put forward, as almost to hide the reality. Endless and perplexing repetitions, which do not confer greater exactitude on the reasoning, render the demonstrations involved and obscure, and conceal from the view of the student the consecution of evidence.} % quotation seems to be from The First Six Books of the Elements of Euclid by Dionysius Lardner https://books.google.ru/books?id=YnkAAAAAMAAJ
+Thus an aversion is created in the mind of the pupil, and a subject so calculated to improve the reasoning powers, and give the habit of close thinking, is degraded by a dry and rigid course of instruction into an uninteresting exercise of the memory. To rise the curiosity, and to awaken the listless and dormant powers of younger minds should be the aim of every teacher; but where examples of excellence are wanting, the attempts to attain it are but few, while eminence excites attention and produces imitation. The object of this Work is to introduce a method of teaching geometry, which has been much approved of by many scientific men in this country, as well as in France and America. The plan here adopted forcibly appeals to the eye, the most sensitive and the most comprehensive of our external organs, and its pre-eminence to imprint its subject on the mind is supported by the incontrovertible maxim expressed in the well known words of Horace:—}
 
 \begin{center}
 \emph{Segnius irritant animos demissa per aurem\\
@@ -116,14 +117,12 @@ \part*{Introduction}
 Than what is by the faithful eye conveyed.
 \end{center}
 
-All language consists of representative signs, and those signs are the best which effect their purposes with the greatest precision and dispatch. Such for all common purposes are the audible signs called words, which are still considered as audible, whether addressed immediately to the ear, or through the medium of letters to the eye. Geometrical diagrams are not signs, but the materials of geometrical science, the object of which is to show the relative quantities of their parts by a process of reasoning called Demonstration. This reasoning has been generally carried on by words, letters, and black or uncoloured diagrams; but as the use of coloured symbols, signs, and diagrams in the linear arts and sciences, renders the process of reasoning more precise, and the attainment more expeditious, they have been in this instance accordingly adopted.
+\charspacing{-1}{All language consists of representative signs, and those signs are the best which effect their purposes with the greatest precision and dispatch. Such for all common purposes are the audible signs called words, which are still considered as audible, whether addressed immediately to the ear, or through the medium of letters to the eye. Geometrical diagrams are not signs, but the materials of geometrical science, the object of which is to show the relative quantities of their parts by a process of reasoning called Demonstration. This reasoning has been generally carried on by words, letters, and black or uncoloured diagrams; but as the use of coloured symbols, signs, and diagrams in the linear arts and sciences, renders the process of reasoning more precise, and the attainment more expeditious, they have been in this instance accordingly adopted.}
 
 Such is the expedition of this enticing mode of communicating knowledge, that the Elements of Euclid can be acquired in less that one third of the time usually employed, and the retention by the memory is much more permanent; these facts have been ascertained by numerous experiments made by the inventor, and several others who have adopted his plans. The particulars of which are few and obvious; the letters annexed to points, lines, or other parts of a diagram are in fact but arbitrary names, and represent them in the demonstration; instead of these, the parts being differently coloured, are made to name themselves, for their forms in corresponding colours represent them in the demonstration.
 
 In order to give a better idea of this system, and of advantages gained by its adoption, let us take a right angled triangle, and express some of its properties both by colours and the method generally employed.
 
-\vfill\pagebreak
-
 \defineNewPicture{
 	pair A, B, C;
 	B := (0, 0);
@@ -175,15 +174,13 @@ \part*{Introduction}
 \item $\drawUnitLine{CA}^2 = \drawUnitLine{AB}^2 + \drawUnitLine{BC}^2$. \\ That is, the square of the yellow line is equal to the sum of the squares of the blue and red lines.
 \end{enumerate}
 
-\vskip \baselineskip
-
 In oral demonstrations we gain with colours this important advantage, the eye and the ear can be addressed at the same moment, so that for teaching geometry, and other linear arts and sciences, in classes, the system is best ever proposed, this is apparent from the examples given.
 
-Whence it is evident that a reference from the text to the diagram is more rapid and sure, by giving the forms and colours of the parts, or by naming the parts and their colours, than naming the parts and letters on the diagram. Besides the superior simplicity, this system is likewise conspicuous for concentration, and wholly excludes the injurious though prevalent practice of allowing the student to commit the demonstration to memory; until reason, and fact, and proof only make impressions of the understanding.
+\charspacing{-2}{Whence it is evident that a reference from the text to the diagram is more rapid and sure, by giving the forms and colours of the parts, or by naming the parts and their colours, than naming the parts and letters on the diagram. Besides the superior simplicity, this system is likewise conspicuous for concentration, and wholly excludes the injurious though prevalent practice of allowing the student to commit the demonstration to memory; until reason, and fact, and proof only make impressions of the understanding.}
 
 Again, when lecturing on the principles or properties of figures, if we mention the colour of the part or parts referred to, as in saying, the red angle, the blue line, or lines, \&c, the part or parts thus named will be immediately seen by all the class at the same instant; not so if we say the angle ABC, the triangle PFQ, the figure EGKt, and so on; for the letters must be traced one by one before students arrange in their minds the particular magnitude referred to, which often occasions confusion and error, as well as loss of time. Also if the parts which are given as equal, have the same colours in any diagram, the mind will not wander from the object before it; that is, such an arrangement presents an ocular demonstration of the parts to be proved equal, and the learner retains the data throughout the whole of reasoning. But whatever may be the advantages of the present plan, if it be not substituted for, it can always be made a powerful auxiliary to the other methods, for the purpose of introduction, or of a more speedy reminiscence, or of more permanent retention by the memory.
 
-The experience of all who have formed systems to impress facts on the understanding, agree in proving that coloured representations, as pictures, cuts, diagrams, \&c.\ are more easily fixed in the mind than mere sentences unmarked by any peculiarity. Curious as it may appear, poets seem to be aware of this fact more than mathematicians; many modern poets allude to this visible system of communicating knowledge, one of them has thus expressed himself:
+\charspacing{-2.5}{The experience of all who have formed systems to impress facts on the understanding, agree in proving that coloured representations, as pictures, cuts, diagrams, \&c.\ are more easily fixed in the mind than mere sentences unmarked by any peculiarity. Curious as it may appear, poets seem to be aware of this fact more than mathematicians; many modern poets allude to this visible system of communicating knowledge, one of them has thus expressed himself:}
 
 \vskip 0.5\baselineskip
 
@@ -204,7 +201,7 @@ \part*{Introduction}
 
 This perhaps may be reckoned the only improvement which plain geometry has received since the days of Euclid, and if there were any geometers of note before that time, Euclid's success has quite eclipsed their memory, and even occasioned all good things of that kind to be assigned to him; like \AE sop among the writers of Fables. It may also be worthy of remark, as tangible diagrams afford the only medium through which geometry and other linear arts can be taught to the blind, the visible system is no less adapted to the exigencies of the deaf and dumb.
 
-Care must be taken to show that colour has nothing to do with the lines, angles, or magnitudes, except merely to name them. A mathematical line, which is length without breadth, cannot possess colour, yet the junction of two colours on the same plane gives a good idea of what is meant by a mathematical line; recollect we are speaking familiarly, such a junction is to be understood and not the colour, when we say the black line, the red line or lines, \&c.
+\charspacing{-1}{Care must be taken to show that colour has nothing to do with the lines, angles, or magnitudes, except merely to name them. A mathematical line, which is length without breadth, cannot possess colour, yet the junction of two colours on the same plane gives a good idea of what is meant by a mathematical line; recollect we are speaking familiarly, such a junction is to be understood and not the colour, when we say the black line, the red line or lines, \&c.}
 
 Colours and coloured diagrams may at first appear a clumsy method to convey proper notions of the properties and parts of mathematical figures and magnitudes, however they will be found to afford a means more refined and extensive than any that has hitherto proposed.
 
@@ -360,7 +357,7 @@ \part*{Introduction}
 
 We are happy to find that the Elements of Mathematics now forms a considerable part of every sound female education, therefore we call the attention to those interested or engaged in the education of ladies to this very attractive mode of communicating knowledge, and to the succeeding work for its future developement.
 
-We shall for the present conclude by observing, as the senses of sight and hearing can be so forcibly and instantaneously addressed alike with one thousand as with one, \emph{the million} might be taught geometry and other branches of mathematics with great ease, this would advance the purpose of education more than any thing \emph{might} be named, for it would teach the people how to think, and not what to think; it is in this particular the great error of education originates.
+\charspacing{-2.5}{We shall for the present conclude by observing, as the senses of sight and hearing can be so forcibly and instantaneously addressed alike with one thousand as with one, \emph{the million} might be taught geometry and other branches of mathematics with great ease, this would advance the purpose of education more than any thing \emph{might} be named, for it would teach the people how to think, and not what to think; it is in this particular the great error of education originates.}
 
 \chapter*{Elucidations}
 
@@ -419,7 +416,7 @@ \chapter*{Elucidations}
 
 A line is said to be \emph{produced}, when it is extended, prolonged, or it has length increased, and the increase of length which it receives is called \emph{produced part}, or its \emph{production}.
 
-The entire length of the line or lines which enclose a figure, is called its \emph{perimeter}. The first six books of Euclid treat of plain figures only. A line drawn from the centre of a circle to its circumference, is called a \emph{radius}. That side of a right angled triangle, which is opposite to the right angle, is called the \emph{hypotenuse}. An oblong is defined in the second book, and called a \emph{rectangle}. All lines which are considered in the first six books of the Elements are supposed to be in the same plane.
+\charspacing{-2.5}{The entire length of the line or lines which enclose a figure, is called its \emph{perimeter}. The first six books of Euclid treat of plain figures only. A line drawn from the centre of a circle to its circumference, is called a \emph{radius}. That side of a right angled triangle, which is opposite to the right angle, is called the \emph{hypotenuse}. An oblong is defined in the second book, and called a \emph{rectangle}. All lines which are considered in the first six books of the Elements are supposed to be in the same plane.}
 
 \charspacing{-3}{The \emph{straight-edge} and \emph{compasses} are the only instruments, the use of which is permitted in Euclid, or plain Geometry. To declare this restriction is the object of the \emph{postulates.}}
 
@@ -3608,7 +3605,7 @@ \part{Book II}
 draw byLabelsOnPolygon(A, C, D, B)(ALL_LABELS, 0);
 }
 \drawCurrentPictureInMargin
-\problem{A}{rectangle}{or a right angled parallelogram is said to be contained by any two of its adjacent or conterminous sides.}
+\problem{A}{ rectangle}{or a right angled parallelogram is said to be contained by any two of its adjacent or conterminous sides.}
 
 Thus: the right angled parallelogram \drawPolygon{ABDC} is said to be contained by the sides \drawUnitLine{AB} and \drawUnitLine{AC}; or it may be briefly designated by $\drawUnitLine{AB} \cdot \drawUnitLine{AC}$.