Elementary Algebra for Schools

This is the wiki page collecting formatting details for Elementary Algebra for Schools {LaTeX}, which is now in F2.proj_unavail. The discussion thread is here.

Preamble

Note: This is only a preliminary draft.

%%%%%%%%%%%%%%%%%%%%%%%%%
%%    Usage summary    %%
%%%%%%%%%%%%%%%%%%%%%%%%%

% Commands
% \CHAPTER{I.}{Definitions. Substitutions}
% \Def{Algebraical Expression}
% \Definition                            (no argument)
% \Art{1.}                               (flag [Art. xx] with % [** Xref])
% \EXAMPLES{I.~a.}

% Environments
% \begin{Note}...\end{Note}
% \begin{Example}{1.}...\end{Example}
% \begin{Exercises}[4]...\end{Exercises} (arg = #columns, omit for 1)
% \begin{Rule}[I.]...\end{Rule}          (omit arg if rule is unlabeled)


%% General set-up
\documentclass[12pt]{book}

\usepackage[latin1]{inputenc}
\usepackage{amssymb,amsmath}

\usepackage{indentfirst}
\usepackage{ifthen}

\usepackage{multicol}

\newcommand{\BeforeSkip}{\smallskip}
\newcommand{\AfterSkip}{\medskip}

\newboolean{InMulticols}

\newlength{\RuleWidth}
\settowidth{\RuleWidth}{{\normalfont\scshape Rule~VIII.}}

\newcommand{\boldlabel}[1]{\bfseries\upshape\normalsize #1}
\newcommand{\textlabel}[1]{\upshape\normalsize #1}

% Standard (sub-)list formatting parameters
\newcommand{\ListInit}{%
  \setlength{\leftmargin}{0pt}%
  \setlength{\labelwidth}{1em}%
  \setlength{\labelsep}{0.5em}%
  \setlength{\itemindent}{2.5em}%
  \renewcommand{\makelabel}{\boldlabel\hss}%
}

\newcommand{\SublistInit}{%
  \setlength{\leftmargin}{3em}%
  \setlength{\rightmargin}{3em}%
  \setlength{\labelwidth}{1em}%
  \setlength{\labelsep}{0.5em}%
  \setlength{\itemindent}{2.5em}%
  \renewcommand{\makelabel}{\textlabel\hss}%
}

%% Formatter macros
% 011.png: \CHAPTER{I.}{Definitions. Substitutions}
\newcommand{\CHAPTER}[2]{%
  \section*{\centering{\Large CHAPTER~#1} \\[0.25in] \textsc{#2}}
}

\newcommand{\Section}[1]{%
  \section*{\centering\textsc{#1}}
}

% 011.png: \Def{Algebraical Expression}
\newcommand{\Def}[1]{\textbf{#1}}

%020.png:
\newcommand{\Definition}{\textsc{Definition.}\quad}

% 011.png: \Art{1.}
\newcommand{\Art}[1]{\BeforeSkip#1\quad}
% Please mark [Art. xx] references with %[** Xref]

% 012.png: \begin{Note}...\end{Note}
\newenvironment{Note}
{\BeforeSkip\normalfont\small\scshape Note.\quad\upshape}
{\normalfont\AfterSkip}

% 013.png: \begin{Example}{1.}...\end{Example}
\newenvironment{Example}[1]
{\BeforeSkip\normalfont\small\itshape Example\upshape~#1\quad}
{\normalfont\AfterSkip}

% 013.png: \EXAMPLES{I.~a.}
\newcommand{\EXAMPLES}[1]{%
  \section*{\centering\normalfont\large\bfseries EXAMPLES~#1}
}

% 013.png: \begin{Exercises}{4}...\end{Exercises} for four columns
% \begin{Exercises}...\end{Exercises} if only one column
\newenvironment{Exercises}[1][]{%
  \ifthenelse{\equal{#1}{}}{}%
        {\setboolean{InMulticols}{true}\begin{multicols}{#1}}%
  \begin{list}{}{\ListInit}}%
{%
  \end{list}%
  \ifthenelse{\boolean{InMulticols}}{\end{multicols}}{}
}

% 020.png: \begin{Rule}[I.]...\end{Rule}
% 024.png: \begin{Rule}...\end{Rule}
\newenvironment{Rule}[1][]{%
  \BeforeSkip%
  \ifthenelse{\equal{#1}{}}
  {\makebox[\RuleWidth][l]{\normalfont\scshape Rule~#1}\ \itshape}
  {\makebox[\RuleWidth][l]{\normalfont\scshape Rule.}\quad \itshape}}
{\normalfont}

Formatting details

Structural divisions

Chapters

Example from 011.png

\CHAPTER{I.}{Definitions. Substitutions.}

• Issues:
  • 082.png 2 parts of the title appear on separate lines

Sections

Example from 025.png

\Section{Addition.}

Articles (numbered paragraphs)

The entire book consists of numbered "articles"--though that term is only used in cross-references to other articles. A new article looks just like a number at the start of a paragraph.

Example from 011.png

\Art{1.} Algebra treats of quantities as in Arithmetic, but with

Notes

Notes begin with the word "Note." in small caps.

Example from 012.png

\begin{Note} When the coefficient is unity it is usually omitted. Thus
we do not write $1a$, but simply $a$.
\end{Note}

Examples (true examples)

These appear within articles, and usually contain the italicized word "Example".

Example from 013.png

\begin{Example}{3.} If $a = 6$, $x = 7$, then
\[
\frac{5}{3} ax = \frac{5}{3} \times a \times x = \frac{5}{3} \times 6 \times 7 = 70.
\]
\end{Example}

• Issues:
  • "Examples." without a number, e.g. on 015.png
  • 106.png "Example." in the singular with no number
  • "Examples." with indented numbers in parentheses, e.g. 045, 083.png
  • 105.png "Example" is abbreviated "Ex."
  • 140.png the work of the example is divided into "First Method" and "Second Method"
  • braces and Roman numerals for examples(?) on 050.png

EXAMPLES (heading for exercises)

Each new group of exercises has a bold "EXAMPLES" heading.

Example from 013.png

\EXAMPLES{I.~a.}

• Issues:
  • asterisk before EXAMPLES on 110.png (I think representing optional--preceding articles also have *s); also 226.png

Exercises

These are lists of numbered problems, often in columns.

Example from 013.png

If $a=7$, $b=2$, $c=1$, $x=5$, $y=3$, find the value of
\begin{Exercises}{5}
\item[1.] $14x$.
\item[2.] $x^3$.
\item[3.] $3ax$.
\item[4.] $a^3$.
\item[5.] $5by$.
\item[6.] $b^5$.
\item[7.] $3b^2$.
\item[8.] $2xa$.
\item[9.] $6c^4$.
\item[10.] $4y^3$.
\item[11.] $7c^5$.
\item[12.] $9b^4$.
\end{Exercises}

If only one column, leave off the column number: \begin{Exercises}...\end{Exercises}

• Issues:
  • What about when the # of columns switches within a block of exercises--e.g. 022.png. Does the markup stop & start each time to give the new column number?
  • In prose exercises sometimes the extra lines wrap to the left of the exercise number (209.png) and other times to the right as a hanging indent (271.png)

Rules

A rule is printed (nearly) entirely in italics and usually has the word "Rule" in small caps before it.

Example from 020.png

\begin{Rule}[I.] The sum of a number of like terms is a like term.\end{Rule}

Example without number, 024.png

\begin{Rule} When an expression within brackets is preceded by the
sign $+$, the brackets can be removed without making any change in
the expression.\end{Rule}

• Issues:
  • 083-4, articles 95-7 begin with rules
  • 066.png at the top--perhaps a rule without the word "Rule"? Also 123, maybe 148.png (rule starts mid-paragraph)
  • 132.png Rules without the word "Rule", but with Roman numerals
  • 102.png rule has 2 parts
  • 157.png has possible rules, in italics but with arabic numerals (with and without parentheses)

Rule-like things

These look like rules (capital Roman numerals and italicized text) but have different names.

• Cases: 043.png, 241.png
• Propositions: 236.png "Prop. I", 232.png without the "Prop." but also appears to be a proposition rather than a rule
• 269.png at top is a "theorem" (see bottom of previous page)--proposition or rule?
• 273.png top, "Cor." presumably is a corrolary to the rule of the previous page

Answers

Starting on 319.png. These are much like the exercises.

Other structural items not yet handled

• 108.png "Explanation." paragraphs, similar to "Example."
• 237.png at bottom, and following pages: articles are starting with italicized paragraph introducing the issue; also 283, 286-7

Text details

Defined terms (bold)

Example from 011.png

\Art[2.] An \Def{Algebraical Expression} is a collection of symbols;

• Issues:
  • 086.png note at the top--are the bold phrases to be considered defined terms, or just use regular bold markup?

Definitions (small-capped, heading-like word)

Example from 020.png

\Art{19.} \Definition When like...

Other text items not yet handled

• equation tags in parentheses with leader dots, e.g. 034.png
• right-aligned cross-references, e.g. 035.png [Art. 13]
• 273.png right-aligned terminology in brackets & italics

Mathematical details

Issues:

• Usually multiplication is × but 017.png and some other pages have dots on the baseline (like decimal points/periods)
• not-quite-parentheses used in division, 047.png
• format of square root appearance on 053.png (with or without overline)
• decimal points on 063.png appear as mid-dots
• overdots on 063 & 065.png represent repeating decimals
• dots like leaders but meaning ditto marks, & needing alignment: 070.png
• complex notation with lines and borders/boxes, e.g. 108, 111, 218, 221.png
• 162.png dark division bars to clarify fractions containing other fractions
• variables within italics are printed as upright, e.g. 230.png at the top and later. This holds even for displayed equations within an italicized paragraph (233.png at top)
• 274.png greater than above equals above less than -- I don't know if there's a LaTeX symbol for it

Back Matter

369-70.png contain some ads for other books

• Any text on the first line is larger than that of the remaining lines.
• The book's title is in a larger sans serif font, except that if it continues for more than one line the text on the 2nd line will be in all caps (in the smaller font always used in the 2nd line).
• Authors are printed in small caps

373.png to the end have other ads

• Each general topic (Math, Science) begins with a large heading followed by a paragraph-style list of the sub-topics.
• Each sub-topic (Arithmetic, Biology) has a smaller heading.
• Book information:
  • Almost all hanging indents
  • Author's last name in a larger, bold font. Followed by a period and em-dash.
  • First title by the author usually follows the em-dash, but sometimes other author details are given there instead
  • Each additional title is its own paragraph. Title printed in all caps.
  • Author's name in small caps within the paragraph
  • Occasionally there's an extra paragraph for a book; it's in a smaller font, and may have a hanging indent or regular (first-line) indent style
  • Occasional right-aligned note such as [In the press.