prepare a new page and insert it following the incorrect one on which write in red ink "Corrected on next page," with date of correction.

10. Solution of Equations. Number equations at the left in a vertical column with Arabic numerals inclosed in a parenthesis.

Separate equations from specified operations by a horizontal rippled line not shorter than half an inch. It must follow each equation except those taken from the text or formed from the conditions specified in the problem. The following model solution shows how to number, how to use the rippled line, and how to abbreviate.

As illustrated, equations from the text or from the conditions of the problem are numbered with the first letters of the alphabet.

Equations resulting from operation are numbered in succession in Arabic numerals.

11. Indication of Results. Indicate final results in all problems by double underlining with parallel hair-lines not over one-sixteenth of an inch apart. Do not write the word "Answer."

On the same line with the result write a statement in initial capitals specifying exactly what the result represents, whether number of revolutions per minute, horsepower, speed, etc.

12. Index.

At the end of the school year arrange all the work-books of the year in order, make an alphabetic index for your combined book, cut the work-book cover

in two through the back, and bind all together with one pair of fasteners.

This shows a student's work-book at the end of the second year.

On the front cover attach a label about 4"X5" with a line border and lettered title enumerating the subjects covered as suggested in the facsimile label below:

13. The Axioms. An axiom is a self-evident truth which does not depend on a simpler truth by means of which it can be proved.

The axioms below are the basis of algebra and are the sole authority for the operations necessary to the solution of an equation.

(1) Equality Axiom. (=ity Ax.) Numbers equal to the same number or to equal numbers, are equal to each other.

(2) Addition Axiom. (Add Ax.) If equations are added together, or if the same number is added to both members of an equation, the result is an equation.

(3) Subtraction Axiom. (Sub Ax.) If one equation is subtracted from another or if the same number is subtracted from both members of an equation, the result is an equation.

(4) Multiplication Axiom. (Mul Ax.) If equations are multiplied together, or if both members of an equation are multiplied by the same number, the result is an equation.

(5) Division Axiom. (Div Ax.) If one equation is divided by another or if both members of an equation are divided by the same number, the result is an equation.

(6) Power Axiom. (Power Ax.) If both members of an equation are raised to the same power, the result is an equation.

(7) Root Axiom. (Root Ax.) If the same root of both members of an equation is indicated or extracted, the result is an equation.

(8) Sum of Parts Axiom. (Sum Pts Ax.) The whole of any quantity equals the sum of its parts and is therefore greater than any of its parts when all the parts are positive.

Make no effort to memorize these axioms as they will become familiar through repeated application.

CHAPTER I

INTRODUCTION

SECTION 1, ALGEBRAIC NOTATION. EXERCISE 1,. LETTERING. EXERCISE 2, RATIO. EXERCISE 3, COMPOUND RATIO. EXERCISE 4, THE EQUATION. EXERCISE 5, COEFFICIENT AND EXPONENT. SECTION 2, SOLUTION OF A SIMPLE EQUATION. SECTION 3, FORMULATION OF MATHEMATICAL LAWS. SEC. TION 4, FORMULATION AND COMPUTATION.

§ 1. ALGEBRAIC NOTATION

Exercise 1. Lettering.

14. Lettering of Label.* With pencil and straightedge rule off three spaces on the first page of the workbook, the size of the gummed label to be attached to the front cover, about 1 by 3 inches.

Carefully letter with pencil each of the spaces in the style of letter shown on page 5, in the following order:

15. Lettering of Title Page. When the lettering has been approved, lightly letter the label itself in pencil; also letter the title page Technical Algebra.

Before the next class period in mathematics letter the title page a second time with greater care than before and attach the label to the front cover of the book. Also write your name, home and rooming address on the inside of the front cover.

Exercise 2. Ratio.

16. Measurement. Carefully draw a straight line A about two-thirds the width of the page. With the scale measure it to the nearest sixty-fourth of an inch and to the nearest millimeter.

How was the length of A determined? *

A equals how many sixty-fourths of an inch?

When a line is measured in sixty-fourths of an inch, what is the unit of measure?

A contains the unit of measure how many times?

When a line is measured in millimeters, what is the unit of measure?

A contains this unit how many times?

Ratio is the quotient relation of one quantity to another, expressed as a fraction.

Denoting the unit of measure by B, express the ratio of A to B.

Express the ratio of H to S; of E to R.

The ratio of two quantities of the same kind always equals a fraction whose numerator is the number of times * In answering all questions in the text include the question in the Thus: The length of A was determined, etc.

answer.