9.91 98.2081 3.14802 9.95490 973.242 2.14795 4.62762 9.92 98.4064 3.14960 9.95992 976.191 2.14867 4.62918 9.93 98.6049 3.15119 9.96494 979.147 2.14940 4.63073 9.97661

9.94 98.8036 3.15278 9.96995 982.108 9.95 99.0025 3.15436 9.97497 985.075 9.96 99.2016 3.15595 9.97998 988.048 9.97 99.4009 3.15753 9.98499 991.027 9.98 99.6004 3.15911 9.98999 994.012 9.99 99.8001 3.16070 9.99500 997.003

1 liter

D. Metric Units to English Units

1000 cu. cm. = = 61.02 cu. in. = 1.0567 liquid quarts

1 quart = .94636 liter 946.36 cu. cm.

=

1 kilogram (Kg.) = 2.2046 pounds (lb.)

453.59 grams

E. Other Numbers

Tratio of circumference to diameter of a circle

1 radian

=

3.14159265

angle subtended by an arc equal to the radius = 57° 17' 44".8 = 57°.2957795 = 180°/π

1 degree = 0.01745329 radian, or π/180 radians

Cancellation, of terms in an equation, Fraction, 140; signs in, 141; re-

73.

Clearing of fractions, 164.
Coefficient, 5.

Consequent, 180.

Coördinates of a point, 207.
Cube of a number, 17.

Cube root of a number, 17.

duction of to lowest terms, 143;
reduction of to common denomina-
tor, 145, 148; multiplication of,
153; division of, 155; complex,
160; rationalizing the denomina-
tor of a, 257.
Fulcrum, 188.

Denominator, 140; lowest common, Gear wheel law, 192.

146.

Dividend, 119.

Graph, 202; use of, 203; of an
equation, 205.

Inconsistent equations, 211.
Index of a root, 247.

Division, of positive and negative
numbers, 44; law of signs for,
119; law of exponents for, 119;
of a monomial by a monomial,
120; of a polynomial by a mo- Lever, 188; law of, 188.
nomial, 122; of a polynomial by
a polynomial, 123; of surds, 257.

Elimination, by substitution, 215;
by addition or subtraction, 218.
Equation, 7; simple, 75; of the
first degree, 75; linear, 75; frac-
tional, 164; literal, 174; graph
of, 205, 208; reciprocal, 223;

Mean proportional, 196.
Means of a proportion, 183.
Monomial, 55; raising of to a power,

81.

Multiple, 136; common, 136; low-
est common, 136.
Multiplication, of positive and nega-
tive numbers, 40; of two mo-

Printed in the United States of America.

By WILLIAM L. VOSBURGH

Head of the Department of Mathematics, Boston Normal School, and

FREDERICK W. GENTLEMAN

Department of Mathematics, Mechanic Arts High School, Boston

A course for the pupil who has mastered the elementary number facts the four processes applied to integers and fractions and the various relations of the commoner denominate units. The method in these books is a preparation for the intelligent application of the student's mathematical powers to the field of practical computation, and it introduces constantly the arbitrary standards of accuracy and individual responsibility that the pupil will meet later in his adult activities. The course represents the Junior High School idea at its best-fullness of development, fullness of service. It is characterized by many attractive features which may be briefly put as follows:

The pupil is required to check all results. He is made personally responsible for his results.

He is taught to make a mental estimate of answers and location of the decimal point. He will not offer absurd results. He gets an idea of number values.

There are no impractical problems. No answers deal with half a man or butter at 14 cents a pound.

Mechanical drill to secure accuracy in arithmetical processes is introduced often and effectively.

The equation is introduced early as a mathematical tool and is used consistently throughout.

The properties of geometric figures are established by actual measurement and mechanical construction before the abstractions of the proofs of any propositions are introduced.

Practical applications of geometric principles are emphasized.