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THE

MECHANIC'S, MACHINIST'S, AND ENGINEER'S

PRACTICAL

BOOK OF REFERENCE:

CONTAINING

TABLES AND FORMULÆ

FOR USE IN

SUPERFICIAL AND SOLID MENSURATION; STRENGTH AND
WEIGHT OF MATERIALS; MECHANICS; MACHINERY:
HYDRAULICS; HYDRODYNAMICS; MARINE ENGINES;
CHEMISTRY; AND MISCELLANEOUS RECIPES.

ADAPTED TO AND FOR THE USE OF

ALL CLASSES OF PRACTICAL MECHANICS.

EDİTED BY

CHARLES W. HACKLEY,

Professor of Mathematics in Columbia College, N. P.

THE

PRACTICAL BOOK OF REFERENCE.

ARITHMETICAL SIGNS.

THE following definitions of arithmetical signs which are employed in mechanical calculations, will be found of great value to those who do not yet understand them, and of some interest to those who are already familiar with their meanings.

This is the sign of equality, and signifies equal to. For example: 12 inches 1 foot (12 inches is equal to 1 foot).

+ This is the sign of addition, and signifies plus, or more. example: 5 + 3 8 (5 added to 3 is equal to 8).

This is the sign of subtraction, and signifies minus, or less. example: 10 82 (10 minus 8 leaves or is equal to 2).

For

For

× This is the sign of multiplication, and signifies multiplied by, or into. For example: 10 × 3 = 30 (10 multiplied by 3 is equal

to 30).

This is the sign of division, and signifies divided by. For example: 156 ÷ 6 = 26 (156 divided by 6 is equal to 26); or, 24 ÷ 4 = 6

24

4

(24 divided by 4 is equal to 6); or = 6 (24 fourths are equal to 6 wholes).

:::: This is the sign of proportion, and signifies proportion. For example: 4: 6 :: 8: 12 (as 4 is to 6, so is 8 to 12); or 3: 5 ::

3 9
15

9:15 (that is, as 3 is to 5, so is 9 to 15); 5

This is the sign of the Square root. When it is placed before a number (as thus, √ 5 = 25), it means that the square root of that number is required. For example: 255, because 5 × 5= 25 or, √ 9 = 3, because 3 × 3 = 9; or, v 64 8, because 8 × 8 = 64. When it is placed before a that number is required. 16, and 4 × 16 = 64); × 36 = 216).

This is the sign of the CUBE root. number, it means that the cube root of For example: 644 (that is, 4 × 4 or, 3/ 216 = 6 (that is, 6 × 6 = 36, and 6

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