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EXPLANATION

OF THE PRINCIPAL

MATHEMATICAL CHARACTERS.

The sign or character

=

(called equality) denotes that the respec

tive quantities between which it is placed are equal; ás 4 poles = 22 yards

1 chain

==

100 links.

The sign+ (called plus, or more) signifies that the numbers between which it is placed are to be added together; as 9 + 6 (read 9 plus 6) 15. Geometrical lines are generally represented by capital letters; thus AB + CD signifies that the line CD is to be added to the line AB.

=

The sign (called minus, or less) denotes that the quantity which it precedes is to be subtracted; as 15 6 (read 15 minus 6) = 9. In geometrical lines also, ABCD signifies that the line CD is to be subtracted from the line AB.

The sign denotes that the numbers between which it is placed are to be multiplied together; as 5 x 3 (read 5 multiplied by 3)

15.

=

The sign signifies division; as 15 ÷ 3 (read 15 divided by 3) = 5. Numbers placed like a vulgar fraction also denote division; the upper number being the dividend, and the lower the divisor; as 15

= 5.

::

The signs (called proportionals) denote proportionality; as 2:5 6:15, signifying that the number 2 bears the same proportion to 5, as 6 does to 15; or, in other words, as 2 is to 5, so is 6 to 15.

The sign

(called vinculum) is used to connect several quantities together; as 9+ 36 x 2 = 126 x 2 = 6 × 2

= 12.

The sign, placed above a quantity, represents the square of that quantity; as 5+32= 82 8 x 8 = 64.

=

The sign, placed above a quantity, denotes the cube of that 83 = 12 813 43 quantity; as 9 + 3

[blocks in formation]

The signor, placed before a quantity, denotes the square root of that quantity; as √9 x 4 = √ 36 = 6.

The sign, placed before a quantity, represents the cube root of

[blocks in formation]

DIRECTIONS TO BOOKBINDER.

Plans VIII., IX., X., XI., XIII., and Earthwork Tables at the end of the work, in the order thus given:

Fold Plans VIII. and IX. to face each other when open.
Fold Plans X. and XI. to face each other when open.
Fold Plan XIII. to face, when open, the work.
Fold Earthwork Tables to face, when open, the work.

LAND-SURVEYING.

PART I.

DEFINITIONS, PROBLEMS, AND THEOREMS IN GEOMETRY.

GEOMETRY originally signified the art of MEASURING the EARTH, or any distance or dimensions upon, or within it; but it is now used for the science of quantity, extension, or magnitude.

GEOMETRICAL DEFINITIONS.

1. A point is considered as having neither length, breadth, nor thickness.

2. A line has length, but

is considered as having A

neither breadth nor thick

ness; as AB.

3. Lines are either right, curved, or parallel.

4. A right or straight line

lies wholly in the same direction between its extremities, and is the shortest distance between two points; as AB.

5. A curved line continually changes its direction between its extremities; as AB.

6. Parallel lines always remain at the same distance from each other, and, though continually produced, would never meet; as AB and CD.

A

B

B

B

B

D

B

D

A

P

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