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THEORY AND FRACTICE

SURVEYING.

TH

HE word Surveying, in the Michematics, signifies the art of measuring land, and cé delineating its boundaries on a map.

The Surveyor, in the practice of this art, directs his attention, at first, to the tracing and measuring of lines; secondly, to the position of these lines in respect to each other, or the angles formed by them; thirdly, to the plan, or representstion of the field, or tract, which he surveys; and fourthly, to the calculation of its area, or superficial content. When this art is employed in observing and delineating Coasts and Harbours, in determining their variation of the Compass, their Latitude, Longitude and soundings, together with the bearings of their most remarkable places from each other, it is usually denominated Maritime-Surveying. This branch of Surveying, however, demands no other qualifications than those, which should be thoroughly acquired by every Land Surveyor, who aspires to the character of an accomplished and skilful practitioner. Surveying, therefore, requires an intimate acquaintance with the several parts of the Mathematics, which are here inserted as an introduction to this treatise.

B

PART I.

Containing Decimal Fractions, Involution and Evolution, the Nature and Use of Logarithms, Geometry and Plane Trigonometry.

SECTION I.

DECIMAL FRACTIONS.

If we suppose unity or any one thing to be di vided into any assigned number of equal parts, this number is called the denominator; and if we chuse to take any number of such parts less than the whole, this is called the numerator of a fraction.

The numerator, in the vulgar form, is always written over the denominator, and these are separated by a small line thus, or; the first of these is called three-fourths, and the latter five-eighths of an inch, yard, &c. or of whatever the whole thing originally consisted: the 4 and the 8 are the denominators, showing into how many equal parts the unit is divided; and the three and the five are the numerators, showing how many of those parts are under consideration.

Fractions are expressed in two forms, that is, either vulgarly or decimally.

All fractions whose denominators do not consist of a cipher, or ciphers, set after unity, arc called vulgar; and their denominators are always written under their numerators. The treatment of these, however, would be foreign to our present purpose. But fractions whose denominators consist of an unit prefixed to one or more ciphers, are called decimal fractions; the numerators of which are written without their denominators, and are distinguished from integers by a point prefixed thus fo, and, in the decimal form, are expressed by 2.42.172.

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ADDITION OF DECIMALS.

Write the numbers under each other according to the value or denomination of their places; which position will bring all the Decimal points into a column, or vertical line, by themselves. Then, beginning at the right hand column of figures, add in the same manner as in whole numbers, and put the decimal point, in the sum directly beneath the other points.

EXAMPLES.

Add 4.7832 3.2543 7.8251 6.03 2.857 and 3.251 together. Place them thus,

4.7832

3.2543

7.8251

6.03

2.857

3.251

Sum-28.0006.

Add 6.2 121.306 .75 27 and 0007 to

gether. 121. 06

.75

2.7

.0007

Sum=130.9567

What is the sum of 6.57 1.026 .75 145 8.7 526. 3.97 and .0271?

Answer 693.5431.

What is the sum of 4.51 146.071 507 .0006 132. 62.71 507 7.9 and 10712?

Answer 354.31272.

SUBTRACTION OF DECIMALS.

Write the figures of the subtrahend beneath those of the minuend according to the denom nation of their places, as directed in the rule of addition; then, beginning at the right hand, subtract as in whole numbers, and place the decimal point in the difference exactly under the other two points.

EXAMPLES.

From 38.765 take 25.3741
25.3741

Difference-13.3909.

From 2.4 take .8472
.8472

Diff.-1.5528

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