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the theorems, or explain the rules given for the various operations; and also to assist those persons to acquire a knowledge of mensuration, who have not the opportunity of wholly devoting their time to that object.

With the view of aiding the public and being useful to the rising generation, and knowing that every work of a literary nature must either stand or fall by its merit or demerit, I submit the following pages to the consideration of a candid and generous community. TOBIAS OSTRANDER.

New York, Sept. 1833.

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COMPLETE SYSTEM

OF

MENSURATION.

SECTION I.

THE area, or superficial contents of any figure, is the space contained within the line or lines by which the figure is bounded.

OF THE SQUARE.

A square is a figure whose sides are of equal length, and each of the angles contains 90 degrees.

PROBLEM I.

To find the area of a square. Rule-Multiply the side by itself; the product will be the area in such terms as correspond with the measure of the sides.

EXAMPLES.

1. What is the area of a square board, each of whose sides are 20 inches in length? Ans. 400 inches. 2. How many square feet in a piece of land ten rods Ans. 27225 square feet.

square.

3. How many acres in a square piece of land 60 rods square? Ans. 22,5 acres. 4. How many men may stand on 5 acres of land, each occupying a space of three feet square? Ans. 24,200.

5. How many square links are contained in a piece of land 14 chains long and 14 wide? Ans. 1,960,000.

PROBLEM II.

The area of a square given, to find the length of the Rule-Extract the square root of the area.

side.

EXAMPLES.

1. The area of a perfect square is 625 feet-What is the length of the side? Ans. 25 feet. 2. What is the length of the sides of a square floor containing 384 square feet? Ans. 19,5959 +.

3. What must be the length of the sides of a square piece of land to contain 6 acres? Ans. 30,9838+perches.

4. How many chains in length are the sides of a square containing 125 acres of land? Ans. 35,3553+.

PROBLEM III.

The diagonal* of a perfect square being given, to find the area. Rule-Divide the square of the diagonal by 2; the quotient will be the area.

EXAMPLES.

1. The diagonal of a perfect square is 16 chainsHow many acres does it contain? Ans. 12,8 acres. 2. The diagonal of a perfect square is 41,3 rodsHow many acres does it contain?

Ans. 5 acres, 1 rood, and 13 perches +. 3. The diagonal of a perfect square is 4,78 chainsHow many acres does it contain?

Ans. 1 acre and 22 perches +.

PROBLEM IV.

The area of a perfect square being given, to find the length of the diagonal. Rule-Extract the square root of double the area.

EXAMPLES.

1. The area of a square piece of land is 64,8 acres What is the length of the diagonal line in chains? Ans. 36 chains.

* The diagonal is a right line extending from angle to angle.

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