Or, reduce the inches and parts to the decimal of a foot and proceed as in the multiplication of decimals.

For example, multiply 2 feet 6 inches by 2 feet 3 inches

=

Here, the 7, which stands in the second place, does not denote square inches, but rectangles of an inch broad and a foot long, which are to be added to the square inches in the third place; so that, 7 × 12 + 6 90 are the square inches, and the product is 5 square feet, 90 square inches. And this manner of estimating the inches must be observed in all cases where two dimensions in feet and inches are thus multiplied together.

Or, the product may be found by reducing the inches to the decimal of a foot: thus 6 inches =.5 of a foot; hence, 2.5×2.25=5.625 square feet, but .625 of a square foot is equal to .625×144-90 square inches, the same as before.

Examples in Duodecimals.

Ex. 1. Multiply 35 feet 4 inches into 12 feet 3 inches. Ans. 434 square feet 47 square inches

Ex. 2. Multiply 7 feet 9 inches by 3 feet 6 inches.

Ans. 27 square feet 18 square inches Ex. 3. Multiply 7 feet 5 inches 9 parts by 3 feet 5 inches 3 parts. Ans. 25 square feet 1023 square inches. Ex. 4. Multiply 75 feet 9 inches by 17 feet 7 inches. Ans. 1331 square feet 135 square inches

Ex. 5. Multiply 97 feet 8 inches by 8 feet 9 inches. Ans. 854 square feet 84 square inch

PRACTICAL GEOMETRY

DEFINITIONS.

1. GEOMETRY is that science which treats of the descriptions and properties of magnitudes in general.

2. A point is that which has position, but not magni. tude.

3. A line is length without breadth; and its bounds or extremes are points.

4. A right line is that which lies evenly between its extreme points.

5. A superficies is that which has length and breadth only and its bounds or extremes are lines.

6. A plane superficies is that which touches in every part any right line that can be drawn in that superficies. 7. A solid is that which has length, breadth, and thickness; and its bounds or extremes are superficies.

8. A plane rectilineal angle is the inclination or open. ing of two right lines which meet in a point.

9. One line is said to be perpendicular to another, when t makes the angles on both sides of it equal to each other.

10. A right angle is that which is formed by two lines that are perpendicular to each other.*

11. An acute angle is that which is less than a right angle.

12. An obtuse angle is that which is greater than a right angle.

* Any angle differing from a right one, is, by some writers, called an oblique angle.

13 A circle is a plane figure, formed by the revolution of a right line about one of its extremities, which remains fixed.*

14. The centre of a circle is the point about which it is described; and the circumference is the line or boundary by which it is contained.

15. The radius of a circle is a right line drawn from the centre to the circumference.

Ө

16. The diameter of a circle is a right line passing through the centre, and terminated both ways by the circumference.

*N. B. The circumference itself, for the sake of conciseness, is sometimes called a circle.

17. An arc of a circle is any part of its periphery or cir cumference.

arc.

18. A chord is a right line joining the extremities of an

19. A segment of a circle is any part of a circle bounded by an arc and its chord.

20. A sector is any part of a circle bounded by an aro and its two radii drawn to its extremities.

N. B. A semicircle is half a circle, and a quadrant the quarter of it.