fector on the fines 90, 90, to the radius C E, and take in your compafies the fine of 80, and fet 10 to 80; take the fine 70, and fet from 70 to 20 on each fide the conjugate diameter; the fine 60, fet from 30 to 60; the fine 50, fet from 40 to 50; the fine 40, fet from 50 to 40; the fine 30, fet from 60 to 30; the fine 20, fet from 70 to 20; the fine 10, fet from 80 to 10; fo will the points 10, 20, 30, 40, 50, 60, 70, 80, CBD A, be in the ellipfis, through which points draw the curve, and you will have a true mathematical ellipfis.

PROB. 29. Any angle being given, to find the number of degrees it contains. Fig. 16.

1. Take 60° out of your line of chords, and set one foot of your compaffes in A, with the other defcribe the arch a b.

2. Take the distance ab in your compaffes, and fet one foot in the beginning of the line of chords, and the other will reach to 60 upon the fame line, the measure of the angle required,

PROB. 30. In a given circle, to infcribe a polygon of any propofed number of fides. Fig. 30.

1. Divide 360° by the number of fides, and make an angle Ac B, at the center, whose measure fhall be equal to the degrees in the quotient. 2. Join the points A and B, and apply the chord AB to the circumference, the given number of times, and you will have the polygon required,

PROB, 31. To defcribe a lune in a quadrant. Fig. 31. Draw the triangle ABC, and on the center B, describe the quadrantal arch AC; upon the middle of the hypothenufe AC, draw the other femi-circle, and you will have the lune A FCD required.

LXVII. MENSURATION

OF

SUPERFICIES.

HE area of any plain furface is the space contained within the

made up of some certain number of fquares, according to the different measures the dimenfions are taken in, viz. a fquare whofe fide is one inch, one foot, one yard, &c. is called the measuring unit, and the content of any figure is computed by the number of thofe fquares contained in that figure.

PROBLEM I. To find the area of a parallelogram; whether it be a Square, a rectangle, a rhombus, or a rhomboides.

RULE. Multiply the length by the perpendicular height, the product is the area or content.

EXAMPLE

EXAMPLE I, What is the area of the fquare SS, whose fide is 5

feet 6 inches?

E. 2.

chains?

By practice,

6 in. =)56

5

27

6

2 9

Answer 30 3

What is the area in acres of a fquare, whofe fide is 35,25 35,25 = Length of the fide

F.

9,25

9,25

4625

1850

1,00

E, 3. Required the area of a fquare, whofe fide is 9 feet 3 inches?

By deicmals,

By practice.
F. I.

3 = 4)9 3

By duodecimals.

In.

8325

Anfwer 85 6 9

85,5625

12

6,7500

12

9,00

Anfwer 85 feet, 6 inches, 9 feconds.

E. 4. What is the area of the rectangle B L, whofe length is 18 feet 6 inches, and breadth 12 feet 6 inches?

E. 5:

What is the fuperficial content of a parallelogram, whofe

length is 68 feet, and breadth 16 feet?

F.

68

16

Anfwer 1088 feet.

E. 6. If one fide of a parallelogram is 130 feet, and the other 50 feet, what is the fuperficial content?

130
50

Anfwer 6500 feet.

are contained in a floor 45 feet 6 inches long,

F:

45.5

9,25

9

6,0 Anfwer 420 feet, 10 inches, 6 parts.

E. 8. Required the fuperficial content of a rhombus, whofe length is 12 feet 6 inches, and perpendicular height 9 feet 3 inches ?

By