PROBLEM I.

To describe a cycloid.

1. Let B C be the edge of a straight ruler: erect A D perpendicular to B C equal to the diameter of the generating circle; upon the diameter A D, describe a circle; through the centre at E, draw Q R parallel to BC.

2. Divide the semicircumference D 1 2 3, &c. to A, into equal parts, and lay the same number of equal parts upon the right line A B, from A towards B; from all the divisions on A C, erect perpendiculars, cutting QR, at the points F, G, H, &c.

3. With the radius E D or E A, on the points F, G, H, &c. as centres, describe arcs 1 f, 2 g, 3 h, &c. take the chords A 1, A 2, A 3. &c. from the semicircle; make the distances 1 f, 2 g, 3 h, &c. respectively to them, then these points will be in the curve of the cycloid.

PROBLEM II.

To describe an epicycloid.

1. Let B A C be the edge of the circle round which the other circle is to turn; through the centre S, and the point A, in the circumference, draw the right line S D: make A D equal to the diameter of the generating circle.

2. Divide the circumference D, 1, 2, 3, &c. into equal parts and place them upon the arc A C, from A to 1, 2, 3, &c. to 8.

3. With the radius S E, on the centre S, describe the arc Q R; through the centre S, and the points 1, 2, 3, &c. draw lines, cutting Q R at F, G, H, &c. and proceed in every other respect, as in the cycloid, and you will get the curve.

END OF THE GEOMETRY.

PRACTICAL ARITHMETIC;

CONTAINING SEVERAL

USEFUL & NEW IMPROVEMENTS

IN THE

PRACTICE OF NUMBERS;

CONSISTING OF FOUR PARTS.

VIZ.

1. WHOLE NUMBERS, : III. DECIMAL FRACTIONS,

II. VULGAR FRACTIONS, IV. DUODECIMALS.

WITH THEIR

APPLICATION TO MANY USEFUL EXAMPLES;

Worked out at full length, to illustrate the whole.

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