Alg. & Arith. Hyp.

Alg.

Another form of Alg. and Arith. illustration. Let

SCH.

GEN. USE AND APP. OF PROP. I—X.

PROP. X.

103

Arith.

104

When lines are expressed numerically.

PROP. X.

1o. Given the sum S, and difference D, of two magnitudes, AB the greater and CD the less; to find the magnitudes themselves.

2. If the Area of a rectangle be divided by one side, the quotient will give the other.

3. There are five quantities depending on a rectangle, any two of which being given, the sides of the rectangle can

be found.

BOOK II.

105

PROP. XI. PROB. To divide a line into two parts, so that the rectangle contained by the whole and one of the

parts shall be equal to the square of the other part.

SOL. 46. I, 10. I, 3. I. Pst. 1. 2.

DEM. 6. II, 47. I, Ax. 3. 1, Def. 30. I.

CoR. 1. To cut a line in extreme and mean ratio, it must first be produced in extreme and mean ratio.

2.

When a line is cut in extreme and mean ratio the rectangle

8.

A line being cut in extreme and mean ratio, the rectangle under its segments equals the difference between their

squares.