7

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PROP. III.

PROP. III. THEOR. If a st. line be divided into any two parts, the rectangle contained by the whole line

and one of the parts, is equal to the rectangle contained by the two parts together with the square of the

aforesaid part.

CON. 46. I, Pst. 2. 31. I.

EXP. 1 Hyp

2 Cone.

DEM. Def. 1. II. Def. 30. I, Ax. 1.

BOOK II.

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PROP. IV. THEOR. If a st. line be divided into any two parts, the square of the whole line equals the squares of the two

parts, together with twice the rectangle contained by the parts.

CON. 46. Pst. 1, 31 I. DEM. 29. I, Def. 30. I, 5. I, Ax. 1. 6. I, Ax. 3. 34. I, 43. I.

Or, Let the line be made up of the parts x + y.

COR. 1.

PROP. IV.

COR. 2,

The square of a line is four times the square of its half.

PROP. IV.

COR. 3. Half the square of a line is equal to double the square of half the line.

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COR. 4. The square of a line will be equal to the sum of the squares of all the parts, together with double the rectangle under every distinct pair of parts.

2.

USE. 1. In Algebra.

To point out a practical way of extracting the square root of a number.