Page:Euclid's Elements 1714 Barrow translation.djvu/22

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10

The firſt Book of

of DE, deſcribe the circle DEH; and let DA ee 2. poſt. be produced to the point G in the circumference thereof. Then AG = CB.

For DG ff 15. def.
g conſtr.
h 2. ax.
k 15. def.
l 1. ax. = DE, and DA g = DC. Wherefore AG b = CE k = BC l = AG. Which was to be done.

The putting of the point A within or without the line BC varies the caſes; but the conſtruction, and the demonſtration, are every where alike.

Schol.

The line AG might be taken with a pair of compaſſes; but the ſo doing anſwers to no Poſtulate, as Proclus well intimates.

PROP. III.

Two right lines, A and BC, being given, from the greater BC to take away the right line BE equal to the leſſer A.

At the point B aa 2. 1. draw the right line BD = A. The circle deſcribed from the center B at the diſtance of BD ſhall cut off BE bb 15. def.
c conſtr.
d 1. ax. = BD c = A d = BE. Which was to be done.

PROP. IV.

If two triangles BAC, EDF, have two ſides of the one BA, AC equal to two ſides of the other ED, DF, each to its correſpondent ſide (that is, BA = ED,

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