Page:Euclid's Elements 1714 Barrow translation.djvu/29

Rh Schol.

If to any right line GH, and in it a point A, two right lines being drawn EA, AF, and not taken on the fame hde,make the vertical (or oppoite) angles D and B equal, thoe right lines EA, AF, do meet directly and make one trait line.

For two right angles are a equal to the angle * T * D-^AtfrB A. b therefore, EA, AF, are in a b x 4- *• trait line. Which was to be demontrated.

Schol.

If four right lines EA, EB, EC, ED, proceeding from one point E, make the angles vertically oppoite equal the one to the other, each two lines, AE, EB, and CE, ED, are placed in one trait line.

For becaue the angle AEC + AED + CEB + DEB a = to 4 right angles, therefore the angleAEC + AED b = CEB + DEB = to two right angles, c therefore CED and AEB are, trait lines. Which was to be demontrated.

One ide BC of any triangle ABC being produc'd, the outward angle ACD will be greater then either of the inward and oppoite angles CAB, CBA.

Let the right lines AH, BE a biect the ides AC, BC; b produce EF = BE, and HI,