Page:Euclid's Elements 1714 Barrow translation.djvu/32

20 the triangle, BA, CA; but do contain a greater angle, BDC.

Let BD be produced to E. Then is CE + ED a CD, and BD common to both, b then hall be BD  DE+ EC  CD + BD. Again, BA AE a  BE. b therefore BA AC  BE + EC. Wherefore 1. BA + AC BD + DC. 2. The angle BDC c DEC c  A. Therefore the angle BDC  A. Which was to be demontrated.

To make a triangle FKG of three right lines FK, FG, GK, which hall be equal to thee right lines given A, B, C. Of which it is neceary that any two taken together be longer than the third.

From the infinite line DE a take DF, FG, GH equal to the lines given, A, B, C. Then it from the b centers F and G by the ditances of FD and GH, two circles be drawn cutting each other in K, and the right lines KF, KG be joined, the triangle FKG hall be made, c whoe ides FK, FG, GK are equal to the three lines DF, FG, GH d that is to the three lines given A, B, C. Which was to be done.

At a point A in a right line given AB to make a right-lined angle A equal to a right-lined angle given D.

Draw the right