Page:Euclid's Elements 1714 Barrow translation.djvu/25

Rh then the angle ADC b = ACD; as alo, becaue BD c = BC, the angle FDC = b ACD. therefore is the angle FDC d ACD, that is, the angle FDC  ADC. d Which is impoible. 3. Cae. If D falls without the triangle ACB, let CD be joined.

Again the angle ACD e = ADC, and the angle BCD e = BDC. f Therefore the angle ACD BDC, viz. the angle ADC  BDC. Which is impoible. Therefore, &c.

If two triangles ABC, DEF, have two ides AB, AC equal to two ides DE, DF, each to each, and the bae BC equal to the bae EF, then the angles contained under the equal right lines hall be equal, viz. A to D.

Becaue BC a = EF, if the bae BC be laid on the bae EF, b they will agree: therefore whereas AB c = DE, and AC = DF, the point A will fall on D (for it cannot fall on any other point, by the precedent propoition) and o the ides of the angles A and D are coincident; d wherefore thoe angles are equal. Which was to be Dem.

1. Hence, Triangles mutually equilateral, are alo mutually e equiangular.

2. Triangles mutually equilateral, e are equal one to the other.