The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...

PROPOSITION XVII. THEOREM.

TWo Angles of any Triangle, are less than Two Right Angles.

Let ABC be the proposed Triangle; I say that Two of the Angles taken to∣gether BAC, BCA, are less than Two Right Angles. Continue the Side CA, to D.

Demonstration. The Interiour Angle C, is less than the Exteriour BAD, (by the 16^th.) Add to both the Angle BAC; the Angles BAC, BCA, shall be less than the Angles BAC, BAD; which latter are equal to Two Right (by the 13^th.) Therefore the Angles BAC, BCA, are less than Two Right.

I might Demonstrate after the same manner, that the Angles ABC, ACB, are less than two Right, by continuing the Side BC.

Coroll. If one Angle of a Triangle be either Right or Obtuse, the other Two shall be Acute.

This Proposition is necessary to Demon∣strate those which follow.