...Proportion, which expreftes the Properties of any Subject ; as when we fay, that in any Right lined Triangle, the Sum of the three Angles is equal to two right ones, and that i* a fpherital Triangle, the Summ of three Angle t is greater than two right ones* An...

...transformed, by • — -', it will become gin c = sin A cos H + sin it cos A, Now, since in every plane triangle, the sum of the three angles is equal to two right angles, A + B = supplement of c ; and, since an angle and its supplement have the same sine, it follows that...

...therefore the lines AB, CD cannot meet, and must be parallel. XXXV. In any right lined triangle ABC, the sum of the three angles is equal to two right angles. To prove this, you must produce BC (in ihefig. art. 33,) towards T), then (by'irt. 33) the external...

...In that case, DEH and BAC would be together equal to two right angles. PROPOSITION XXVII. THEOREM. In every triangle, the sum of the three angles is equal to two right angles. Let ABC be any triangle. Produce the side CA towards D ; and, at the point A, draw AE parallel to BC....

...sides. 196. The longest side bf any triangle is opposite the greatest angle. 195. In all plane triangles the sum of the three angles is equal to two right angles, or 180 deg. 198. An angle in a segment less than a semicircle is greater than a right angle. 197. An...

...equal to two right angles ; therefore, in every triangle the sum of the three angles is equal to too right angles. We see by this that the theorem, considered...propositions, but is deduced immediately from the principle of homogeneity, a principle which exists in every relation among quantities of whatever kind. But we proceed...

...this case the angle DEH and the angle BAC would together make two right angles. 27 THEOREM. A. ' 72. In every triangle the sum of the three angles 'is equal to two right angles. Pig. 41. Demonstration. Let ABC (fig. 41) be any triangle ; produce the side CA toward D, and draw...

...equal. In this case the angle DEH and the angle BA C would together make two right angles. THEOREM. 72. In every triangle the sum of the three angles is equal to tm* right angles. Fig.41. Demonstration. Let ABC (fig. 41) be any triangle; produce the side CA toward...

...exterior angle ACD. Cor. 1. Since the angle ACD together with ACB make two right angles, it follows that in every triangle the sum of the three angles is equal to two right angles. Cor. 2. Hence if two angles in one triangle be equal to two in another, the third angle in the one...

...three angles of the triangle ABC make up the same sum as the three angles CAB, BAE, EAD ; hence, (31.) the sum of the three angles is equal to two right angles. 73. Cor. I. Two angles of a triangle being given, or merely their sum, the third will be found by subtracting...