...angles ; but this triangle represents all triangles ; therefore we infer the general truth — the sum of the three angles of a triangle is equal to two right angles. 3. Self, as reason, verifies his conclusions. By analysis we reduce our arguments to judgments,...

...doubt. We may never have seen London, but we have not a whit more doubt that London exists than we have that the sum of the three angles of a triangle is equal to two right angles. We never saw Napoleon the First, but we are not less certain that Napoleon lived than we are...

...third side, and their difference is less than the third side. PROPOSITION XXIII. THEOREM. -/ 138. The sum of the three angles of a triangle is equal to two right angles. A Let ABC be a triangle. To prove Z B + Z BCA + ZA = 2 rt. A. Proof. Suppose CE drawn II to...

...Thales can be drawn from the preceding notices. First inference. — Thales must have known the theorem that the sum of the three angles of a triangle is equal to two right angles. Pamphila, in (d), refers to the discovery of the property of a circle that all triangles described...

...side of a triangle is less than the sum of the other two, and greater than their difference. 98. The sum of the three angles of a triangle is equal to two right angles. Sug. Consult Theorems 58 and 87. 99. If one side of a triangle be extended, the exterior angle...

...triangle, formed by extending the sides in the same order, is equal to six right angles. PROP. XVII. The sum of the three angles of a triangle is equal to two right angles. PROP. XVIII. The sum of any two angles of a triangle is equal to the supplement of the third...

...the place of mathematieal demonstration. No experimental process can ever establish the general truth that the sum of the three angles of a triangle is equal to two right angles. We should not confound " geometrical recreations " with geometrical science. — (P.) f Isoperimetric...

...the place of mathematical demonstration. No experimental process can ever establish the general truth that the sum of the three angles of a triangle is equal to two right angle?. We should not confound " geometrical recreations " with geometrical science.—(P.) f Isoperimetric...

...equal to the three angles of the triangle, and their sum is equal to two right angles. Therefore, the sum of the three angles of a triangle is equal to two right angles. On one side of a triangle (Fig. 50) construct a triangle equal to the first, with opposite...

...axioms, and, in short, came to make perfect demonstrations. In this way he arrived unaided at the theorem that the sum of the three angles of a triangle is equal to two right angles. His father caught him in the act of studying this theorem, and was so astonished at the sublimity...