...The sacred import of the equilateral triangle has already been explained. Now, as the sum of all the angles of any triangle is equal to two right angles, or 180°, it follows that each of the equal angles of any equilateral triangle is equal to one (180° \ — s—...

...this and some other initial axioms he could deduce many facts about geometrical figures (for example, "the sum of the three angles of any triangle is equal to the sum of two right angles"). Now one of his axioms (about parallel lines) did not seem very obvious...

...offered solution. * Kritik dr Vern., p. 32. For an illustration, let the following theorem be taken : " The sum of the three angles of any triangle is equal to two right angles." We draw or conceive a particular triangle for the sake of the demonstration ; and, having gone through...

...opposite ; and the sum of the lesser angles of each, being each equal to a right angle, it follows that the sum of the three angles of any triangle is equal to two right angles. Thus are all of the fundamental propositions of geometry rigorously demon; strated without the aid...

...The exterior angle of a triangle is equal to the sum of the two interior and opposite angles ; and the sum of the three angles of any triangle is equal to two right angles. The three larger angles of a quadrilateral are respectively twice, four times and five times the least....

...the other two angles must in either case be acute. This follows from the fact (proved in i, 32) that the sum of the three angles of any triangle is equal to two right angles. i DEFINITION 22. Quadrilaterals are now classified with reference to the attributes ' equilateral '...