...to 47°, and the other equal to 105° 30', it will be easy to find the third angle, by recollecting that the sum of the three angles of a triangle is equal to two right angles (Geom. Theorem 15), or 180° ; therefore subtracting the sum of the two given, 47° + 105°...

...in which some property is asserted, and the truth of it required to be proved : thus when it is said that the sum of the three angles of a triangle is equal to two right angles, that is a theorem, the truth of which is demonstrated hy geometry. A set, or collection, of...

...second, by Prob- VIII ; then will the angle HEF be equal to the third angle of the triangleFor, the sum of the three angles of a triangle is equal to two right angles (Bk- I- Th- xvii) ; and the sum of the three angles on the same side of the line DE is equal...

...; but the sum of the two angles BAC, BAD, is equal to two right angles (theorem 1) ; therefore the sum of the three angles of a triangle is equal to two right angles. 80. COROLLARY 1. — If two angles of one triangle be equal to two angles of another triangle,...

...in the first book of the ' Elements.' The proposition required by Euclid is the thirty-second, viz. that the sum of the three angles of a triangle is equal to two right angles ; given that proposition, the difficulty about parallels disappears, inasmuch as their properties...

...also the arc BD is the supplement of the arc AB ; and BCD is the supplement of the angle ACB. 11. The sum of the three angles of a triangle is equal to two right angles, or 180°. Hence, if the sum of any two angles of a triangle be subtracted from 180°, the remainder...

...three angles about the point A, and their sum is plainly two right angles. 37. The mode of proving that the sum of the three angles of a triangle is equal to two right angles, by cutting a piece of card, is called experimental proof. It is of very little use in mathematics,...

...sum of the three angles of any triangle is equivalent to two right angles. 32. Thus we have analyzed the proposition that the sum of the three angles of a triangle is equivalent to two right angles, and found that it resolved itself at last into saying that two lines...

...second, by Prob- VIII ; then will the angle HEF be equal to the third angle of the triangleFor, the sum of the three angles of a triangle is equal to two right angles (Bk- I- Th- xvii) ; and the sum of the three angles on the same side of the line DE fe equal...

...the necessaries of life, or of filling the pocket, it may be difficult to determine. That the s\im of the three angles of a triangle is equal to two right angles, and that the Greeks drove back the Persian invaders, are facts which per se might appear to...