| Olinthus Gregory - Plane trigonometry - 1816 - 244 pages
...• — -', 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... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...case the angle DEH and the angle BAC would together make two right angles. THEOREM. In. every triangle **the sum of the three angles is equal to two right angles.** , 41. Demonstration. Let ABC (Jig. 41) be any triangle; produce the side CA toward D, and draw to the... | |
| Nautical astronomy - 1821
...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... | |
| Navigation - 1822 - 64 pages
...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... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...Note II. of his Geometry, gives of the fundamental proposition, that, in every rectilineal triangle, **the sum of the three angles is equal to two right angles.** This demonstration is the more remarkable, as it makes no use of the theory of parallels, but, on the... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...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... | |
| John Radford Young - Geometry, Plane - 1827 - 208 pages
...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... | |
| Ira Wanzer - Arithmetic - 1831 - 396 pages
...acute angle ; and one which is greater than 90 degrees, is said to |-" obtuse. — In every triangle, **the sum of the three angles is equal to two right angles,** or 180 degrees. Right angled triangles are in called because the angle included between lhe base and... | |
| Charles Hutton - Mathematics - 1831
...— — , it will become a sin. A = sin. n . cos. c+sin. c . cos. B. But, in every plane triangle, **the sum of the three angles is equal to two right angles** ; therefore, B and c are equal to the supplement of A : and, consequently, since an angle and its supplement... | |
| Charles Bonnycastle - Geometry - 1834 - 631 pages
...the latter will immediately follow from the principle already demonstrated, that in every triangle **the sum of the three angles is equal to two right angles.** For since the angle at C is a right angle, the sum of the remaining angles will be together equal to... | |
| |