| Olinthus Gregory - 1816 - 276 pagine
...• — -', 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 - 1819 - 574 pagine
...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... | |
| 1821 - 708 pagine
...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... | |
| George Watson - 1822 - 72 pagine
...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 - 1822 - 394 pagine
...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 - 1825 - 294 pagine
...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 - 1827 - 228 pagine
...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 - 1831 - 408 pagine
...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 - 1831 - 656 pagine
...— — , 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 - 1834 - 678 pagine
...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... | |
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