In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side. Elements of Geometry - Page 168by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...then cannot be supposed unequal to AC; therefore the sides AB, AC, opposite to the equal angles It. **C, are equal. 484. Scholium. It is evident, from the...triangle to the middle of the base, is perpendicular** lo this base, and divides the angle opposite into two equal parts. THEOREM. Fig. 332. 485. In any spherical... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...demonstration proves the angle BAD=DAC, and the angle BDA=ADC. Hence the two 172 last are right angles ; hence **the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is** at right angles to that base, and bisects the opposite angle. PROPOSITION XVI. THEOREM. In a spherical... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...BC, are equal to the two AC, BC ; and the angle OBC contained by the first is equal to the angle ACB **contained by the second. Consequently the two triangles...and divides the angle opposite into two equal parts.** I s~ THEOREM. I ' 485. In any spherical triangle ABC (fig. 232), if the angle A is greater than the... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...cannot be supposed unequal to AC; therefore the sides AB, AC, opposite to the equal angles B, C, arc **equal. 484. Scholium. It is evident, from the same...from the vertex of an isosceles spherical triangle to** ihe middle of the base, is perpendicular to this base, and divides the angle opposite into two equal... | |
| Adrien Marie Legendre - 1825 - 224 pages
...DAC, and the angle BDA = ADC. Consequently the two last arc right angles ; therefore, the arc draxn **from the vertex of an isosceles spherical triangle to the middle of** iht base, is perpendicular to this base, and divides the angle opposite into two equal parts. THEOREM.... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 317 pages
...sides, they will be symmetrically equal, and the proposition has been already proved. (152.) Cor. Hence **the arc drawn from the vertex of an isosceles spherical triangle to the** point of bisection of the base, bisects the vertical angle, and is perpendicular to the base. * In... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...demonstration proves the angle BAD = DAC, and the angle BDA— ADC. Hence the two last are right angles ; hence **the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is** at right angles to that base, and bisects the vertical angle. PROPOSITION XIV. THEOREM. In any spherical... | |
| Benjamin Peirce - Geometry - 1837 - 159 pages
...Corollary. Also the angle ADB = ADC, and, therefore, each is a right angle ; and also DAB = DAC, that . is> **The arc, drawn from the vertex of an isosceles spherical...triangle to the middle of the base, is perpendicular to** the base, and bisects the angle at the vertex. 454. Corollary. An equilateral spherical triangle is... | |
| Nathan Scholfield - Conic sections - 1845
...demonstration proves the angle BAD =DAC, and the angle BDA— ADC. Hence the two last are right angles ; hence **the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is** at right angles to the base, and bisects the vertical angle. PROPOSITION XVI. THEOREM. In any spherical... | |
| Nathan Scholfield - Conic sections - 1845 - 232 pages
...demonstration proves the angle BAD =DAC, and the angle BDA=ADC. Hence the two last are right angles ; hence **the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is** at right angles to the base, and bisects the vertical angle. PROPOSITION XVI. THEOREM. In any spherical... | |
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