 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 162by Adrien Marie Legendre - 1819 - 208 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1822 - 394 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, John Farrar - Geometry - 1825 - 294 pages
...then cannot be supposed unequal to AC; therefore the sides AB, AC, opposite to the equal angles B, C, are equal. 484. Scholium. It is evident, from the...triangle to the middle of the base, is perpendicular to this base, and divides the angle opposite into two equal parts. I s~ THEOREM. I ' 485. In any spherical... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...then cannot be supposed unequal to AC; therefore the sides AB, AC, opposite to the equal angles B, C, are equal. 484. Scholium. It is evident, from the...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, John Farrar - Geometry - 1825 - 280 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... | |
 | Dionysius Lardner - Plane trigonometry - 1828 - 434 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 - 394 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 - 216 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... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...then cannot be supposed unequal to AC ; therefore the sides AB, AC, opposite to the equal angles B, C, are equal. 484. Scholium. It is evident, from the...triangle to the middle of the base, is perpendicular to this base, and divides the angle opposite into two equal parts. THEOREM. . 232. 485. In any spherical... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 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... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 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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