 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
 | Nathan Scholfield - 1845 - 894 pages
...demonstration proves the angle BAD =DAC, and the angle BDA=ADC. Hence the two last are ri^rht 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 - Geometry - 1845 - 506 pages
...BAD =DAC, and the angle BDA=ADC. Hence the two last are right angles ; hence the arc drawn from Ike 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... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...ADB^ADC, and, Isosceles Triangle. therefore, each is a right angle ; and also DAIi = 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. 455. Corollary. An equilateral spherical triangle is... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...that the angle BAD = DAC, and the angle BDA = ADC. Hence the two last are right angles ; consequently the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to that bose, and bisects the opposite angle. X 2 PROPOSITION XXIX. THEOREM. In any... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...and the angle ADB to the angle ADC ; therefore each of the last two angles is a right angle. Hence 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 vertical angle. PROPOSITION XVII. THEOREM. In a spherical triangle, the greater... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...that the angle BAD=DAC, and the angle BDA - ADC. Hence the two last are right-angles ; consequently 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 XXIX. THEOREM. In any spherical... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...parts (P. 10), the angle BAD=DAC, and BDA— ADC: consequently, ADB and ADC, 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 XII. THEOEEM. In any spherical,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...parts (P. 10), the angle BAD=DAC, and BDA — ADC: consequently, ADB and ADC, 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. BOOK IX. 237 PROPOSITION XII. THEOREM.... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...that the angle BAD = DAC, and the angle BDA = ADC. Hence the two last are right angles ; consequently, 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. THEOREM XIv. In any spherical triangle,... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...and the angle ADB to the angle ADC ; therefore each of the last two angles is a right angle. Hence 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 vertical angle. In a spherical triangle, the greater side is opposite the... | |
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