 | Benjamin Greenleaf - 1862 - 532 pàgines
...DAC, and the angle BDA is equal to AD С ; the last two are therefore right angles ; 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 XVI. — THEOREM.... | |
 | Adrien Marie Legendre - 1863 - 464 pàgines
...each to each, the angle ADB is equal to ADC, and the angle DAB is equal to l)AC ; that is, if an are of a great circle be drawn from the vertex of an isosceles spherical triangle to the middle of its base, it wiU be perpendicular to the base, and will bisect the vertical angle of the triangle.... | |
 | Benjamin Greenleaf - 1863 - 504 pàgines
...to DAC, and the angle BDA is equal to ADC ; the last two are therefore right angles ; 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 XVI. — THEOREM.... | |
 | Benjamin Greenleaf - 1868 - 340 pàgines
...to DAC, and the angle BDA is equal to ADC ; the last two are therefore right angles ; 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 XVI. — THEOREM.... | |
 | William Chauvenet - 1871 - 380 pàgines
...angle BAD equal to the angle CAD, and the angle ADB equal to the adjacent angle ADC; therefore, the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base is perpendicular to the base and also bisects the vertical angle. 80. Scholium. This proposition... | |
 | Elias Loomis - 1871 - 302 pàgines
...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 -t perpendicular to the base, and bisects the vertical aigle. GEOMETRY PROPOSITION XVH.... | |
 | William Chauvenet - 1872 - 382 pàgines
...angle BAD equal to the angle CAD, and the angle ADB equal to the adjacent angle ADC; therefore, the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base is perpendicular to the base and also bisects the vertical angle. 80. Scholium. This proposition... | |
 | Adrien Marie Legendre - 1874 - 500 pàgines
...equal, each to each, the angle ADB is equal to AD C, and the angle DAB is equal to DA C ; that is, if an arc of a great circle be drawn from the vertex of an isosceles spherical triangle to the middle of its base, it will be perpendicular to the base, and will bisect the vertical angle of the triangle.... | |
 | Aaron Schuyler - 1876 - 384 pàgines
...equal, since they an opposite the common side AD. . 463. Corollaries. 1. The arc of a great circle drawn from the vertex of an isosceles spherical triangle to the middle point of the base bisects the vertical angle, is perpendicular to the base, and divides the triangle into two symmetrical... | |
 | George Albert Wentworth - 1877 - 426 pàgines
...(7, (since they are homologo'a A of symmetrical &). QED < 746. COROLLARY. The arc of a great circle drawn from the vertex of an isosceles spherical triangle to the middle of the base bisects the vertical angle, is perpendicular to the base, and divides the triangle into... | |
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In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side. 
