 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
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...is equal 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. • 553. In a spherical triangle,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...equal to 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. 553. In a spherical triangle,... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...equal to ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of au isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle. PROPOSITION XVI. — THEOREM. 553. In a spherical triangle,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...is equal 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. 553. In a spherical triangle,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...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. 553. In a spherical triangle,... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...is equal 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. 553. In a spherical triangle,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...equiangular, we have the 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...triangle to the middle of the base is perpendicular to the base and also bisects the vertical angle. 80. Scholium. This proposition and its corollary may... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...and tho 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. THEOREM. In... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...equiangular, we have the 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...triangle to the middle of the base is perpendicular to the base and also bisects the vertical angle. 80. Scholium. This proposition and its corollary may... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...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.... | |
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