 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
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...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... | |
 | Elias Loomis - Conic sections - 1877 - 458 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 tJie base is perpendicular to the base, and also bisects the vertical angle. PROPOSITION XVI. THEOREM.... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...(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 two symmetrical... | |
 | Elias Loomis - 1880 - 456 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 also bisects the vertical angle. PROPOSITION XVI. THEOREM. In a spherical triangle, the... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...triangles ABD, ADC, AB = AC, by hypothesis; AU = AD ; BD = DC, by construction ; B = C. QED Cor.—The arc 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 two symmetrical... | |
 | William Chauvenet - Geometry - 1884 - 384 pages
...angle BAD equal to the angle CAD, and the angle ADB equal to the adjacent angle ADC; therefore, the are 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 and its corollary may... | |
 | William Chauvenet - Geometry - 1887 - 342 pages
...— In an isosceles spherical triangle the angles opposite the equal sides are equal. 2. Theorem. — The arc drawn from the vertex of an isosceles spherical triangle to the middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem. — If... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...Theorem.—In an isosceles spherical triangle the angles opposite the equal sides are equal. 2. Theorem.—The arc drawn from the vertex of an isosceles spherical triangle to the middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem.—If two... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...Theorem.—In an isosceles spherical triangle the angles opposite the equal sides are equal. 2. Theorem.—The arc drawn from the vertex of an isosceles spherical triangle to the middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem.—If two... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...angle BAD equal to the angle CAD, and the angle ADB equal to the adjacent angle ADC; therefore, the are 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 and its corollary may... | |
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