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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. "
Elements of Geometry - Page 168
by Adrien Marie Legendre - 1841 - 235 pages
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...ACD are mutually equiangular. § 810 • ' • £- B = £- CQED 813. COR. 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...
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Treatise on Elementary Geometry

William Chauvenet - 1905 - 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.—Tf two...
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Plane Trigonometry

Daniel Alexander Murray - 1906 - 466 pages
...isosceles spherical triangle the angles opposite the equal sides are equal. (4) The arc of a great circle 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. (5) If two angles of a spherical triangle are unequal, the...
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Plane [and Spherical] Trigonometry for Colleges and Secondary Schools

Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...isosceles spherical triangle the angles opposite the equal sides are equal. (4) The arc of a great circle 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. (5) If two angles of a spherical triangle are unequal, the...
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Spherical Trigonometry: For Colleges and Secondary Schools

Daniel Alexander Murray - Spherical trigonometry - 1908 - 132 pages
...isosceles spherical triangle the angles opposite the equal sides are equal. (4) The arc of a great circle 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. (5) If two angles of a spherical triangle are unequal, the...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...means of Theorem XIV, Book VI. 4. The base angles of an isosceles spherical triangle are equal. 298 5. The arc drawn from the vertex of an isosceles spherical triangle to the midpoint of the base bisects the vertical angle and is perpendicular to the base. 6. If two angles...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...the vertex of an isosceles spherical triangle is perpendicular to the base and bisects it. Ex. 1527. The arc drawn from the vertex of an isosceles spherical triangle to the mid_point of the base bisects the vertex angle and is perpendicular to the base. Ex. 1528. State and...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...symmetrical if the equal 1x1rts occur in opposite orders. Ex. 98. Prove that the arc of a great circle 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. PROPOSITION XXV. THEOREM...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...from the vertex of the A to the mid-point of the base, and consult Prop. 334. COR. The great circle arc drawn from the vertex of an isosceles spherical triangle to the mid-point of base bisects the vertical angle and is perpendicular to the base. * Proposition 337 Theorem...
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