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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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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...mutually equilateral, and . • . mutually equiangular. (706) 713. COR. 2. 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. POLAR TRIANGLES. V14. One spherical triangle is called the...
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Elementary Geometry

William Chauvenet - 1893 - 340 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...
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...triangle is less than the sum of the other two. SUG. See Art. 388. Ex. 345. 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. Ex. 346. The angles...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...spherical triangle, the angles opposite the equal sides are equal. 754. 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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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...spherical triangle, the angles opposite the equal sides are equal. 509. Tlie 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. 510. If with the vertices of a spherical triangle as poles...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...ABD and ACD are mutually equiangular. § 810 . ' . Z. B = ZCQED 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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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...ABD and ACD are mutually equiangular. § 810 '' ' Z B = Z- C. QED 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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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 396 pages
...are mutually equiangular. Hence, Z. B = Z C. Therefore, etc. QED 714. 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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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 180 pages
...of n sides is greater than 2 n — 4, and less than 2 n, right angles. 6. 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. PROP. XXXI. THEOEEM....
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...ABD and ACD are mutually equiangular. § 810 .'. Z .B = Z C'. QED 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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