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
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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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