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" The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC... "
An Elementary Treatise on Plane and Solid Geometry - Page 138
by Benjamin Peirce - 1871 - 150 pages
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Bulletin of the American Mathematical Society

Mathematics - 1900
...by side. In one respect; at least, the spherical geometry is the simpler, for it may be shown that the sum of the angles of a spherical triangle is greater than jr. In the plane geometry one must content himself with the theorems that the sum of the angles of...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...triangle are 20, 90, 80. Find the sides of the polar triangle. PROPOSITION XVl. THEOREM 731. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Hyp. ABC is a spherical triangle. To prove ZA+ZB+ZC> 180, and ZA+ZB+ZC<...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...20, 90, 80. Find the sides of the polar triangle. POLAR TRIANGLES PROPOSITION XVI. THEOREM 731. The sum of the angles of a spherical triangle is greater than two and less than six right angks. (729) Hyp. ABC is a spherical triangle. To prove ZA + ZB + ZO 180,...
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Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1902 - 256 pages
...conversely. 2. The sum of the sides of a spherical triangle is less than 360. FIO. 79 FIo. 80 3. The sum of the angles of a spherical triangle is greater than 180 and less than 540. 4. If, from the vertices of a spherical triangle as poles, arcs of great...
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Executive Documents, Minnesota ..., Volume 1

Minnesota - 1903
...are unequal, the opposite sides are unequal, and the greater side is opposite the greater angle. 7. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. ENGLISH LITERATURE. 1. Why does the study of English literature have...
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Five-place Logarithmic and Trigonometric Tables

George Albert Wentworth, George Anthony Hill - Logarithms - 1903 - 348 pages
...conversely. 2. The sum of the sides of a spherical triangle is less than 360. Fio. 79 FIG. 80 3. The sum of the angles of a spherical triangle is greater than 180 and less than 540. 4. If, from the vertices of a spherical triangle as poles, arcs of great...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...spherical triangles each of which is the polar triangle of the other. PROPOSITION XIV. THEOREM 783. The sum of the angles of a spherical triangle is greater than 180, and less than 540. \b <*] ^0 ' a' Given the spherical triangle ABO. To prove A + B + 0 > 180...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...spherical triangles each of which is the polar triangle of the other. PROPOSITION XIV. THEOREM 783. The sum -of the angles of a spherical triangle is greater than 180, and less than 540. Given the spherical triangle ABO. To prove A + B + C > 180 and < 540....
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The Elements of Solid Geometry

Charles Davison - Geometry, Solid - 1905 - 140 pages
...angles, .'. L HOK + L B'OC' = two right angles, .'. A + a' = two right angles, etc. 106. PROP. 70. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Since A+a' = B + 6' = C + c' = two right angles, .'. A + B + C = six...
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School Science and Mathematics, Volume 12

Education - 1912 - 916 pages
...spherical triangle is measured by the supplement of the opposite side of its polar triangle. Corollary i. The sum of the angles of a spherical triangle is greater than one, and less than three straight angles. Corollary 2. The sum of the dihedral angles of a trihedral...
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