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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... "
Elements of Precise Surveying and Geodesy - Page 151
by Mansfield Merriman - 1899 - 261 pages
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Elements of Spherical Trigonometry

Augustus De Morgan - Spherical trigonometry - 1833 - 40 pages
...together are less than a whole circle. In this proposition we must remember (5) that no side or angle of a spherical triangle is greater than two right angles, and that no side or angle can be considered as negative. Now, «, 6, and c being positive, not more. than one...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...proposition asserted. (B.) The greater angle of a spherical triangle is opposite, to the greater side, and the sum of the angles of a spherical triangle is greater than two and less than six right angles. Also the sum of any two angles is less than the, third increased by...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...semicircumference, which is the measure of two right angles ; hence, in the second place, the sum of all the angles of a spherical triangle is greater than two right angles. Cor. 1 . The sum of all the angles of a spherical triangle is not constant, like that of all the angles...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...— c; and the sides of the polar triangle ISO° — ,4, 180° — B, 180° — C. \ 447. Theorem. The sum of the angles of a spherical triangle is greater than two right angles. Demonstration. Let A, B, C be the angles of the spherical triangle. The sides of its polar triangle...
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The elements of plane trigonometry

John Charles Snowball - 1837 - 322 pages
...triangle, V+6'>c'; .-. (тг- А) + (тг-B)>(ж-С); .: тг>A + B-С. Or, A + B - С < тг. 21. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let A, B, С be the angles, and a, b, с the sides of a triangle;...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...180° — c; and the sides of the polar triangle 180° — .#, 180° — B, 180° — C. 447. Theorem. The sum of the angles of a spherical triangle is greater than two right angles. Proof. Let A, B, C be the angles of the spherical triangle. The sides of its polar triangle are 180°...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...Astronomy, which, as a science of observation, depends entirely on angular measurements. PROP. XIV. The sum of the angles of a spherical triangle is greater than two and less than six right angles, For each angle is less than two (note to Prop. 8), hence the sum of...
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A Treatise on Plane and Spherical Trigonometry ...

Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...the sign of the square root appears to be a negative quantity ; but it is really positive. For since the sum of the angles of a spherical triangle is greater than two right angles, but less than six, S is always greater than 90°, and less than 270° ; and therefore cos. S is negative....
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The Elements of Spherical Trigonometry

James Hann - Spherical trigonometry - 1849 - 84 pages
...BС=180°— D; AС=180°— E; A=180— FE; B = 180° — FD; С = 180° — DE. The sum of the three angles of a spherical triangle is greater than two right angles, and less than six right angles. For if a' + b' + c' be the sides of the supplemental or polar triangle,...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...semicircumference. which is the measure of two right angles; hence, in the second place, the sum of all the angles of a spherical triangle is greater than two right angles. Cor. 1. The sum of all the angles of a spherical triangle is not constant, like that of all the angles...
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