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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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...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 - 359 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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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 - 150 pages
...180° — b, 180° — c; and the sides of the polar triangle 180° — .#, 180° — B, 180° — C. 447. Theorem. The sum of the angles of a spherical...440, less than 360°, that is, 360° >(180° — A) + (180°— B) + (180°— C) or, 360° >540° — A — B— C, or, by transposition, A + B + C >...
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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 - 194 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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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 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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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852
...circumstances ? What point in Reaumur's and in Centigrade scale correspond to 44° Fahrenheit. (8.) The sum of the angles of a spherical triangle is greater than two right angles, and less than six. Show that the angles at the base of an isosceles triangle are equal. (9.) Express...
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General Report on Public Instruction in the Bengal Presidency

Education - 1852
...all circumstances ? What point in Reaumur's and in Centigrade scale correspond to 44° Fahrenheit. 8. The sum of the angles of a spherical triangle is greater than tno right angles, and less than six. Show that the angles at the base of an isosceles triangle are...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 235 pages
...however easily shown that this is not the case. For (Geom. B. VIII., T. XV.) we know that the sum of all the angles of a spherical triangle is greater than two right angles, and less than six right angles. Consequently, A + B + C > 180° and < 540°. And rS> 90°and<270°....
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