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" 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 + ZG> 180°, and ZA + ZB + ZC<5±0°. Proof. Construct the polar triangle A'B'C', and denote the number... "
Alma Mater, Or, Seven Years at the University of Cambridge - Page 263
by John Martin Frederick Wright - 1827
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An Account of the Operations Carried Out for Accomplishing a ..., Volume 2

William Mudge, Isaac Dalby, Thomas Colby - Arc measures - 1801 - 690 pages
...Steeple. Frant Steeple. Excess of the Angles of Spherical above those of Plane Triangles. 56. Since the sum of the three angles of a spherical triangle is greater than' two right angles, it follows, that the sum of the three observed angles of each of the following triangles...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...be greater than a serai- . circumference, which is the measure of two right angles ; therefore the sum of the three angles of a spherical triangle is greater than two right angles. 490. Corollary i. The sura of the angles of a spherical triangle is not constant like...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...measure of D, and В С the supplement of the measure of F. PROPOSITION VIII. The sum of the interior angles of a spherical triangle is greater than two, and less than six right angles. For (see last figure) the measures of the angles А, В, С, in the triangle ABC, together with the...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...triangle being gives, find each of the sides. TRINITY COLLEGE. 1816. SPHERICAL TRIGONOMETRY. 1. EVERY plane section of a sphere is a circle. 2. The sum...angles. 3. The angles of a spherical triangle are А, В, С ; the sides respectively opposite to them, (а), (Ь), (с); the rad. of the sphere = 1....
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...will be greater than a semicircumference, which is the measure of two right angles ; therefore the sum of the three angles of a spherical triangle is greater than two right angles. 490. Corollary i. The sum of the angles of a spherical triangle is not constant like...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...will be greater than a semicircumference, which is the measure of two right angles ; therefore the sum of the three angles of a spherical triangle is greater than two right angles. 490. Corollary i. The sum of the angles of a spherical triangle is not constant like...
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Alma mater; or, Seven years at the University of Cambridge. By a Trinity-man ...

John Martin F. Wright - 1827 - 632 pages
...of projection and the particular curve described. TRINITY COLLEGE. SPHERICAL TRIGONOMETRY. 1. EVERY plane section of a sphere is a circle. 2. The sum...A, B, C ; the sides respectively opposite to them, io), i/l), (c) ; the rad. of the sphere = 1. Prove the following theorems : cos. c — cos. a xcos....
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A London Encyclopaedia, Or Universal Dictionary of Science, Art ..., Volume 10

Thomas Curtis - Aeronautics - 1829 - 814 pages
...of D, and В С the supplement of the measure of F. THEOREM XCI. — TKč sum of the interior augles of a spherical triangle is greater than two, and less than six right angles. For (fig. 106, p. III.) the measures of the angles А, В, С, together with the sides of the supplemental...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...(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 180°. The first part appears from...
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The elements of plane trigonometry

John Charles Snowball - 1837 - 322 pages
...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; A', B', C' and a', 6', c, the angles...
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