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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 Geometry, Conic Sections, and Plane Trigonometry - Page 187
by Elias Loomis - 1877 - 443 pages
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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
...1816. SPHERICAL TRIGONOMETRY. 1. EVERY plane section of a sphere is a circle. 2. The sum of the three angles of a spherical triangle is greater than two, and less than six, right angles. 3. The angles of a spherical triangle are А, В, С ; the sides respectively opposite to them, (а),...
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Alma Mater, Or, Seven Years at the University of Cambridge, Volume 1

John Martin Frederick Wright - 1827 - 344 pages
...COLLEGE. SPHERICAL TRIGONOMETRY. 1. EVERY plane section of a sphere is a circle. 2. The sum of the three angles of a spherical triangle is greater than two, and less than six, right angles. 3. The angles of a spherical triangle are A, B, C; the sides respectively opposite to them, (a), (b),...
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Alma mater; or, Seven years at the University of Cambridge. By a Trinity-man ...

John Martin F. Wright - 1827 - 638 pages
...COLLEGE. SPHERICAL TRIGONOMETRY. 1. EVERY plane section of a sphere is a circle. 2. The sum of the three angles of a spherical triangle is greater than two, and less than six, right angles. 3. The angles of a spherical triangle are A, B, C ; the sides respectively opposite to them, io), i/l),...
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A London Encyclopaedia, Or Universal Dictionary of Science, Art ..., Volume 10

Thomas Curtis - Aeronautics - 1829
...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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...than two right angles, and less than six right angles. For the arcs which measure the three angles together with the three sides of the polar triangle are equal to three semicircumferences (Г.), or six quadrants : therefore, the former alone are less than six quadrants, and consequently...
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Elements of Spherical Trigonometry

Augustus De Morgan - Spherical trigonometry - 1833 - 40 pages
...asserted. (B.) The greater angle of a spherical triangle is opposite, to the. greater side, and the mm of the angles of a spherical triangle is greater than two and Ins than six right angles. Also lhe sum of any two angles is less than the. third increased by 180°....
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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 180°. The first part appears from...
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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; A', B', C' and a', 6', c, the angles and sides...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...6, 180° — 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...
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