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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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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...measures the angle E ; and AB is the supplement of the arc which measures the nnjrle F. PROPOSITION X. THEOREM The sum of the angles of a spherical triangle, is greater than two, and less than six right angles. Let A, B, and C be the angles of a spherical triangre. The arcs which...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 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 C)orS> 90°and<270°....
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1861 - 244 pages
...measures the anglexE ; and AB is the supplement of the arc which measures the angle F. PROPOSITION X. THEOREM The sum of the angles of a spherical triangle, is greater than two, and less than six right angles. Let A, B, and C be the angles of a spherical triangle. The arcs which...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...subtracting one of the isosceles triangles from the sum of the other two. 794. It has been shown that the sum of the angles of a spherical triangle is greater than the sum of the angles of a plane triangle (771). Since any spherical polygon can be divided into triangles...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 182 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...less than 360°, that is, 360° > (180°— A] -f (180°— B) + (180°— C) or, 360° > 540° — A — B — C, or, by transposition, A _j_ B -f C...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1865 - 186 pages
...180° — 6, 180° — c; and the sides of the polar triangle 180° — ^, 180° — B, 180° — C. 447. Theorem. The sum of the angles of a spherical...these sides, is, by § 440, less than 360°, that is, 360°>(180° — A) -f (180°— B) + (180°— C) or, 360° >540° — A — B— C, or, by transposition,...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 436 pages
...subtracting one of the isosceles triangles from the sum of the other two. 794.. It has been shown that the sum of the angles of a spherical triangle is greater than the sum of the angles of a plane triangle (771). Since any spherical polygon can be divtded into triangles...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 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...by § 440, less than 360°, that is, 360° > (180° — ,2) + (180°— B) + (180°— C) or, 360° >540° — A — B— C, or, by transposition, A +...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...the centre of the sphere is less than four right angles (VI. 70). PROPOSITION XXIX.— THEOREM. 87. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. For, denoting the angles of a spherical triangle by A, B, C, and the...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...the centre of the sphere is less than four right angles (VI. 70). PROPOSITION XXIX.—THEOREM. 87. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. For, denoting the angles of a spherical triangle by A, B, C, and the...
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