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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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Harvard Examination Papers

1873 - 164 pages
...triangular pyramid is a third part of a triangular prism of the same base and altitude. 5. Prove that the sum of the angles of a spherical triangle is greater than two right angles. 6. Given the radius of a sphere = 2 inches. Compute the volume and convex surface. III. 1. If two planes...
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Catalogue - Harvard University

Harvard University - 1876 - 554 pages
...opposite to it in the other. 8. Any side of a spherical triangle is less than the sum of the other two. 9. The sum of the angles of a spherical triangle is greater than two and less than six right angles. 10. The volume of a spherical pyramid is equal to the area of its base...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...angle BAC is greater than the angle ABC. Therefore, in a spherical triangle, etc. PROPOSITION XVII. 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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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 442 pages
...relations polar triangles are often called supplemental triangles. PROPOSITION XVIII. ТНЕOДЕМ. 732. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let ABC be a spherical triangle. We are to prove ZA + ZB + ZC greater...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...theorem AC <^ AB, which is also contrary to the hypothesis. Hence the angle ABC>C. THEOREM XV. 37 1 The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. The sum of the arcs which measure the angles of a spherical triangle...
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The Elements of Plane and Spherical Trigonometry: With the Construction and ...

John Charles Snowball - Trigonometry - 1880 - 240 pages
...В) < \тг. .... COR. 4. a', V, c', being the sides of the polar triangle, . + BC; o?,A + BC<v. 21. The sum of the angles of a spherical triangle is greater than two right angles, and less than six, Let А, Б, О be the, angles, and а, Ъ, с the sides, of a triangle; А', В',...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...theorem AC <^ AB, which is also contrary to the hypothesis. Hence the angle ABC>C. THEOREM XV. 37i The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. The sum of the arcs which measure the angles of a spherical triangle...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1880 - 452 pages
...is greater than the angle ABC. Therefore, in a spherical triangle, etc. PROPOSITION XVII. THEOEEJI. 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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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 292 pages
...spherical polygon of any number of sides, is less than the circumference of a great circle. Proposition 16. Theorem. — The sum of the angles of a spherical triangle is greater than two, and less than six right angles. For an angle of a triangle, together with the opposite side of the...
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A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1883 - 214 pages
...spherical triangle is less than the circumference of a great circle ; that is, less than 360. (/). 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...
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