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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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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 393 pages
...SCH. Two polar triangles are also called supplemental triangles. Proposition 14. Theorem. 718. TJie sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Hyp. Let A, B, C denote the three Z s of the spherical A ABC. To prove...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 426 pages
...a spherical polygon is at a quadrant's distance from every point in the side. PROPOSITION XI. 57O. Theorem : The sum of the angles of a spherical triangle is greater than two, and less than six right angles. Statement : Let ABC be any spherical triangle. The sum of its angles...
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Year Book ... with Announcements

Mining schools and education - 1891 - 862 pages
...triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. 6. The sum of the angles of a spherical triangle is greater than two and less than six right angles. ?. The area of a spherical triangle, expressed in spherical degrees,...
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An Introduction to Spherical and Practical Astronomy

Dascom Greene - Astronomia esferica y practica - 1892 - 176 pages
...middle meridian. SPHEKICAL EXCESS or TRIANGLES ON THE EARTH'S SURFACE. 159. It is shown in geometry that the sum of the angles of a spherical triangle is greater than two right angles, and that the excess of this sum over two right angles is to eight right angles as the area of the triangle...
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The Elements of Solid Geometry

William C. Bartol - Geometry, Solid - 1893 - 106 pages
...right angles. Use the diagram of (209), and complete the demonstration by (45). PROPOSITION XXXIV. 211. THEOREM. The sum of the angles of a spherical triangle is greater than 180 and less than 5J THE ELEMENTS OF SOLID GEOMETRY. Now, A = 180 - B'C' . . . (205) and B = 180...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 148 pages
...Scholium. Polar triangles are sometimes called supplementary triangles. PROPOSITION XII. THEOREM. 280. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Notation. Same as in 278. To prove A + B+O 180 < 540. Proof....
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...of a convex spherical polygon is less than the circumference of a great circle. PROPOSITION XVIII. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. PROPOSITION XIX. Two symmetrical spherical triangles are equivalent....
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...sides of a convex spherical polygon is less than 360, or four right angles. PROPOSITION XXVII. 688. Theorem. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Let ABC represent a spherical triangle. To prove that the sum 0} the...
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...sides of a convex spherical polygon is less than the circumference of a great circle. PROPOSITION XXVI. The sum of the angles of a spherical triangle is greater than two and less than six right angles. PROPOSITION XXVII. Two symmetrical spherical triangles are equal in...
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Bulletin of the American Mathematical Society

American Mathematical Society - Mathematics - 1905
...the triangle can be read off as L. e., p. 595. pure spherics. The proof of the theorem ( 567) — the sum of the angles of a spherical triangle is greater than two and less than six right angles — assumes that a spherical triangle is always positive. The theorem...
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