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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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Annual Report of the Commissioners ..., Volume 50

1884
...calculated. 5 marks. 9. A spherical triangle is equiangular; prove that it must be equilateral 5 marks. 10. The sum of the angles of a spherical triangle is greater than two right angles, but less than six ; prove this. 6 marks. ENGLISH LITERATURE. One hour and a half allowed. NB — Only...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...angle, .-. 2 "A ABC = lune whose is (A + B 4- C — st. 4.} = lune whose ^ is e. 727. COROLLARY I. The sum of the angles of a spherical triangle is greater than a straight angle and less than 3 straight angles. 728. COROLLARY II. Every angle of a spherical triangle...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...BC, and CA are the measures of the angles AOB, BOC, and COA ( 200). PROPOSITION XV. THEOREM. 668. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let ABC be any spherical triangle. To prove that A + B+C>180, and...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...angle, .-. 2 A" ABC = lune whose is (A + B + C — st. ) = lune whose is e. 727. COROLLARY I. The sum of the angles of a spherical triangle is greater than a straight angle and less than 3 straight angles. 728. COROLLARY II. Every angle of .a spherical triangle...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 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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The Essentials of Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1887 - 196 pages
...greater side ; and conversely. (c) The sum of the sides of a spherical triangle is less than 360. (d) The sum of the angles of a spherical triangle is greater than 180, and less than 540. (e) If A'B'C' is the polar triangle of ABC, ie, if A, B, and C are the...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1888
...dimensions. 3. A triangular pyramid is one third of a triangular prism of the same base and altitude. 4. The sum of the angles of a spherical triangle is greater than two right angles and less than six right angles. 5. The volume of a sphere is equal to the area of its surface multiplied...
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The Elements of Solid Geometry

Robert Baldwin Hayward - Geometry, Solid - 1890 - 130 pages
...may in fact be regarded as the polar triangle of A'BC. V.— Spherical Excess. We can now prove that the sum of the angles of a spherical triangle is greater than two right angles. For the sum of the angles of the triangle and the sides of the polar triangle is equal to six right...
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Elements of Precise Surveying and Geodesy

Mansfield Merriman - Geodesy - 1903 - 274 pages
...triangle is one included by three arcs of great circles. It is a well-known geometrical theorem that the sum of the angles of a spherical triangle is greater than two right angles, and that the excess above two right angles bears the same ratio to a right angle as the area of the...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...717. Sen. Two polar triangles are also called supple* mental triangles. Proposition 14. Theorem. 718. The 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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