 | Harvard University - Geometry - 1899 - 39 pages
...sides of a convex spherical polygon is less than the circumference of a great circle. THEOREM XVI. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 28 THEOREM XVIII, If two arcs of great circles intersect on the surface of a hemisphere, the sum of... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...+ CD + DA < 360°. (By § 458, sum of AAOE, BOC, COD, and DOA is < 360°.) PROP. XX. THEOREM. 596. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 341 o' Given A, B, and C the A, expressed in degrees, of spherical A ABC. To Prove A + B + C > 180°,... | |
 | Mansfield Merriman - Geodesy - 1899 - 276 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 sight angle as the... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...way all the other relations are proved. QED BOOK VIII. SOLID GEOMETRY. PROPOSITION XV. THEOREM. 795. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Let ABC be a spherical triangle, and let A, B, C denote the values of its... | |
 | Mathematics - 1900 - 646 pages
...by side. In one respect; at least, the spherical geometry is the simpler, for it may be shown that the sum of the angles of a spherical triangle is greater than jr. In the plane geometry one must content himself with the theorems that the sum of the angles of... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...triangle are 20°, 90°, 80°. Find the sides of the polar triangle. PROPOSITION XVl. THEOREM 731. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Hyp. ABC is a spherical triangle. To prove ZA+ZB+ZC> 180°, and ZA+ZB+ZC< 540°. Proof. Construct the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...20°, 90°, 80°. Find the sides of the polar triangle. POLAR TRIANGLES PROPOSITION XVI. THEOREM 731. The sum of the angles of a spherical triangle is greater than two and less than six right angks. (729) Hyp. ABC is a spherical triangle. To prove ZA + ZB + ZO 180°, and ZA+ZB+ZC< 540°. Proof.... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...triangles are mutually equilateral ; and conversely. PROPOSITION XV 637. The sum of the angles of any spherical triangle is greater than two, and less than six, right angles. First, let A, B, C be the measures of the angles of a spherical triangle, and a', b', c' the measures... | |
 | George Albert Wentworth - Trigonometry - 1902 - 256 pages
...conversely. 2. The sum of the sides of a spherical triangle is less than 360°. FIO. 79 FIo. 80 3. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. 4. If, from the vertices of a spherical triangle as poles, arcs of great... | |
 | Minnesota - 1903 - 1096 pages
...are unequal, the opposite sides are unequal, and the greater side is opposite the greater angle. 7. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. ENGLISH LITERATURE. 1. Why does the study of English literature have such prominence in our college... | |
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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... 
