 | Benjamin Peirce - Geometry - 1871 - 192 pages
...and the angle E, are respectively supplements of each other. 446. Corollary. If therefore we denote the angles of a spherical triangle by A, B, C ; and the sides respecf'Voly opposite by a, b, c ; the angles of the polar triangle must be 180° — a, 180° —... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...subtracting one of the isosceles triangles from the sum of the other two. *794i. 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... | |
 | 1873 - 192 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.... | |
 | Harvard University - 1876 - 554 pages
...circles is measured by an arc drawn from the vertex as a pole, and included between its sides. Prove. 9. The sum of the angles of a spherical triangle is greater than two right angles ; and either angle is greater than the difference between the turn of the other two and... | |
 | George Albert Wentworth - Geometry - 1877 - 436 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 than 2, and less than 6, right... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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 measure the angles A, B, and... | |
 | 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 together with the three sides... | |
 | 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 together with the three sides... | |
 | John Charles Snowball - Trigonometry - 1880 - 256 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;... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...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 polar triangle, is equal to 180° (IX.... | |
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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... 
