 | William Chauvenet - Mathematics - 1872 - 382 pages
...of the sphere is less than four right angles 70,. PROPOSITION XXIX.— THEOREM. 87. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. For, denoting the angles of a spherical triangle by A, B, C, and the sides respectively opposite to... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...birectangular, and trirectangular, according to their triedrals. 771. Corollary. — The sum of the angles of a spherical triangle is greater than two, and less than six right angles (591). 772. Corollary An isosceles spherical triangle is 1 equal to its symmetrical, and has equal... | |
 | Harvard University - 1876 - 554 pages
...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 multiplied by one-third of the... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...triangles are often called supplemental triangles. PROPOSITION XVIII. THEOREM. 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 + Z. B + Z. C greater than 2, and lees than 6,... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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 - 1880 - 260 pages
...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... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...angle A = 180°. QED In the same way all the other relations may be proved. THEOREM XXIV. 797. The sum of the three angles of a spherical triangle is greater than a straight angle and less than three straight angles. Proof. Let A, B, and C be the three angles of... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...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°... | |
 | Webster Wells - 1883 - 298 pages
...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°. (g'). If A'B'C' is the polar triangle of ABC, that... | |
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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 + ZG> 180°, and ZA + ZB + ZC<5±0°. Proof. Construct the polar triangle A'B'C', and denote the number... 
