| Elias Loomis - Conic sections - 1858 - 234 pages
...measures the angle E ; and AB is the supplement of the arc which measures the nnjrle F. PROPOSITION X. **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 triangre. The arcs which... | |
| George Roberts Perkins - Geometry - 1860 - 443 pages
...however easily shown that this is not the case. For (Geom. B. VIII., T. XV.) we know that the sum of all **the angles of a spherical triangle is greater than two right angles,** and less than six right angles. Consequently, A + B + C > 180° and < 540°. And C)orS> 90°and<270°.... | |
| Elias Loomis - Conic sections - 1861 - 244 pages
...measures the anglexE ; and AB is the supplement of the arc which measures the angle F. PROPOSITION X. **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... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...subtracting one of the isosceles triangles from the sum of the other two. 794. 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... | |
| Benjamin Peirce - Geometry - 1869 - 182 pages
...180° — b, 180° — c; and the sides of the polar triangle 180° — ^, 180° — B, 180° — C. **447. Theorem. The sum of the angles of a spherical...less than 360°, that is, 360° > (180°— A] -f** (180°— B) + (180°— C) or, 360° > 540° — A — B — C, or, by transposition, A _j_ B -f C... | |
| Benjamin Peirce - Geometry - 1865 - 186 pages
...180° — 6, 180° — c; and the sides of the polar triangle 180° — ^, 180° — B, 180° — C. **447. Theorem. The sum of the angles of a spherical...these sides, is, by § 440, less than 360°, that is,** 360°>(180° — A) -f (180°— B) + (180°— C) or, 360° >540° — A — B— C, or, by transposition,... | |
| Eli Todd Tappan - Geometry - 1868 - 436 pages
...subtracting one of the isosceles triangles from the sum of the other two. 794.. 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 divtded into triangles... | |
| Benjamin Peirce - Geometry - 1869 - 150 pages
...180° — b, 180° — c; and the sides of the polar triangle 180° — ^, 180° — B, 180°— C. **447. Theorem. The sum of the angles of a spherical...by § 440, less than 360°, that is, 360° > (180°** — ,2) + (180°— B) + (180°— C) or, 360° >540° — A — B— C, or, by transposition, A +... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...the centre of the sphere is less than four right angles (VI. 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...the centre of the sphere is less than four right angles (VI. 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... | |
| |