 | William Mudge, Isaac Dalby, Thomas Colby - Arc measures - 1801 - 690 pages
...Steeple. Frant Steeple. Excess of the Angles of Spherical above those of Plane Triangles. 56. Since the sum of the three angles of a spherical triangle is greater than' two right angles, it follows, that the sum of the three observed angles of each of the following triangles... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...be greater than a serai- . circumference, which is the measure of two right angles ; therefore the sum of the three angles of a spherical triangle is greater than two right angles. 490. Corollary i. The sura of the angles of a spherical triangle is not constant like... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...measure of D, and В С the supplement of the measure of F. PROPOSITION VIII. The sum of the interior angles of a spherical triangle is greater than two, and less than six right angles. For (see last figure) the measures of the angles А, В, С, in the triangle ABC, together with the... | |
 | John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...perimeter and the three angles of a triangle being gives, find each of the sides. TRINITY COLLEGE. 1816. SPHERICAL TRIGONOMETRY. 1. EVERY plane section of...angles. 3. The angles of a spherical triangle are А, В, С ; the sides respectively opposite to them, (а), (Ь), (с); the rad. of the sphere = 1.... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...will be greater than a semicircumference, which is the measure of two right angles ; therefore the sum of the three angles of a spherical triangle is greater than two right angles. 490. Corollary i. The sum of the angles of a spherical triangle is not constant like... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...will be greater than a semicircumference, which is the measure of two right angles ; therefore the sum of the three angles of a spherical triangle is greater than two right angles. 490. Corollary i. The sum of the angles of a spherical triangle is not constant like... | |
 | John Martin Frederick Wright - 1827 - 358 pages
...point of contact and the vertex. 16. Prove that the force tending to the focus of a parabola a -pj. 17. The velocity of a body revolving in a parabola round...A, B, C ; the sides respectively opposite to them, (a), (6), (c) ; the rad. of the sphere = 1. Prove the following theorems : cos. c — cos. ox cos.... | |
 | John Martin Frederick Wright - 1827 - 344 pages
...axis, and find the distance from the centres at which the forces are equal. 19. If the force oc =-^ and a body be projected in any direction, except directly...A, B, C; the sides respectively opposite to them, (a), (b), (c) ; the rad. of the sphere = 1. Prove the following theorems: I. Cos. C = II. cos. c—cos.... | |
 | John Martin Frederick Wright - 1827 - 344 pages
...projection and the particular curve described. • TRINITY COLLEGE. SPHERICAL TRIGONOMETRY. 1. EVEE.Y plane section of a sphere is a circle. 2. The sum...A, B, C ; the sides respectively opposite to them, (a), (b}, (c) ; the rad. of the sphere = 1. Prove the following theorems : cos. c — cos. ax cos.... | |
 | Thomas Curtis - Aeronautics - 1829 - 814 pages
...of D, and В С the supplement of the measure of F. THEOREM XCI. — TKè sum of the interior augles of a spherical triangle is greater than two, and less than six right angles. For (fig. 106, p. III.) the measures of the angles А, В, С, together with the sides of the supplemental... | |
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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... 
