| 1884 - 654 pages
...calculated. 5 marks. 9. A spherical triangle is equiangular; prove that it must be equilateral 5 marks. 10. **The sum of the angles of a spherical triangle is greater than two right angles,** but less than six ; prove this. 6 marks. ENGLISH LITERATURE. One hour and a half allowed. NB — Only... | |
| George Bruce Halsted - Geometry - 1885 - 389 pages
...angle, .-. 2 "A ABC = lune whose £ is (A + B 4- C — st. 4.} = lune whose ^ is e. 727. COROLLARY I. **The sum of the angles of a spherical triangle is greater than** a straight angle and less than 3 straight angles. 728. COROLLARY II. Every angle of a spherical triangle... | |
| Webster Wells - Geometry - 1886 - 392 pages
...BC, and CA are the measures of the angles AOB, BOC, and COA (§ 200). PROPOSITION XV. THEOREM. 668. **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. Let ABC be any spherical triangle. To prove that A + B+C>180°, and... | |
| George Bruce Halsted - Geometry - 1886 - 394 pages
...angle, .-. 2 A" ABC = lune whose £ is (A + B + C — st. £) = lune whose £ is e. 727. COROLLARY I. **The sum of the angles of a spherical triangle is greater than** a straight angle and less than 3 straight angles. 728. COROLLARY II. Every angle of .a spherical triangle... | |
| William Chauvenet - Geometry - 1887 - 331 pages
...of a convex spherical polygon is less than the circumference of a great circle. PROPOSITION XVIII. **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. PROPOSITION XIX. Two symmetrical spherical triangles are equivalent.... | |
| Webster Wells - Trigonometry - 1887 - 196 pages
...greater side ; and conversely. (c) The sum of the sides of a spherical triangle is less than 360°. (d) **The sum of the angles of a spherical triangle is greater than** 180°, and less than 540°. (e) If A'B'C' is the polar triangle of ABC, ie, if A, B, and C are the... | |
| Trinity College (Hartford, Conn.) - 1888
...dimensions. 3. A triangular pyramid is one third of a triangular prism of the same base and altitude. 4. **The sum of the angles of a spherical triangle is greater than two right angles** and less than six right angles. 5. The volume of a sphere is equal to the area of its surface multiplied... | |
| Robert Baldwin Hayward - Geometry, Solid - 1890 - 156 pages
...may in fact be regarded as the polar triangle of A'BC. V.— Spherical Excess. We can now prove that **the sum of the angles of a spherical triangle is greater than two right angles.** For the sum of the angles of the triangle and the sides of the polar triangle is equal to six right... | |
| Mansfield Merriman - Geodesy - 1903 - 274 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 right angle as the area of the... | |
| Edward Albert Bowser - Geometry - 1890 - 418 pages
...717. Sen. Two polar triangles are also called supple* mental triangles. Proposition 14. Theorem. 718. **The sum of the angles of a. spherical triangle is greater than two,** and less than six, right angles. Hyp. Let A, B, C denote the three Z s of the spherical A ABC. To prove... | |
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