 | Webster Wells - 1883 - 234 σελίδες
...spherical 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°. (gr). If A'B'C' is the polar triangle of ABC, that... | |
 | 1884 - 648 σελίδες
...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.... | |
 | George Bruce Halsted - 1885 - 389 σελίδες
...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 - 1886 - 392 σελίδες
...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 < 540°. Let A'B'C' be the polar... | |
 | George Bruce Halsted - 1886 - 394 σελίδες
...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, William Elwood Byerly - 1887 - 342 σελίδες
...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. PROPOSITION XX. If two arcs of... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 σελίδες
...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. PROPOSITION XX. If two arcs of... | |
 | Webster Wells - 1887 - 196 σελίδες
...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... | |
 | William Chauvenet - 1888 - 826 σελίδες
...of the corresponding polyedral angle at the centre of the sphere is less than four right angles (VI. 70). PROPOSITION XXIX.— THEOREM. 87. The sum of...angles. For, denoting the angles of a spherical triangle A' by A, B, C, and the sides respectively opposite to them in its polar triangle by a', b', c', we... | |
 | Trinity College (Hartford, Conn.) - 1888 - 978 σελίδες
...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... | |
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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... 
