 | William Frothingham Bradbury - 1877 - 262 pàgines
...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... | |
 | Elias Loomis - 1877 - 458 pàgines
...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,... | |
 | George Albert Wentworth - 1877 - 416 pàgines
...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... | |
 | William Frothingham Bradbury - 1880 - 260 pàgines
...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... | |
 | Simon Newcomb - 1881 - 418 pàgines
...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 - 1882 - 286 pàgines
...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... | |
 | Webster Wells - 1883 - 298 pàgines
...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... | |
 | Webster Wells - 1886 - 392 pàgines
...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... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 pàgines
...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... | |
 | Edward Albert Bowser - 1890 - 420 pàgines
...polar triangles are also called supplemental triangles. Proposition 14. Theorem. 718. TJie 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 A + B + C > 180° and... | |
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... the sum of the three angles of a spherical triangle is greater than two right angles. 
