 | 1836 - 366 pages
...determine its area, 38. In a spherical triangle any one side is less than the sum 1833 of the two others, and the sum of the three angles is greater than two right angles, and less than six. 39. By what alteration of the circular parts are Napier's rules applicable to the... | |
 | James Bates Thomson - 1844 - 148 pages
...be less than 90°; while 8 must be between 90° and 270°. By doubling these, we find that 2 S, or the sum of the three angles is greater than two right angles, and less than six; and that 2 S — 2 A, or B+C — A, that is, the excess of the sum of two angles... | |
 | Anthony Dumond Stanley - 1848 - 134 pages
...great circle. PROP. XXHI Each of the angles of a spherical triangle is less than two right angles, and the sum of the three angles is greater than two right angles. Let ABC be a spherical triangle ; each of its angles A, B, and C, is less than two right angles, and... | |
 | James Hann - 1849 - 80 pages
...any plane angle is two right angles, and this is also the limit of any plane face of a solid angle. The sum of the three angles is greater than two right angles and less than six right angles. If the three sides of a spherical triangle he equal, the three [angles... | |
 | Robert Main - 1852 - 186 pages
...angles, together with the third angle of the triangle, are accurately measured, it is always found that the sum of the three angles is greater than two right angles ; and this circumstance is invariably expected, and made in some degree a test of the accuracy of the... | |
 | William Chauvenet - 1871 - 380 pages
...+ C= 540° - («' + b' + c'). But a' + b' + c' < 360° (86); therefore, A + B + C > 180°; that is, the sum of the three angles is greater than two right angles. Also, since each angle is less than two right angles, their sum is less than six right angles. 88.... | |
 | William Chauvenet - 1872 - 382 pages
...C= 540° — (a' + b' + c'). But a' + b' + c' < 360° (86) ; therefore, A + B + C > 180°; that is, the sum of the three angles is greater than two right angles. Also, since each angle is less than two right angles, their sum is less than six right angles. 88.... | |
 | John J. Prince - 1877 - 184 pages
...slightest error, and also as a check to see if the two angles obtained are correct, it is always found that the sum of the three angles is greater than two right angles, which could not occur if the earth was a plane flat surface ; but those of our readers who are conversant... | |
 | Sydney Barber Josiah Skertchly - 1878 - 248 pages
...different shapes. 6. When a triangle is carefully measured on the earth's surface, it is found that the sum of the three angles is greater than two right angles. This can never be the case on a plane surface, but must always be the case on a curved surface. Exact... | |
 | James Gow - 1884 - 350 pages
...of the following kind. In every spherical triangle any two sides are greater than the third (i. 5) : the sum of the three angles is greater than two right angles (i. 11) : equal sides subtend equal angles and the greatest side the greatest angle (i. 8, 9) : the... | |
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C= 540° — (a' + b' + c'). But a' + b' + c' < 360° (86) ; therefore, A + B + C > 180°; that is, the sum of the three angles is greater than two right angles. 
