 The three angles of a spherical triangle are together greater than two right angles and less than six right angles. Let A, B, C be the angles of a spherical triangle ; let a', b', o' be the sides of the polar triangle. Then by Art. 30, a...  Spherical trigonometry - Pàgina 75per Benjamin Martin - 1736Visualització completa - Sobre aquest llibre
 | Pierce Morton - 1830 - 584 pàgines
...measured over that surface, is the spherical arc between them. See Book I. prop. 10. Scholium. PROP. 10. The three angles of a spherical triangle are together greater than two right angles, and less than six right angles. For the arcs which measure the three angles together with the three sides... | |
 | Alexander Ingram - 1830 - 458 pàgines
...is opposite. Cor. Hence these two triangles are called supplemental or polar triangles. PROP. XIII. The three angles of a spherical triangle are together greater than two and less than six right angles. Cor. 1. The three angles, together with twice the supplement of the... | |
 | 1835 - 684 pàgines
...measured over that surface, is the spherical arc between them. See Book I. prop. 10. Scholium. PROP. 10. The three angles of a spherical triangle are together greater than two right angles, and less than six right angles. For the arcs which measure the three angles together with the three sides... | |
 | John Charles Snowball - 1837 - 322 pàgines
...2 о соs(л - Д) .cos (л - С) cos 2 . а а And sin а = 2 sin - . cos 2 2 *D NOTE. Since the angles of a spherical triangle are together greater than two right angles and less than six, S' is greater than one right angle and less than three, and its cosine is therefore... | |
 | Isaac Todhunter - 1859 - 156 pàgines
...circumference of a great circle. This follows from Euclid, xi. 21, in the manner shewn in Art. 30. 32. The three angles of a spherical triangle are together greater than two riglit angles and less than six right angles. Let A, B, C be the angles of a spherical triangle; let... | |
 | Isaac Todhunter - 1863 - 182 pàgines
...circumference of a great circle. This follows from Euclid, xi. 21, in the manner shewn in Art. 30. 32. The three angles of a spherical triangle are together greater than two right angles and less than six right angles. Let A, B, C be the angles of a spherical triangle; let of, b', c be the... | |
 | Woolwich roy. military acad - 1864 - 588 pàgines
...AC equals 100 feet. PURE MATHEMATICS. Section II. 12 to 11 PM REV. CANON HEAVISIDE, MA 1. Show that three angles of a spherical triangle are together greater than two right angles, and less than six right angles. If A, B, C be the angles of a spherical triangle, (r) the radius of the... | |
 | William Thomas Read - 1864 - 10 pàgines
...are equal to one another. The greater side of every spherical triangle is opposite the greater angle. The three angles of a spherical triangle are together greater than two, and less than six, righi angles. In the polar triangle (a), the angular points of the polar triangle... | |
 | Braithwaite Arnett - 1874 - 130 pàgines
...Hydrometer, and its use in comparing the specific gravities of two liquids. PURE MATHEMATICS. 1. Prove that the three angles of a spherical triangle are together greater than two right angles, and less than six right angles. 2. If ABC be a spherical triangle, prove that sin A _ sin-B _ sin C sina... | |
 | Henry Major - 1876 - 784 pàgines
...conld be no other form. 10. Three angles of every plaue triangle are together=two right angles, while three angles of a spherical triangle are together greater than two right angles. In trigonometrical surveys it has been observed that the sum of three angles of triangles drawn on... | |
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