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" 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 - Side 75
av Benjamin Martin - 1736
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 sider
...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...
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A Concise System of Mathematics ...

Alexander Ingram - 1830 - 458 sider
...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...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 sider
...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...
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The elements of plane trigonometry

John Charles Snowball - 1837 - 322 sider
...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...
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Spherical Trigonometry ...

Isaac Todhunter - 1859 - 156 sider
...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...
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Spherical Trigonometry: For the Use of Colleges and Schools

Isaac Todhunter - 1863 - 182 sider
...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...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 sider
...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...
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Formulæ of plane and spherical trigonometry

William Thomas Read - 1864 - 10 sider
...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...
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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 sider
...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...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 sider
...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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