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" The sines of the sides of a spherical triangle are to each other as the sines of the opposite angles. Let abc (fig. "
Popular and Mathematical Astronomy, with the principal formulę of Plane and ... - Page 64
by William Thomas READ - 1862
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...angle ; that is, double the sine of that angle measured in the circle ; therefore the sides of the triangle are to each other as the. sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in a circle...
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The Elements of Plane and Spherical Trigonometry: And Its Application to ...

Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...c=log a + 10— cos 6: from this c=760.129. (48.) The sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be a plane triangle (fig. 8.), and BD the perpendicular from B upon the side AC ; then by (470, BD=AB . sin A, also BD=BC...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 168 pages
...secant of one of them takes, may be given to the cosine, cotangent, or cosecant of the other. 2 Th. The sides of a plane triangle are to each other as the sines of the angles opposite to them. In right angled triangles this proposition is obvious: for if the subtense...
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An Essay on the Theory and Practice of Setting Out Railway Curves

William Hill (land surveyor.) - Railroad engineering - 1847 - 32 pages
...angle ; that is, double the sine of that angle measured in the circle ; therefore the sides of the triangle are to each other as the sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in the circle...
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Iconographic Encyclopaedia of Science, Literature, and Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...rfe-f-the angle i«c = 90°; as also bed-^-lhe side ac = 90°. The sines of the sides of a spherical triangle are to each other as the sines of the opposite angles. Let abc (fig. 1 14) be a spherical triangle, whose sphere has its centre in o, and unity for radius. If now...
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Young Scientist: A Practical Journal for Amateurs, Volume 1

1851 - 716 pages
...-f- the angle bac = 90° ; as also bed -j- the side ac = 90°. The sines of the sides of a spherical triangle are to each other as the sines of the opposite angles. Let abc (Jig. 1 14) be a spherical triangle, whose sphere has its centre in o, and unity for radius. If now...
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The Belfast Queen's College Calendar

Queen's University of Belfast - Education, Higher - 1852 - 306 pages
...lines over rugged and uneven ground? 11. The fundamental proposition in plane trigonometry is that the sides of a plane triangle are to each other as the sines of their respective opposite angles; prove this, and state its application to land surveying. 12. Give...
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An elementary course of practical mathematics, Part 3

James Elliot - 1851 - 162 pages
...problem. The rules for both problems are expressed by the following THEOREM : — The Sides of any Plane Triangle are to each other as the Sines of the opposite Angles. NOTE. Since, by the rule, we find the sine of the required angle, and not the angle itself, and since...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...BD : : sine D : sine A ; and therefore, also, BA AD : : sine D : sine B. The above proposition, that the sides of a plane triangle are to each other as the sines- of the opposite angles is a fundamental one in trigonometry, and on it are based all the former observations that have been...
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Iconographic Encyclopaedia of Science, Literature & Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 pages
...de-|-the angle foze — 90 0 ; as also bed-\-i\\z side ac = 90°. The sines of the sides of a spherical triangle are to each other as the sines of the opposite angles. Let abc (fig. 114) be a spherical triangle, whose sphere has its centre in o, and unity for radius. If now...
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