 | 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... | |
 | Charles Davies - Geometry, Analytic - 1836 - 370 pages
...the axis of ordinates, the angle API) is equal to PA Y : that is, equal to /3 — *. Now, since the sides of a triangle are to each other as the sines of their opposite angles, we have, PD : AD : : sin * : sin (/3 - *). But PD is to AD, as any ordinate... | |
 | Charles Davies - Geometry, Analytic - 1838 - 366 pages
...the axis of ordinates, the angle APD is equal to PA Y : that is, equal to ft — *. Now, since the sides of a triangle are to each other as the sines of their opposite angles, we have, PD : AD : : sin * : sin (ft — *). But PD is to AD, as any ordinate... | |
 | 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... | |
 | 1851 - 716 pages
...For acute angled triangles, the following two propositions are of the greatest importance : — 1, any two sides of a triangle are to each other as the sines of their opposite angles (pi. 3,fgs. 107, 108). In jig. 107, the triangle abc is divided into two riglft... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...For acute angled triangles, the following two propositions are of the greatest importance : — 1, any two sides of a triangle are to each other as the sines of their opposite angles (pi. 3, figs. 107, 108). In fig. 107, the triangle abc is divided into two right... | |
 | 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... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...; 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... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 pages
...triangles. For acute angled triangles, the following two propositions are of the greatest importance:—1, any two sides of a triangle are to each other as the sines of their opposite angles (pL 3, Jigs. 107, 108). Infig> 107, the triangle abc is divided into two right... | |
 | William Thomas Read - 1862 - 144 pages
...2 be cos A = 62 + c2 — a2, and cos A = — "v, ~ a • 2 be Proposition II. The sides of a plane triangle are to each other as the sines of the opposite angles. Let ABC be a plane triangle ; draw CD perpendicular to AB, and, as before, let the sides be represented... | |
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These formulae contain the so-called law of sines, which may be expressed in words as follows : any two sides of a triangle are to each other as the sines of the opposite angles. 
