 | Rev. John Allen - Astronomy - 1822 - 516 pages
...the tangents of the same arches. PROP. XXVII. THEOR. The sines of the sides of spherical triangles, are to each other, as the sines of the opposite angles. In the case of right angled spherical triangles, (he proposition is manifest from 21 Sph. Tr., 16. 6 Eu. and... | |
 | Rev. John Allen - Astronomy - 1822 - 508 pages
...as the sine of the angle CBA to the sine of A. In like manner it may be proved,/ that any other two sides are to each other, as the sines of the opposite angles. Otherwise. The same construction remaining, the perpendicular CD being radius, the sides AC and CB... | |
 | John Radford Young - Astronomy - 1833 - 308 pages
...sin. В very same result for ; hence sm. b sin. A sin. В sin. С , sin. a sin. b sin. с that is, in any spherical triangle the sines of the sides are...to each other as the sines of the opposite angles ; so that when two of the three given quantities are a side and its opposite angle, the unknown, which... | |
 | Francis Lieber, Edward Wigglesworth - Encyclopedias and dictionaries - 1835 - 624 pages
...the sides are to each other as the sines of the opposite angles ; in spherical triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence it appear) how important the sine is for finding certain parts... | |
 | John Radford Young - Geometry, Solid - 1848 - 384 pages
...resultier — — r; hence — •= — — r= -. .... (3). sin. ft sin. a sin. ft sin. с that is, in am/ spherical triangle the sines of the sides are to each other as the sines of the opposite angles ; so that when two of the three given quantities are a side and its opposite angle, the unknown, which... | |
 | Francis Lieber - Encyclopedias and dictionaries - 1851 - 618 pages
...the sides are to each other as the sines of the opposite angles ; in spherical' triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence it appears how important the sine is for fmding certain parts... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...And we may reduce the resolution of plane right-angled triangles to the following analogies. Sinee the sides are to each other as the sines of the opposite angles, then Sine A : sine B :: BC : BA. But A is a right angle, the sine of which = radius, by some termed... | |
| |
Trigonometry (qv) teaches that, in plain triangles, the sides are to each other as the sines of the opposite angles ; in spherical... 
