 | William Leybourn - 1704 - 432 pages
...being demonftrated, will clear. THEOREM I. In any Spherical Triangle, whether Right or Oblique-angled. The Sines of the Angles are Proportional^ to the Sines of their cffofite Sides : & contra. This is demonftrared in Sett. i. Chap. 4, of Right-fined Trm-. gles, and... | |
 | Charles Hutton - 1811 - 404 pages
...cos c + sin a . sin c . cos u> (I.) cos C = cos a . cos b -f- sin a . sin b . cos c J , THEOREM VII; In Every Spherical Triangle, the Sines of the Angles...Sides. If, from the first of the equations marked i, the value of cos A be drawn, and substituted for it in the equation sin1 A = 1 — CDS'* A, we shall... | |
 | Charles Hutton - 1811 - 424 pages
...sin b . cos cS THEOREM VII. In Every Spherical Triangle, the Sines of the Angles are Fro' portional to the Sines of their Opposite Sides. If, from the first of the equations marked i, the value of cos A be drawn, and substituted for it in the equation sin1 A = 1 — cos7 A, we shall... | |
 | Charles Hutton - 1812 - 624 pages
...cos c -j- sin a . sin c . cos B v (I.) cos c -- cos a . cos b + sin a . sin b . cos c J THEOREM VII. In Every Spherical Triangle, the Sines of the Angles...A be drawn, and substituted for it in the equation sin2 A = 1 — cos2 A, we shall have . , , cos2 a + cos» 4. cos2 c— 2 cos a . cos b. cose Sin* A... | |
 | Charles Hutton - 1816 - 618 pages
...cos c -f- sin a . sin c . cos H v (I. cos e a™ cos a . cos l> + sin a . sin b . cos c J THEOREM VH. In Every Spherical Triangle, the Sines of the Angles...sides. If, from the first of the equations marked I, the value of cos A be drawn, and substituted for it. in the equation sin* A «= 1 — cos* A, we... | |
 | Charles Hutton - 1818 - 652 pages
...с -j- sin a . sin с . cos в \ (I. cos с = cos a . cos 6 + sin a . sin 6 . cos с ) THEOREM Vn. r In Every Spherical Triangle, the Sines of the Angles are Proportional to the-Sines of their Opposite sides. If, from the first of the equations marked 1 , the value of cos... | |
 | Charles Hutton - 1826 - 682 pages
...+ sin a . sin c . co« B > (1.) cos c = cos a . cos 6 -j- ai« a . tin b . cos c ) THEOREM VII. ID Every Spherical Triangle, the Sines of the Angles are Proportional to the Sines of iheir Opposite sides. If, from the first of the equations marked 1. the value of cos A be drawn, and... | |
 | John Farrar - 1827 - 464 pages
...and the side PS, the complement of the declination, opposite to the angle PP'S, or 90 — Z; and as, in every spherical triangle, the sines of the angles are proportional to the sines of the opposite sides, this proportionality will give, in the case before us, cos I cos I cos a = ; —... | |
 | Louis-Benjamin Francœur - 1830 - 506 pages
...thus the 1st must continue constant, and we shall have sin A __ sin В _ sin С sin a sin b sin с In every spherical triangle, the sines of the angles are proportional to the sines of the opposite sides. According to the property of the supplemental triangle, change, in equ. (3), a... | |
 | John Farrar - 1834 - 504 pages
...not commonly observed, and which only serves to connect our two triangles. The process is simple, for in every spherical triangle the sines of the angles are proportional to the siws of the opposite sides. Thus, in our triangle ZP8 referred to the . sin P' . sin Z' true places,... | |
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In Every Spherical Triangle, the Sines of the Angles are Proportional to the Sines of their Opposite sides. If, from the first of the equations marked 1, the value of cos A be drawn, and substituted for it in the equation sin2 A = 1 — cos2 A, we shall... 
