| William Leybourn - Geometry - 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 - Mathematics - 1812 - 624 pages
...b . sin c . cos A 1 cos 6 = cos a . 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...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... | |
| Charles Hutton - Mathematics - 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...be drawn, and substituted for it. in the equation sin* A «= 1 — cos* A, we shall have . cos* i + *-o** b cos' c— 5 cosn co« A. rose sin* A = 1... | |
| Charles Hutton - Arithmetic - 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 - Mathematics - 1822 - 680 pages
...cos b == cos a -.4 cos c -4- sin ^ . sinvd . cos, B > (1. cos c = cos a .cos 6 4- sin a . sin b . cos In Every Spherical Triangle, the Sines of the Angles...sides. If, from the first of the equations marked 1, the value of cos A be drawn, and substituted for it in the equation sin2A= 1— cos2 A, we shall... | |
| Charles Hutton - Geometry - 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 - Astronomy - 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 - Mathematics - 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... | |
| Charles Hutton - Mathematics - 1831 - 656 pages
...6 •» cos a . cos c + sin a . sin c . cos B > (I.) cos c = cos a . cos b + sin o . sin 6 . cos cj THEOREM VII. In every spherical triangle, the sines...and substituted for it in the equation sin1 A — 1 — cos1 A, we shall have _:_> . _. i _ cos3 a -f ro»2 b . rnff c— 2 ens « . cos /; . ro« e fin*... | |
| Charles Hutton - Mathematics - 1831 - 662 pages
...a . cos c + sin a . sin c . cos B > (I.) cos c = cos a . cos b -f- sin a . sin 6 . cos c J THtOKEM VII. In every spherical triangle, the sines of the...and substituted for it in the equation sin1 A = 1 — cos" A, we shall have • j •. cos3 n + cos-' 6 . cm* c— 2rosn . en* b . ro«e sin A - I t«*t.tm*e... | |
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