 | Robert Simson - Trigonometry - 1827 - 546 pages
...than a quadrant. PROP. XXIII. FIG. 16. In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them. First, let ABC be a right angled triangle, having a right angle at A; therefore,... | |
 | William Galbraith - Astronomy - 1834 - 454 pages
...oblique-angled spherical triangles may be solved by the following theorems : — THEOREM I. In every spherical triangle the sines of the sides are proportional to the sines of the angles opposite to them,* or, sin AB : sin AC : : sin C : sinB. THEOREM II. In oblique-angled spherical... | |
 | Euclid - 1835 - 540 pages
...AC. QED 2i 497 PROP. XXIII. FIG. 16. In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them. First, Let ABC be a right angled triangle, having a right angle at A ; therefore,... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...Triangles, . . .' . 26 SECTION I. Theorems- for the solution of spherical oblique triangles, . . 26 The sines of the sides are proportional to the sines of the opposite angles (598), ........ 26 Bowditch's Rules (604), (605), . ... . .27 SECTION II. Solution of Spherical Oblique... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...Oblique Triangles, . . . 26 SECTION I. Theorems for the solution of spherical oblique triangles, . . 26 The sines of the sides are proportional to the sines of the opposite angles (598), . . 26 Bowditch's Rules (604), (605), 27 SECTION II. Solution of Spherical Oblique Triangles,... | |
 | Mathematics - 1836 - 488 pages
...the sine of the other angle. XXIV. In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them. XXV. In oblique angled spherical triangles, a perpendicular arch being drawn... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...: cos. ABC : sin. BCA. PROP. XXIV. In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them. 255 of the rigbt angle at A), as the sine of the side AC to the sine of the... | |
 | A. Bell - Conic sections - 1837 - 180 pages
...the other angle ACB. PROPOSITION VII. In spherical triangles, whether right-angled or obliqueangled, the sines of the sides are proportional to the sines of the angles opposite to them. First, let ABC he a right-angled triangle, having a right angle at A ; therefore... | |
 | Roswell Park - Best books - 1841 - 722 pages
...arcs, by the number of degrees which they subtend, at the centre of the sphere. In spherical triangles, the sines of the sides are proportional to the sines of the opposite angles. In a right angled spherical triangle, if we omit the right angle, we have five parts left, sides and angles... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...: : cos. ABC : sin. BCA. PROP. XXIV. In spherical triangles, whether right angled or oVKque angled, the sines of the sides are proportional to the sines of the angles opposite to them. First, let ABC be a right angled triangle, having a right angle at A ; therefore... | |
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The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C... 
