 | John Playfair - 1819 - 354 pages
...cos ABC : sin BCA. Q, ED 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. First, Let ABC be a right angled triangle, having a right angle at A ; therefore,... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...has one obtuse angle. And an acute-angled triangle is that which has all its angles acute. In every triangle the sines of the sides are proportional to the sines of the opposite angles; also the sine of all the three angles is equal to two right ones ; and the external angle, made by... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...has one obtuse angle. And an acute-angled triangle is that which has all its angles acute. In every triangle the sines of the sides are proportional to the sines of the opposite angles; also the sine of all the three angles Vs equal to two right ones: and (he external angle, made by any... | |
 | Nautical astronomy - 1821 - 708 pages
...question is between two sides and the opposite angles; which may be solved by the noted theorem, that the sines of the sides are proportional to the sines of the opposite angles, or as it may be expressed in an abridged form or more easy reference. 2. Sine side (X sine opp. angle.... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...of Napier are therefore identical with those which have been directly demonstrated. PROPOSITION XVI. In any spherical triangle the sines of the sides are proportional to the sines of their opposite angles. In the right angled spherical triangle ABC (see the last figure) we have (Prop.... | |
 | Ferdinand Rudolph Hassler - Astronomy - 1826 - 640 pages
...Spherical Trigonometry, a general principle analogous to that found in Plane Trigonometry ; viz : that the sines of the sides are proportional to the sines of the opposite angles. The formulae 5 and 6, transformed into proportions, give the following results, viz : 12 Fi-om No.... | |
 | Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...having found BC, the angle A may be found by the equations marked (A) (47), which are equivalent to 5. The sines of the sides are proportional to the sines of the opposite angles. This rule gives sin AB : sin C : : sin BC : sin A. Otherwise ; if the side BC be not required, the... | |
 | Ferdinand Rudolph Hassler - Trigonometry - 1826 - 208 pages
...Spherical Trigonometry, a general principle analogous to that found in Plane Trigonometry 5 viz : that the sines of the sides are proportional to the sines of the opposite angles. The formulée 5 and 6, transformed into proportions, give the following results, viz : 12 From No.... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 764 pages
...question is betw> sides and the opposite angles, which may be solved by the noted theorem, that ti of the sides are proportional to the sines of the opposite angles, or as it may be i cd in an abridged form or more easy reference. 2. Sin-; »iiic oc sintopp. angle.... | |
 | William Galbraith - Astronomy - 1827 - 412 pages
...will give, when corrected for dip, &c., the true time of rising or setting. (к) 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:sin. B. THEOREM II. In oblique-angled spherical... | |
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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... 
