 | Mathematics - 1899 - 744 pages
...36—38). K 20 f. J. JACK. A New Proof of the Formulae for RightAngled Spherical Triangles. Assuming that the sines of the sides are proportional to the sines of the opposite angles, the formulae for the rightangled spherical triangle are obtained by the aid of a slight modification... | |
 | Alfred Hix Welsh - Plane trigonometry - 1894 - 228 pages
...is middle. When complement of В is middle. § 3. PRINCIPLES. THEOREM I. In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let ABC be a spherical triangle on a sphere whose centre is 0. From any point in О В let fall a perpendicular... | |
 | William Macfarland Patton - Civil engineering - 1895 - 1710 pages
...the solution of plane triangles. The only relations that are necessary in most cases are, first, that the sides are proportional to the sines of the opposite angles, or, in case of a right-angle triangle, either side about the right angle is equal to the other side multiplied... | |
 | William Chauvenet - Geometry - 1896 - 274 pages
...fundamental formulae from a direct consideration of the solid angle itself. 3. In a spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let ABC, Fig. 1, be a spherical triangle, 0 the center of the sphere. The angles of the triangle are... | |
 | Edinburgh Mathematical Society - Electronic journals - 1897 - 316 pages
...New Proof of the Formulae for Right-Angled Spherical Triangles. By Professor JOHN JACK. It is assumed that the sines of the sides are proportional to the sines of the opposite angles. ACB (Fig. 9) is a spherical Д, with С a right angle. Produce AC, AB to D and E so that AD = AE =... | |
 | James William Nicholson - Trigonometry - 1898 - 204 pages
...in the form of a proportion, as shl о : sin b : : sin A : sin B. That is, in spherical triangles, the sines of the sides are proportional to the sines of the opposite angles, which property is called the Law of Sines. 143. Relation of the half of one angle to the three sides.... | |
 | 1899 - 760 pages
...— 38). K 20 f. J. JACK. A New Proof of the Formulae for RightAngled Spherical Triangles. Assuming that the sines of the sides are proportional to the sines of the opposite angles , the formulae for the rightangled spherical triangle are obtained by the aid of a slight modification... | |
 | Daniel Alexander Murray - 1906 - 466 pages
...sin A sin B . sin a _ sin b _ sin ct .... " sin ^~ sin .B~ sin C' W In words : /na spherical triangle the sines of the sides are proportional to the sines of the opposite angles. (Compare Plane Trigonometry, Art. 54, I.) B B. Derivation of the Law of Cosines. cos BC = cos CD cos... | |
 | Daniel Alexander Murray - Spherical trigonometry - 1908 - 132 pages
...shown that sin A sin B . sin a sin 6 sine sin A sin JB sin C (1) In words : In a spherical triangle the sines of the sides are proportional to the sines of the opposite angles. (Compare Plane Trigonometry, Art. 54, I.) and B. Derivation of the Law of Cosines. cos BC = cos CD... | |
 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...that sin A sin B , sin a — sin b sine sin . I sin B sin C (1) In words : In a spherical triangle the sines of the sides are proportional to the sines of the opposite angles. (Compare Plane Trigonometry, Art. 54, I.) B. Derivation of the Law of Cosines. cos EC = cos (7Z) cos... | |
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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. 
