 | Webster Wells - 1896 - 236 pàgines
...TRIANGLES. GENERAL PROPERTIES OF SPHERICAL TRIANGLES. 151. In any spherical triangle, the sines of the sides are proportional to the sines of their opposite angles. Let ABC be any spherical triangle, and draw the arc CD perpendicular to AB. There will be two cases according... | |
 | George Albert Wentworth - 1897 - 234 pàgines
...also be written in the form of proportions sin a : sin b : sin с = sin A : sin B : sin C. That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. be employed in the above proof instead of sin A, sin B, or sin C. These sines,... | |
 | George Albert Wentworth - 1897 - 384 pàgines
...also be written in the form of proportions sin a : sin b : sin c = sin A : sin B : sin C. That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. be employed in the above proof instead of sin A, sin B, or sin C. These sines,... | |
 | Pitt Durfee - 1900 - 340 pàgines
...theor. 8. XOTE 1. If the theorem be regarded as relating to a spherical triangle, it may be written : The sines of the sides of a spherical triangle are proportional to the sines of the opposite angles ; and the law of cosines may be expressed in like form. QUESTIONS. If ABC be any... | |
 | Reginald Empson Middleton - 1902 - 370 pàgines
...and angle C, and we may saysin A : sin B : sin C : : sin a : sin b : sin c . . (I) That is to say, ' the sines of the sides of a spherical triangle are proportional to the sines of the angles to which they are opposite.' Other fundamental formulas relating to spherical triangles... | |
 | 1902 - 366 pàgines
...and angle C, and we may saysin A : sin B : sin C : : sin a : sin b : sin c . . (I) That is to say, ' the sines of the sides of a spherical triangle are proportional to the sines of the angles to which they are opposite.' Other fundamental formulae relating to spherical triangles... | |
 | George Albert Wentworth - 1903 - 346 pàgines
...also be written in the form of proportions : sin a : sin b : sin c = sin A : sin B : sin C. That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. 4> In Fig. 99 the axe CD cuts the side AB within the triangle. If CD falls without... | |
 | James Morford Taylor - 1905 - 256 pàgines
...obtain sin a /sin A = sin¿ /sin Л. sin a _ sinb _ sine sin A sin В sin С Hence (1) [41] That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Ex. I. Compare [41] with [23] in Plane Trigonometry. Observe that when two of... | |
 | Robert Édouard Moritz - 1913 - 562 pàgines
...equations may also be written in the form sin a _ sin Ь _ sin с sin A ~ sin B sinC (i) or in words, The sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. (b) Second Proof. Let ABC (Fig. 34) be a spherical triangle and O the center of... | |
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That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. 
