Elements of Geometry And Trigonometry
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Prop. VII. ) : hence, omitting the ', since the equa- tions are applicable to any triangle, we shall have cos }. =R^/ ^^^I^ + B-C) '^^^ i (A + C-B) ' sin B sin C cos i h=n^ Ao^ i (A + B-C) cos i (B + C-A) sin A sin C cos I c=Ry/ cos i (A+C-B) cos j (B+C— A) sin A sin B. 32 he-) 250 SPHERICAL TRIGONOMETRY.
Putting S=A + B + C, we shall have JS~A =i{A + B— A), ^S— B =i (A + C— B) and JS— C=KA+B— C), hence cos J^a=R\/ '="^ (tS-C) cos gS-B) sin B sin C cos JL&=R^ A°« (JS-C) cos gS-A) sin A sin C ^ .../cos(iS-B)cosaS-A) COS|C=R V : r— sm A sm B M^O VII. If we apply equations (2. ) to the polar triangle, we shall have — R^ cos A'=R cos B' cos C — sin B' sin C cos a\ Or, omitting the ', since the equation is applicable to any tri- angle, we have the three symmetrical equations, R^. Cos A=sin B sin C cos a — ^R cos B cos C R^. Cos B=sin A sin C cos b-^R cos A cos C W8. ) R^. Cos C=sin A sin B cos c — R cos A cos b) That is, radius square into the cosine of either angle of a sphe- rical triangle^ is equal to the rectangle of the sines of the two other angles into the cosine of their included side, minus radius into the rectangle of their cosines.
What to read after Elements of Geometry And Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by A M Adrien Marie Legendre to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Prop. VII. ) : hence, omitting the ', since the equa- tions are applicable to any triangle, we shall have cos }. =R^/ ^^^I^ + B-C) '^^^ i (A + C-B) ' sin B sin C cos i h=n^ Ao^ i (A + B-C) cos i (B + C-A) sin A sin C cos I c=Ry/ cos i (A+C-B) cos j (B+C— A) sin A sin B. 32 he-) 250 SPHERICAL TRIGONOMETRY.
Putting S=A + B + C, we shall have JS~A =i{A + B— A), ^S— B =i (A + C— B) and JS— C=KA+B— C), hence cos J^a=R\/ '="^ (tS-C) cos gS-B) sin B sin C cos JL&=R^ A°« (JS-C) cos gS-A) sin A sin C ^ .../cos(iS-B)cosaS-A) COS|C=R V : r— sm A sm B M^O VII. If we apply equations (2. ) to the polar triangle, we shall have — R^ cos A'=R cos B' cos C — sin B' sin C cos a\ Or, omitting the ', since the equation is applicable to any tri- angle, we have the three symmetrical equations, R^. Cos A=sin B sin C cos a — ^R cos B cos C R^. Cos B=sin A sin C cos b-^R cos A cos C W8. ) R^. Cos C=sin A sin B cos c — R cos A cos b) That is, radius square into the cosine of either angle of a sphe- rical triangle^ is equal to the rectangle of the sines of the two other angles into the cosine of their included side, minus radius into the rectangle of their cosines.
What to read after Elements of Geometry And Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by A M Adrien Marie Legendre to read onlineMoreLess
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