. The Philosophical magazine; a journal of theoretical, experimental and applied physics. e ho- * I would here obseive, that in this Society the members lecture to eachother on the- different departments of science, &c., at their own cost re-^pectively. nour Causes of the EartNs rotary Motion. 181 nour which may attach to it; and as this is often all that thephilosopher obtains, it should in justice be awarded to him towhom, asbein^ the first publisher, it is unquestionablv tlue;and that Mr. Herapath was so in the present instance vouwill be convinced irom the report of his lecture, which 1 ha
. The Philosophical magazine; a journal of theoretical, experimental and applied physics. e ho- * I would here obseive, that in this Society the members lecture to eachother on the- different departments of science, &c., at their own cost re-^pectively. nour Causes of the EartNs rotary Motion. 181 nour which may attach to it; and as this is often all that thephilosopher obtains, it should in justice be awarded to him towhom, asbein^ the first publisher, it is unquestionablv tlue;and that Mr. Herapath was so in the present instance vouwill be convinced irom the report of his lecture, which 1 havetaken the liberty to hiclose. I am, sir, yours, &, Fell. 24, J^MES P. Bevan. XXVIII. Demonstrations of Trigonometrical Formula. To the Editor of the Philosophical Magazine arid , T FLATTER myself the demonstrations of the followino--?? trigonometrical formulae are neo:: but if I am mistaken, per-haps the circumstance of their not being in general use mayprocure them insertion in your Magazine. I am, sir, yours, ^ Inn, Feb. 14, 1825. C. Theorem 1. Let ABC be atriangle havi;g thea^.gle?^ A, B, C towhich the sides op-posite are a, b^c —Then by trigo-nometry, a sm C = c sin A or a sin (A + B) = c sin A Hence sin (A + B) = ~ sin A Again, if a perpendicular be drawn from C to the opposite side c, we have c = a cos B + i cos A c T^ ^ A r> I sin B . .-. — = cos B -I cos A = cos B + -. - , cos A a a sin A Hence by substitution sin (A + B) = (cos B + ^-^ cos A sin A and .S sin (A + B) = sin A cos B + cos A sin B Theorem sill A B6 . T> sin B • + COS A = COS r> 4- —.—- cos A a sin A 182 Demonstrations of Trigonometrical Farmulce. Theorem 2. If a perpendicular be let fall from B to theopposite side b, we have b ?= a cos C -f c cos A= c cos A — a cos (A + B) Hence cos (A + B) = — cos A = ^ cos A — ^ Now c ?=? a cos B + i cos A= cos B + a Hence by substitution cos (A + B) = (cos B + ^-^^—r cos a) cos a — ^!^r ^ V sin A sin A
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