A Treatise On Plane And Spherical Trigonometry; Including the Construction of the Auxiliary Tables; a Concise Tract On the Conic Sections, And the Principles of Spherical Projection

Cover A Treatise On Plane And Spherical Trigonometry; Including the Construction of the Auxiliary Tables; a Concise Tract On the Conic Sections, And the Principles of Spherical Projection
A Treatise On Plane And Spherical Trigonometry; Including the Construction of the Auxiliary Tables; a Concise Tract On the Conic Sections, And the Principles of Spherical Projection
Lewis, Enoch, 1776-1856
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In these investigations, the radius is taken ::= L Now (Art. 62), 1 : cos A : : tan b : land.
But (Art. 23), sin cosm tan •* sin d . sin ft • r — y = cos A. r .
cos a cos b Again (Art 66).
cos b : cos a i: cosd X cos (c— rf)^ wherefore.
Digiti ized by Google SECTION IIL 105 cosa ^ c^c^^ 3 p^^ co8c.co8rf+8mc.ri.>^ COS b cos a . ^ ^ cos a . . sin d . . sin ft , = cos c + sine. % = cos c + cos A.smc. r; by putting cosd cosi* -^^^ ® . sin ft . ^ ^ ^ sin rf cos A. ; instead of :;.
cos ft cos a Clear
...ing this equation of fractions, cos a = cos ccos ft + cos Ajsin csin ft. (I) By Art- 64, A « T» -r^ . * ^^v sin B cos E As 1 : cos a : : tan B : cot E : : (Art. 23) 5 • - — rr ••• ^ ^ cos B sin E cos E sin B = cos a.. s.
cos B By Art. 68, As cos B : cos A : : isin E : sin (C — E) .*.
cos A __ sin (C — E) _^ ^ ^^ sin Ccos E— cos Csin E S5iB - ~ihi"E ^^''^- ^^' * • ^> snr'.
. _, cos E ^ . _, sin B ^ . .
= sm C.-n — « — cos C. = cos a.sin C. 5 — cos C ; subst^ sin £4 cos D cos E tuting for-i — p.


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