A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects (1852)
Robinson, Horatio N[elson], 1806-1867. [from old catalog] · Cincinnati, J. Ernst · leaf 59
e, the difference of the seg-ments is A G. As A is a point without a circle, by theorem 18, book 3, we have, AEXAF=ABXAGHence, . . AB : AE=AF: AG Q.ED. PROPOSITION 7. The sum of any two sides of a triangle, is to their difference, asthe tangent of the half sum of the angles opposite to these sides,… … PLANE TRIGONOMETRY. 55 But, tan. ( —-— ): tan. [ —-— J =sin.-4+sin.-B : sin«4—sm.B(eq.(l), trig.) Comparing the two latter proportions (th. 6, b. 2), we have, iA+B A—B CB+AQ : CB—AC= tan. ( =-£=- ) : tan. ( —— \ Q. E. D PROPOSITION 8. Given the three sides of any plane triangle, to find some…
Surveying · Navigation
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