A treatise on surveying and navigation: uniting the theoretical, practical, and educational features of these subjects (1857)
Robinson, Horatio N[elson], 1806-1867. [from old catalog] · Cincinnati, J. Ernst; Toledo, Anderson, Burr, & co. · leaf 140
h P, which divides thepolygon as required ; but this line diminishes the area HABCK, bythe triangle PKk, and increases it by the triangle PUh. Therefore the difference of these triangles must equal d. The sine of the angle AHP, has the same numerical value as thesine of PHh, and the sine of the… … In the triangle Phil, we have sin. u : x : Whence, sin. (u—P)a sin. u Similarly, sin. (u—P)b sin. v y- (i) (2) sin. {y—P)The area of the triangle PhB=^ax sin. PAlso, PkK=\by sin. P Whence, b sin. Py—a sin. Px=2d (3) By substituting the values of x and y, taken from (1) and (2),we have, 138…
Surveying · Navigation
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