A treatise on land-surveying; comprising the theory developed from five elementary principles; and the practice with the chain alone, the compass, the transit, the theodolite, the plane table, &cIllustrated by four hundred engravings, and a magnetic chart . -^n Cf^:^ iquired distance to (436) Problem. Three points, A, B, C, being given by theirdistances from each other, and two other points, P and Q, beingso situated that from each of theyn two of the three points can beteen and the angles APQ, BPQ, CQP, BQP, be measured, it isrequired to determine the positions of P ayid Q. See Article (458)
A treatise on land-surveying; comprising the theory developed from five elementary principles; and the practice with the chain alone, the compass, the transit, the theodolite, the plane table, &cIllustrated by four hundred engravings, and a magnetic chart . -^n Cf^:^ iquired distance to (436) Problem. Three points, A, B, C, being given by theirdistances from each other, and two other points, P and Q, beingso situated that from each of theyn two of the three points can beteen and the angles APQ, BPQ, CQP, BQP, be measured, it isrequired to determine the positions of P ayid Q. See Article (458) for a solution of this problem by the 294 OBSTACLES IN ANGULAR SURVEYIIVO. [part vii Construction. Begin,as in Art. (397), hj describ-ing a circle passing throughA and B, and having the cen-tral angle subtended by AB,equal to twice the given an- p^-—gle APB. and thus contain-ing that angle. The point ^v,^ ^v^^,- ,yP will lie somewhere in its circumference. Describe another circle passing through B and C,and having a central angle subtended by BC equal to twice thegiven angle BQC. The point Q will lie somewhere in its :ir-cumference. From A draw a line making with AB an angle =BPQ, and meeting at X the circle first drawn. From C draw aline making with CB an angle = BQP, and meeting the secondcircle in Y. Join XY and produce it till it cuts the circles inpoints P and Q, which will be those required ; since BPX = BAX= BPQ ; and BQY = BCY = BQP. Calculation. In the triangle ABC, the sides being given, theangle ABC is known. In the triangle ABX, a side and all theangles are known, to find BX. In the triangle CBY, BY is simi-
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectsurveying, bookyear18
