. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. 140 From the given point P, draw PG, by Case 1, Problem V,so as to divide the polygon into the two parts (mc-\-nc) and (pc-\-qc). We have now to divide the polygon PAEG into two parts, mc,nc, by the line PL, and the polygon PBCDG into two parts, pcand qc, by the line PH. Case 2. When the given point is within the polygon. Let ABODE be the given poly-gon and P the given point within. Draw lik through P, by Case 2,Problem V, so that the area AlikDEshall eq
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. 140 From the given point P, draw PG, by Case 1, Problem V,so as to divide the polygon into the two parts (mc-\-nc) and (pc-\-qc). We have now to divide the polygon PAEG into two parts, mc,nc, by the line PL, and the polygon PBCDG into two parts, pcand qc, by the line PH. Case 2. When the given point is within the polygon. Let ABODE be the given poly-gon and P the given point within. Draw lik through P, by Case 2,Problem V, so that the area AlikDEshall equal mc, and the area likCBshall equal (nc-\-pc), when the wholeis required to be divided into threeparts in the ratio of m,n, p. When the whole is to be divided into four parts, in the ratio of m,n, p, q, then draw hh, so that one portion shall be (mc-\-nc) andthe other {pc-\-qc). + Then we have P as a given point, in one side of the polygon,AhJcDE, to divide it into two parts, in the ratio m to n, and P a givenpoint on one side of the polygon, lik CB, to divide it into two parts,in the ratio of p to q, and this is done by Case 1, Problem
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Keywords: ., boo, bookcentury1800, booksubjectnavigation, booksubjectsurveying
