. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. nto 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 V. Case 3. When the given point is without the polygon. Let ABCDEF be the given poly-go
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. nto 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 V. Case 3. When the given point is without the polygon. Let ABCDEF be the given poly-gon, and P the given point without it. Divide the numeral area into therequired proportional parts, mc, nc,pc,&c, as many as required. From the point P draw the line PIT,as directed in Case 3, Problem V, di-viding the polygon into two parts, mcand (nc-\-pc-\-&c). Then divide the polygon, GHED OB, into two parts, one of whichis nc, and the other (pc-\-qc, &c), and thus we can proceed andcut off one portion after another, as many as may be required. The application of the foregoing principles will meet any case that. DIVISION OF LANDS. 141 can occur in the division of lands ; and we now close this subjectwith the following practical e xample s. 1. A triangular field, whose sides are 20, 18, and 16 chains, is tohave a piece of 4 acres in content fenced off from it, by a right linedrawn from the most obtuse angle to the opposite side. Required thelength of the dividing line, and its distance from either extremity of theline on which it falls ? Ans. Length of the dividing line, 13 chains, 95 links, if runnearest the side 16. Distance it strikes the base from the next mostobtuse angle is chains. 2. The three sides of a triangle are 5, 12, and 13. If two-thirdsof this triangle be cut off by a line drawn parallel to the longest side, itis required to find the length of the dividing line, and the distance ofits two extremities from the extremities of the longest side. Ans. Distance f
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