. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. Whence, PEsin. PEG DIVISION OF LANDS. 137. This determines the point G, and PG divides the polygon asrequired. Case 2. When the given point is within the polygon. Let AB CDEF be the polygon as before, and (mc-\-nc) expressits numerical area ; also, let P be the given point within. ThroughP let the surveyor run the randomline, HPK, measuring from Hto P,and from P to K, let him alsoobserve the angles that this linemakes with the sides of the polygon^li^and CD, and com
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. Whence, PEsin. PEG DIVISION OF LANDS. 137. This determines the point G, and PG divides the polygon asrequired. Case 2. When the given point is within the polygon. Let AB CDEF be the polygon as before, and (mc-\-nc) expressits numerical area ; also, let P be the given point within. ThroughP let the surveyor run the randomline, HPK, measuring from Hto P,and from P to K, let him alsoobserve the angles that this linemakes with the sides of the polygon^li^and CD, and compute the areaHABCK, and note the differencebetween it and mc, the requiredportion of the polygon ; call thisdifference d, a known quantity. Let hPk represent the true line through P, which divides thepolygon as required ; but this line diminishes the area HAB CK, bythe triangle PKk, and increases it by the triangle PHh. Therefore the difference of these triangles must equal d. The sine of the angle AHP, has the same numerical value as thesine of PBh, and the sine of the angle PKD has the same numeri-cal value as the sine of the angle PKk. Put the angle AHP=u, and th
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Keywords: ., boo, bookcentury1800, booksubjectnavigation, booksubjectsurveying
