. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. (1) Rmy -f- Qmx=a, ( 2 ) and From (1), whence, y- Px X2 aRm~Px~a -f- Qmx=a ; mQ aR . This value put in (2), gives(3)(4) We now find the numerical values of and by logarithms, mQ PQ as follows : As our radius is unity, we diminish the indices of the logarithmicsines by 10. log. a, log. a, log. m, log. R— log. §,— i log. P,— §,— ? ? Equ
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. (1) Rmy -f- Qmx=a, ( 2 ) and From (1), whence, y- Px X2 aRm~Px~a -f- Qmx=a ; mQ aR . This value put in (2), gives(3)(4) We now find the numerical values of and by logarithms, mQ PQ as follows : As our radius is unity, we diminish the indices of the logarithmicsines by 10. log. a, log. a, log. m, log. R— log. §,— i log. P,— §,— ? ? Equation (4) now becomes x2— *=—;whence x= GH— : from which subtract GA=, andwe have All the distance required =, which differs from thegiven answer about one link of the DIVISION OF LANDS. 145 Lemma. Find the point in any trapezoid, through which anystraight line which meets the parallel sides will divide the trapezoid intotwo equal parts. Let AB CD be the trapezoid. Bisect the parallel sides AB and CD inthe points n and m. Join mn, and bisectmn in 0, and 0 is the point required. Any line meeting the parallel sides, and passing through O, willdivide the trapezoid into two equal trapezoids. It is obvious thatthe line mn divides the figure into two equal parts, because the sumof the parallel sides is the same in each. Now draw any other linethrough 0, as p Oq : the trapezoid pqBD=mnBD ; because thetriangle Omp=q On, and one triangle is cut off and the other is puton at the same time. The triangles are equal, because mO= On,the angle pm 0= Onq, and the opposite angles at 0 are equal:therefore pm=nq; and whatever more than Cm is taken on oneside, the equal quantity qn less than An is taken on the other side. Another method of finding the point 0, is to bi
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Keywords: ., boo, bookcentury1800, booksubjectnavigation, booksubjectsurveying
