. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. suppose, 5ac. 2iv Up. Draw AB cutting off thepart ABC as nearly as canbe judged equal to the quan-tity proposed ; and supposethe true quantity of ABC,when calculated, be only 20p. which is less than 14p. the true quantity, by2r. 34p. or 71250 square measure AB, whichsuppose = 1234 links, anddivide 71250 by 617 the halfof it, and the quotient 115links will be the altitude of the triangle to be ad
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. suppose, 5ac. 2iv Up. Draw AB cutting off thepart ABC as nearly as canbe judged equal to the quan-tity proposed ; and supposethe true quantity of ABC,when calculated, be only 20p. which is less than 14p. the true quantity, by2r. 34p. or 71250 square measure AB, whichsuppose = 1234 links, anddivide 71250 by 617 the halfof it, and the quotient 115links will be the altitude of the triangle to be added, and its base is AB. Therefore,if on the centre B, with the radius 115, an arc be de--scribed ; and a line be drawn parallel to AB, touching thearc, and cutting BD in D ; and if AD be drawn, it willbe the line cutting off the required quantity ADC A. Note. If the first piece had been too much, then Dmust have been set below B. In this manner the several shares of commons, to be di-vided, may be laid down on the plan, and transferredthence to the ground itself. Also for the greater ease and perfection in this business,the following Problems may be added. Vol. II. Z. 186 MATHEMATICS, PROBLEM- III. From an angle, in a given triangle, to draw lines to the oppo-site side, dividing the triangle into any number of parts,xVhich shall be hi any assigned proportion to each other. Divide the base into the same number of parts, and inthe same proportion, by Prob. I ; then from the severalpoints of division draw lines to the proposed angle, andthey will divide the triangle as required.* EXAMPLE. Let the triangle ABC, of 20acres, be divided into five parts,which shall be in proportion tothe numbers 1,2, 3, 5, 9 ; thelines of division to be drawnfrom A to CB, whose length is1600 links.
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