. 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]. se means divided into seve-ral triangles and trapezoids, all whose parallel sides are per-pendicular to the base line ; and the sum of these trianglesand trapeziums will be equal to the figure proposed, if thebase line fall within it ; if not, the sum of the parts, whichare without, being taken from the sum of the whole, whichare both within and without, will leave the area of the fig-ure proposed. SURVEYING. 145 In piece
. 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]. se means divided into seve-ral triangles and trapezoids, all whose parallel sides are per-pendicular to the base line ; and the sum of these trianglesand trapeziums will be equal to the figure proposed, if thebase line fall within it ; if not, the sum of the parts, whichare without, being taken from the sum of the whole, whichare both within and without, will leave the area of the fig-ure proposed. SURVEYING. 145 In pieces, which are not very large, it will be sufficientlyexact to find the points in the base line, where the severalperpendiculars will 1aL, by means of the cross, and meas-ure thence to the corners for the lengths of the perpendic-ulars.—And it will be most convenient to draw the lineso, that all the perpendiculars may fall within the figure-Thus, in the following figure, beginning at A, andmeasuring along the line AG, we find the distances andperpendiculars, on the right and left, to be as follow. Ab 315Ac 440Ad 585Ae 610Af 990AG 1020 350 bB 70 cC 320 dD 50 eE 470 /F0. PROBLEM VII. To survey a field with a Plane Table. 1. From one station* Plant the table at any angle,as C, whence all the other an-gles, or marks set up, can beseen ; and turn it about tillthe needle point to the flower-de-luce, and there screw it a point for C on the pa-per, on the table, and lay theedge of the index to C, turn-ing it about C till, through the sights, you see the mark D ; Vol. II. T
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