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Having set up marks at the corners, which is to be done in all cases where there are not marks; measure with the chain from A to P, where a perpendicular would fall from the angle C, and set up a mark at P, noting the distance AP. Then complete the distance AB, by measuring from P to B. Having set down this measure, return to P, and measure the perpendicular PC. And thus, having the base and perpendicular, the area is easily found from them ; and having also the place P of the perpendicular, the triangle is easily constructed.

Or, measure all the three sides with the chain, and note them from these the content is easily found, or the figure constructed.

2. By taking one or more of the angles. (^

Measure two sides AB, AC, and the angle A between them. Or, measure one side AB, and the two adjacent angles A and B. From either of these sets of measures the figure is easily planned; and then by measuring the perpendicular CP on the plan, and multiplying it by; half AB, the content is obtained.

PROBLEM

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Measure along either of the diagonals, as AC; and ether the two-perpendiculars DE, BF, as in the last problem; or else the sides AB, BC, CD, DA. From either of these sets of measures the figure may be planned and computed, as before directed.

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ed Measure, on the longest side, the distances AP, AQ2 AB; and the perpendiculars PC, QD.

2. By taking one or more of the angles.

Measure the diagonal AC, and the angles CAB, CAD, ACB, ACD. Or measure the four sides, and any one of the angles, as BAD.

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Having set up marks, where necessary, at the corners of the proposed field ABCDEFG; walk over the ground, and consider how it can best be divided into triangles and trapeziums; and measure them separately, as in the two last problems. And in this way it will be proper to divide it into as few separate triangles, and as many trapeziums, as may be, by drawing diagonals from corner to corner; and so, that all the perpendiculars may fall within the figure. Thus, the following figure is divided into the two trapeziums ABCG, GDEF, and the triangle GCD. Then, in the first, beginning at A, measure the diagonal AC, and the two perpendiculars Gm, Bn. Then the base GC, and the perpendicular Dg. Lastly, the diagonal DF, and the two perpendiculars pE, OG. All which measures

write against the corresponding parts of a rough figure, drawn to resemble the figure to be surveyed, or set them down in any other form you choose.

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Measure all the sides AB, BC, CD, DE, EF, FG, GA; and the diagonals AC, CG, GD, DF.

Otherwise.

Many pieces of land may be very well surveyed, by meas uring any base line, either within or without them, together with the perpendiculars let fall upon it from every corner of them. For they are by these means divided into several triangles and trapezoids, all whose parallel sides are perpendicular to the base line; and the sum of these triangles and trapeziums will be equal to the figure proposed, if the base line fall within it; if not, the sum of the parts, which are without, being taken from the sum of the whole, which are both within and without, will leave the area of the figure proposed.

In pieces, which are not very large, it will be sufficiently exact to find the points in the base line, where the several perpendiculars will fall, by means of the cross, and measure thence to the corners for the lengths of the perpendiculars. And it will be most convenient to draw the line so, that all the perpendiculars may fall within the figure.

Thus, in the following figure, beginning at A, and measuring along the line AG, we find the distances and perpendiculars, on the right and left, to be as follow:

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ing it about C till, through the sights, you see the mark D;

and

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