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EXAMPLE.

Ch. L. There is a ditch 14. 25 long, by the side of which it is required lo lay out an oblong piece of ground, which shall contain SA. OR. 27P : what breadth must be laid off at each end of the ditch to enclose the 3A. OR. 37P?

A. R. P.
3. 0. 27.
4

12
40

Perch. Ch. L.
29)507(17.48=8. 37. breadth

21

140

240

8

The map is done as the last.

PROBLEM V.

To find the content of a piece of ground, in form

of an oblique angular parallelogram ; or of a rhombus, or rhombodies.

Multiply the base into the perpendicular height. The reason is plain from theo. 13. sect. 1.

EXAMPLE.

Plate VII. fig. 2.

Let ABCD be a piece of ground in form of a rhombus, whose base AB is 22 chains, and perpendicular DE, or FC, 20 chains. Required the content.

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The converse of this is done by prob. 4. and the map is drawn, by laying off the perpendicular on that part of the base from whence it was taken : joining the extremity thereof to that of the base, by a right line, and thence complete the parallelogram.

PROBLEM VI.

To find the content of a triangular piece of ground.

Multiply the base by half the perpendicular, or the perpendicular by half the base; or take half the product of the base into the perpendicular.

The reason hereof is plain, from cor. 2. theo. 12. sect. 1.

EXAMPLE

Plate I. fig. 16.

Let ABC be a triangular piece of ground, whose longest side or base BC, is 24C. 38L. and perpendicular AD, let fall from the opposite angle, is 13 C. 28L. Required the content.

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Ch. L. Ch. L.
Perp. 13. 28=6.78 four-pole chains, by prob.

perp. 6.39=3.39 1. sect. 3.
Or 2dly. Perp. 6.78 of four-pole chains.

1 base 6.19

[graphic]

6102

678 4068

A. R. P.

4119682=4. 0. 31. Or 3dly. Base 12.38 four-pole chains.

Perp. 6.78

83.9364

A. R. P.
Its į=4 | 19682 = 4. 0. 31.

Or the base and perpendicular may be reduced to perches; and the content may be thence obtained, thus :

Ch. L. Perches.
Perp. 13. 28 = 27.12
Half the

By prob. 4. sect. 3.
perp

13.56

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But, square perches may be reduced to acres, &c. rather more commodiously, by dividing by 40 and 4, than by 160; thus,

410)6711.

4)16. 31

A. 4. 0.31

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