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Ex. 2. Required the area of a triangular garden, whose side is 6co, and the perpendicular falling upon it, from the oppofite angle, 756 links of the Scots 'chain.

756 600

2)453600

2.26800

4

C

1.07200

40

2.88000

36

528000 264000

32.68000

A. R. F. Ells.
Anf. 2 1 2 31

Ex. 3. How many acres are in a triangular field, whose two fides are 1900, and 1700 links of the English chain, and the angle contained between them 48° 13'?

1900 1700 Ta 1330000 1900

2)3230000

1615000

As

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Ex. 4. Required the area of a triangular field, whose three lides are 600, 1000, 800 links of the Scots chain.

Anf. 2 ac. i ro. 24 falls. . How

many acres are in a triangular field, whose base is 1900 links, and perpendicular 1500 links of the English chain ?

Anf. 14 ac. i ro. Ex. 6. Required the area of a triangular field, whereof one of the angles is 54°, and containing lides 1400 and 1500 links of the Scots chain.

Anf. 8 ac. i ro. 39 f. 9 ells.

PROBLEM IV.

To find the area of a field in the form of a trapezoid. See Prob

lem 8. of surfaces.

EXAMPLE I.

Required the area of a trapozoid, whose parallel fides are 'L

3000

3000 and 1500 links of the Scots chain, and perpendicular distance 1200 links.

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Ex. 2. Required the area of a field in the form of a trapozoid, its parallel fides being 1260 and 1500 links, and perpendicular breadth 1000 links of the English chain.

Anf. 13 ac. 3 ro. 8 poles. Ex.

3. How many acres are in a field in the form of a trapozoid, its parallel fides being 1000 and 1 200 links, and perpendicular breadth 650 links of the Scots chain ?

Anf: 7 ac. o ro. 24 falls.

PROBLEM V.

To measure off-fets. Fig. 2.

In actual surveying, it often happens that a field is bounded by a river, a crooked hedge, &c. in which case it will be necessary to observe the following directions :-Let A bcdef represent a river or hedge. From A, in the direction of the river, measure the straight line AB. In doing of which, observe the bendings of the hedge; from thence measure the off-sets perpendicular upon the straight line AB, and note them down on the eye-draught, or record them in a field-book. When the off-sets are small, measure them with an off-set

staff

staff of 10 links; but when they are large, the chain is more expeditious.

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Here the figure is divided into triangles and trapezoids. The most accurate method to find the area, is, to compute the area of each separately by the rule for their proper form, and the sum of these will be the area of the whole. Thus,

hi 501

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Ag 300
gh 1001

ik 50 km 120
bg 130 ch + bg 290 ch+di 322 ditch 262 178

2)3900 2)29000 20161002)1 3.1002)21360 Agb 19500! 145001

8550 65501 10680

1040 910

2)10140

50.70

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Sometimes such a figure as that above is computed by finding a mean breadth, and reckoning the product of the mean breadth into the whole length of the station-line AB for the area. Thus, add all the off-set lines into one fum, and divide it

by their number, reckoning 1 for each time the irregular boun. dary meets the station-line, as at A and B; the quot gives the mean breadth, which, being multiplied into the length, produces the area.

However expeditious this method may be considered, it is always false, except in the case when the off-sets are equi-diftant from each other, as may be seen from the following computation of the above figure.

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To find the area of an irregular field. Fig. 3:

RULE.

Compute the areas of the figures into which the field is divi: ded, whether triangles or trapeziums, &c. by the rules proper for the several figures ; add the several results together, and the sum will give the content.

"

Let

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