To find the double area of the triangle IAB. As rad.

10.00000 : sin. AIB 13° 45'

9.37600 SIA

log. 1.46937 :: IAXIB, IB

1.54943

: 2.IAB 248.2

2.39480

To find the double area of the triangle IBC. As rad.

10.00000 : sin. BIC 9° 15'

9.20613

log 1.54943 :: IBRIC, IC

1.47463

SIB

To find the double area of the triangle ICD.

To find the double area of the triangle IDE.

To find the double area of the triangle IEF.

To find the double area of the triangle IFG.

To find the double area of the triangle IAG.

The bearings and distances of the sides, if required, might readily be obtained. For, having found the distances IA, IB, we have in the triangle IAB, two sides, and an included angle; whence the angle IAB and side AB may be found. The angle IAB applied to the bearing of JA, will give the bearing of AB. In the same manner the bearings and distances of the other sides

may be found.

EXAMPLE 2.

Being required to calculate the area of a field, the own. er of which refuses permission to go on it, I choose two all the angles of the field are visible. The bearing and distance of the stations, and the bearings of the angles, from each station, are as follow. What is the area of the field?

The station G bears from the station F, N 43° W. 20 ch.

FE N. 60; E. GEIS. 84 E.

Ans. 33 A. IR. 7 P.,

LAYING OUT AND DIVIDING LAND.

PROBLEM I.

To lay out a given quantity of land in a square form.

RULE.

Reduce the given quantity to chains or perches, and extract the square root, which will be the length of a side, of the same denomination to which the given quan. tity is reduced.

EXAMPLES.

1. Required the side of a square that shall contain 9 A. 3 R, 28 P.

40)28 Per.

4)3.7 R.

9.925 A. = 99.25 Ch.

Ch.
99.25(9.96 Ch, the length of a side.
81

189)1825

1701

1986)12400

11916

484