Measuring Surface and Solidity. 237 



Let ABODE represent any rec- 

 tilineal figure ; the plane of the pa- 

 per being the horizontal plane, and 

 the lines ON, OM the intersections 

 of the vertical planes. If the co-or- 

 dinates of any point A are assumed, 

 and if the bearings, lengths and in- 

 clinations of the sides, are given, the 

 co-ordinates of the other points are 



determined in the following manner. The altitude of B is equal 

 to the altitude of A added to the distance AB, into the sine of 

 the inclination of AB. The latitude of B is the latitude of A 

 added to the distance AB into the sine of the bearing of AB 

 into the cosine of the inclination of AB ; and the longitude of B 

 is the longitude of A added to the distance AB, into the cosine 

 of the bearing of AB into the cosine of its inclination. In the 

 same manner, with the other points. The co-ordinates of the 

 several points, therefore, may be calculated with facility. If a 

 common table, giving the functions of an arc to 90 only, be 

 used, 90, 180, and 270 must be deducted from the bearings, 

 as they lie respectively in the second, third, or fourth quadrant, 

 and attention must be paid to the change, under these circum- 

 stances, of the sine into the cosine, and the cosine into the sine, 

 which, together with the change of signs omitted in these tables 

 are thus exhibited. 



It is, however, far more convenient for these, as for all other 

 trigonometrical calculations, to use a table titled with the de- 



See Davidson's Mathematics, new Edition, 1832, p. 280. 



