26 ASTRONOMICAir AND ' 



hig the area of a field, which I fliall attempt to communicate 

 as it occurred to me, in the following manner : 





Let it be fuppofed that the fides A B, B C, C D, D A, (Plate L 

 fig. 6,) of a field are hypothenufes of right angled triangles, 



the bafes of which are eafl and wefl lines, and are either eaft- 

 ings, as E B, F C,' or weftings, as G D, H A ; and the perpen- 

 diculars north and fouth lines, being either northings, as A E, 

 B F, or fouthings as C G, D H according to the bearings of 

 the fides. The eaftings, weftings, northings, and fouthings are 

 denoted by the initial letters E. W. N. S. in the exprefTion of the 

 courfe. The caiculatrix is an eaft and weft line, which may 



po fiefs any affignable place EW,ew (Plate I. fig. 7,) ad libitum : 

 but to fliorten the operation it is fuppofed to bife6: the firft fide, 



with which the operation commences. A perpendicular line 

 C O, drawn from the further extremity of a fide B G to the 



calculatrix, is the ultimate calculatral dljlance of that fide ; and 



r 



a perpendicular S M, drawn from the middle of a fide B C, is 

 the mean calculatral di/iance of that fide. In the following meth- 



- ■ . 



od the calculatral diftance is taken double. To the triangle 

 A B N add the trapezium N B C O ; the fum is the area ABC 

 O ; from which fubtraA the trapezium O C D P, and it leaves 



the area A B C D P ; and from this fubtra(5l the triangle PDA, 

 and the remainder is the area of the field A B C D. The areas 

 of thefe triangles and trapezia, and from thence the area of 

 the field may be obtained by the following 



2 



RULE. 



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