"^^ 



S6 ASTRONOMICAL and 



double. Find the bafes and perpendiculars of the feveral 



fides ; placing the bafes in the fecond column iiiiderneatli the 

 fides, and the perpendiculars in the third column. Prefix the 

 negative fign - — to thofe bafes and perpendiculars, whofe pofi- 

 tions are defignated by B. Paffmg over the prime fide, the 



mean calctdatral dijiance of the fecond fide is equal to ; and its 

 perpe?idtciilar is equal to its ultimate calculatrat dtjlance. Take 



''um of the ultimate calculatrat diftance of the fecond fide, 

 and tlie perpendicular of the third according to the rules of 

 Algebra, and it will be the mean calculatral dijlance of the 

 third fide. Again take xhtfum of the '^iox^{2^A perpendicular 



and jncan calculatral dijlance^ and it will be the ultimate calcu- 

 latral dijlance. of tlie third fide. In hke manner proceed with 



h 



each of the remaining fides. Multiply the mean calculatral 

 dijlance of each fide by its bafe : then halfxh^ Algebraic /um 

 of thefe producfts will be the required area of the polygon. 

 It may here be obferved, that when the work is c{one right, 



m _ 



the angle of comrfiutation for the lafl fide is equal to the given 

 angle at the beginning of the operation : alfo the fum of the 

 afKrmative bafes is equal to the fum of the negative bafes ; 

 and the fum of the affirmative perpendiculars is equal to the" 

 fum of the negative, which is the cafe, when twice the perpen- 

 dicular of the prime fide being added to the ultimate calculat- 

 ral diftance of the lafl fide, the refult is equal to the perpendi- 



of the fecond fide, but of a contrary value. 



EXAMPLE 



d? 



