J4 



ASTRONOMICAL and 



glcs of commutation may be 

 which contains two cafes. 



r 



u _ 



found by the following rule. 



Case I. When the letters affixed to the angle of commuta- 

 tion la/l found, are xhzfame, 



4 



Take theyu'm of the angle of commutation lafl found and the 

 given angle, if the given angle be inward : but if it be outward^ 

 take their difference^ 



Case II. When the letters affixed to the angle of commu- 



lail found 



difft 



\ 



Take the difference of the angle of commutation lail found 



and the given angle, if the given angle be inisoard i but if it 



be outward^ take 'Clci€\Y fiim ; and the refuk is denominated the 



faElum . 



In both cafes when the fa(5lum is lefs than 90, it is 



the angle of commutation fought : but when it exceeds go 

 fubtrad it from 180; and when it exceeds 180, fubtrad 180 

 from it, and the remainder will be the required angle of com- 



mutation. 



Nextly the pofitions of the bafes and perpendiculars may be 



eafily difcovered from the foregoing operation by infpeaion 

 thus : 



Case I 



Pr 



When the fadlum is le/s than 90. 



i 



. If the angle of commutation be fubtraSied from the 

 given angle, the letters prefixed to the two angles of commuta- 



laft found, will be unlike, and the letters fuffixed will be 



like. 



2 



Prop. 



V 



4 * 



