IVIATHEMATICAL PAPERS. 



35 



Prop. 2, If the 2ing\e of com?nufatwn he ?iot/ukra&ed from. 



tlie given angle, the letters prefixed will be utilih, and the 

 letters fuffixed unlike. 



" j- 



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Case II, When the fadum is greater than 90. 



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Prop. \^ If the fum of the angle of commutation Sind given 



angle hefubtraSledfvova 180, the letters prefixed will be like^ 

 and the letters fliiExed unlike. 



Prop. d. If the aforefaidy2/?B be not fubtra&ed from 180, the 

 letters prefixed will be like^ and the letters fixffixed like. 



r < 



When the facfl^m ia 90, it may be confidered as belonging 

 either to Cafe I, or Cafe II ; and when the fa(ft\im is i8o, it 

 may be confidered as belonging either to Cafe II. Prop, i , or 



Cafe II. Prop. 2, ad libitum ; each fuppofition leading to a true 



difcovery of the pofitions of the fubfecjuent bafes and per- 

 pendiculars, 



* 



The calculatrix is a line K L (Plate I. fig. 12.) bifedling the 

 fecond fide B G, and at right angles with the prime fide A B. 



r 



A perpendicular D L drawn from the farther extremity of a 

 fide C D to the calculatrix^ is the ultimate calculatrat dijiance 

 of that fide. ' 



A perpendicular M S, drawn from the middle of a fide C D> 



the mean calculatral dijiance of that fide. 



In the following method the calculatral diftance is taken 



double. 



