AD QUESTION EM BIATHEMATICAM. 27 



i 4- o* 4" ^"' 4" c *' + elc - = \ 



i -L aft 4- bfl* -\- cfl* 4- elc. =. o >....() 



I i t i i \ y 



i -\-ov-\-bv'' -H fry ' 4* e * c> 0*0 1 

 etc. 



Eritque ( a3 ) aequatio linalis quam n vocare placet , haec 



n r= ( i + a* 4. b*' + c 3 4- etc.) ( i + a/a 4- bft" 4- c 3 + etc.) 



( i 4- ay + yl + cyj -h etc O ( + a^ 4- W' + c^' 4- etc> ) etc< 



cujus factorum numerus = m. In eo igitur jam versatur cardo difticultatis , ut 

 lateutibus aequatiouis (A) radicibus exliibeatur aequatio n. In hunc finem 

 utriusque membri logaritbmos sumentibus exslabit : 



/n= l(\ + a * 4- &' 4- etc.) + l(\ -\-afl + b/*' 4- etc.)+/(i 4-ay+ty 1 4-etc.)+etc. 

 Jam vcro ex supra dictis : 



f ft 4" b* 4* c* 1 4* etc. ) 



c- J 



etc.) = 



etc. 



quae , spcctando quantitates a', 6', d etc. a", &", c" etc. ceu compositas ex 

 coefficientibus a,6,c,d, etc. sicuti supra has A', B', (7, etc., A",B", C",etc. 

 per coeflicientes A,B,C, etc. expressimus , mulabilur in sequentem: 



/(i + a* 4- 6*' + c 3 4-etc. ) = 



Hoec vero pariter , positis compendii causa : 



-f- 



d* 



' 3 



etc.) 

 etc. ) 



"' 4" etc< ) etc> 



o' 



abibitin /(i+a+ &' +c J + etc.) =^ 

 Eadem omuiiio ratione inveniretur : 



/( i + aft + bP + cjs ] + etc.) = 



/( i + ay -j- ^v 1 + cy 3 + etc - ) = 



j c' i V' a'" 



= d +- etc - 



etc. 



5 + etc. 



