PROBLEMA ALGEBRAICVM. 117 



Si aiitem I defignet coefficientem quantitatis [d—e). 

 ^^V""'""'* atoue fit 2 x << « — I , erit 



prout vero s fuerit numerus par vel impar, I figno 

 4- vel — afficietur. Terminus itaque vltimus po~ 

 flerioris membri aequationis , pro eo cafu , quo n 

 numtrus par , ponendo « zz 2 x H- 2 , habetur 



— J2 - , !',.%'".' .''. T^ ^ ±{^ -^ ^)-> ^^^ ^^ ^ numerus 

 impar et :r: 2 j- -4- i fit 



I. 2. 3 ■ • • • 9 ' — 



Hinc proinde fi n fit numerus par , erit acquationis 

 propofitae terminus is , quem quantitas incognita u 

 non in^reditur ^^ (^ 4- ^) ^*^""', fin vero impar erit 

 ille terminus -zz -^ { d -^ e \ e^"'. Denique et ex 

 his coUigitur, quod prout numeri terminorum con- 

 tinue proportionalium , aflfumantur ex quatuor hifcft 

 progreflionibus arithmeticis : 



4, 12, 20, 28, 36^ etc. 



6, 14, 22, 30, 38 etc. 



8, 16, 24, 32, 40 etc. 



10, I 8, 25, 34, 42 etc. 



terminos aequationis conrtantes , fore ex quatuor his 

 progreffionibus geometricis 



-{e^d).e -{e-\-d).e'--{e-\-d).e'' -(^-f^).^"-(^+^).^'' etc* 



--{d—e^.e^—^d—e^e^—id—e^.e^^-ld—e^e^^-id—eXe^' etc. 



{d-\-e).e {d-\-e).e id-\-e).e'' {d-\-e).e'' {d^e).e'' cic 



(d—e).e* {d—eye* (^— ^).^" {d—e)*e^ {d—eye^^ttz, 



P 3 %o. 



