ao2 ANALTSIS AEQ^VATIOKFM 



niti pendeant omnes a quadratura circulivel hyperbolr, 

 itautnondefit lafpicionilocus^aequationes algebraicas ex - 

 hiberi non polTe nifi fimul yel circuli vel hypcrbolae qua- 

 dratura innotefcat. Dabo in {equentibus paradoxi folu- 

 tionem , nunc ipfom analyfin aggrediar. 



VII. Cum fuerit ^—2 fit sequatio (C) talis 

 (M) ax^^dx^bjydxiiidj 

 ponatur miizo , & erit (N) adx-^-byydx-^y, vel 

 dx—-^^-) cuius asquationis conftru£Ha pendet a qua- 



dratura circuli , fi ambse quantitates « & ^ fint affirmati- 

 vge vel amb^ negativas , fecus poftulat quadraturam hy- 

 perbolae. Nuncoftcndam quomodo ex cafu wzzovtA.- 

 niti alii deduci pofiTint. In asquatione (M) ponatura:" 

 (m-^^^f^ ^2;^'-'"^3&^.j-x(w-f-3)r'--^y • ^"3 



^l^[m-\-if-^-p-^^^-^^q-\ atque fic cbtiucbitnr 

 nova squatio priori plane fimilis, nempe talis 

 (N) ap-=^-'^' ^'^dp-^hqqdp-=^q. 

 Ex hac autem fimilitudine asquationum (M) & (N) 

 concluditur quod quoties m eft cafus feparabilitatis , fit 

 quoque ~^- talis : hincque ftatim infiniti oriuntur j fii 

 tnim;;;=z^fit^=-^ ; deinfi m:^-%, fit=^-|=-|, 

 6t fic porro:omnes hi cafus mzzj)^ mziz--^ j m——\ &c. 

 continentur in hac formula generali mzz-^^ intelligerj- 

 do per n numerum integrum, 



VIII. Ex proecedenti ^. patet polTe hanc ae- 

 quationem ax~'^'''- ^^' dx-^hyydx—dy femper geome- 

 trice ope quadraturae circuli vel hyperboIiE conftrui , 

 quoties n eft numerus integer , quia femper poteft redu- 

 «i ad haiic sequationem a ds-\-httds:iidt;kd pro hac rc- 



dudio- 



