TAVTOCHRONA IN fLVlDO. 541 



non fueriot inter fe aequaks. Hoc cafu peipenfo in 

 geiie.rje coUigimus ftatui debeie 



y — e 'j^iacVz et e ' ~j — \ctfVz 

 fic enim quoque tertiae noftrae aequatiqni fatisfit > 

 et nunc bina tempora defcenfus et afcenfus non am^ 

 plius funt aequaiia. Tenendum autem eft > quanti- 

 tatem j pro pundo infimo O in vnitatem abire 

 debere , quoniam hoc loco quantitas z euanefcit , ex- 

 ponentialia autem abeunt in vnitatem. Hinc iam 

 pro defcenfu ob 



— 15 — ^ 



Vz^^aCy^e ^) u zzzaa{y^^je '-^e^'^), 



habebimus 

 dzzn^aadyO-e ^ ) ^aac/iSCje «-.<?-« ^j 



vnde pro curua deducitur ifta aequatio 



dX-2aadj{je'^''^—e'^ '^ + aacdSlje^ » — j). 

 Eodcm modo pro afcenfu , quum fit 



V zzza (e ^^j) 

 ideoque 



zz^ aa (e-^"" 2j e^ » ^jy) , 

 dif!erentiando nancifcimur 



t c S \ti 



dz — aacds^e^^^^—je^ * )— 2<7<!f(//(^"'"a -^) 

 zze^''^ dx y vnde fit 



dx=:aacd^{i^jf ^^-^naadj^e * -jd^'')^ 



V V $ qua« 



