velnti euenit in piincflo A; et quoniam eft ^=0, pro fingu* 

 lis erit etiam angulus ACZmCj), fcilicet ipfi amplitudiui ae- 

 qualis, ex quo forma harum curuarum haud difficulter colli- 

 gi poteft. 



Alla folutio problematls, 



ex radio ve^lore CZ—z et angulo defcripto AC2=m, 



deriuata. 



§. 31. Ex his binis variabilibus 2; et w primo arca 

 ACZ~X ita exprimitur, vt fit X — l/as^u; deinde ve- 

 ro pro arcu curuae A Z — j habebimus: 



s =:// (jd z" -\- z z d hr) ^ 

 quibus formuiis inuentis noftrum problema poflulat vt fit 

 s s zz: ^n^ziz ^ nf zzd (j::^ 



quae aequatio quo euolui queat, (latuamus s9m — ^Ss;, vt flt 

 ^ui^^Ar, ficque loco anguli co nouam variabilem q introdu- 

 cimus, Qxit(\\\Q fzzd b^—fq zd z; tum vero fiet 



y {d z^ ~\- z z d (^r) — d z Y {'^ -\- q q^' 

 DifFerentiemus nunc noftram aequationem, prodibitque •z.sds 

 z=. 2. n q zd z, ideoque s ~ jrrr^ — 1' ^"^^ denuo diflferentia- 

 ta praebet 



3 



quae duc^a in (i ~\~ q qf dat hanc aequationem rationalem: 

 d z {1 -^- q qf ~ n q d Z {l -{- q q) -\- n zd q. 



§. 32. Ifla aequatio porro infigne hoc commodum 

 praeftat, vt binae variabiles a fe inuicem feparari queant; inde 



2 enim 



