TAVTOCHRONIS IN FACIO 5- 



§. 14. Qiiacniinns cflfiis, quibus ambae cui- 

 ua -• lint nucr lc acqualcs. Eric igicur szzzt. (^iiarc 

 cu'ii fit s-\-l—2V'^x\ erit 2f— slV/.v j feu s—Vax. 

 \ix quo cognofcitur, vtramquc curuam cfTc cycloi- 

 (icni , ncquc alias hoc fenfu fatisfaccre curuas prae- 

 ter cycloidcm: Supra enim dcmonftratum e(\. nnftra 

 mcthodo problcma propofitum gcncraliirimc folvi. 

 Qiiemadmodum hic pofitum erat s—t, fic quaccun- 

 quc acquatio intcr j ct / potcfl accipi , et dcinde 

 duac curuac dari, \t arcus afcenfus ct defcenfus eam 

 habcant intcr fe rclationcm. Vt, li quacrantur duae ^'^z- ^ 

 curuae problcmati fatisficicntcs CA , DA , ut fit 

 fcmpcr AM : ANzrw : ;/, erit mtzzins ^ ct t—ns : ;;/. 

 Ergo s-\-tzz{ms-\-ns):vi—zVaXy undc ctlicitur 

 ^—li^ny^x- Pcrfpicuum ergo eft, curuam AC cfTc 

 femicycloidem diamctri - """" , ct altcram ADN 



2 

 n a 



quoque fcmicycloidcm diamctri 



(m-HH)* 



§. 15. Cum cfTc dcbcat .f-f-/— -aV^.v, yt am- 

 bac curuae pracbcant tautochronam ofciiiationcs 

 ifochronas pcnduli longitudinis In habcntcm ; Sit 

 s—Vax-i-v , et t—Vax-v. Hoc igitur modo 

 duae curuac inucnicntur fatisfacicntes. Erit itaquc 

 ^•^=r;^-+-^'^' , et fit—j^^^-dv. Ponatur dvz^dx: 

 hihclmui- ds-fj^^-^-u^x y ct dt-^^^-ucJx. Qnarc 

 fi y lihus et z hujus curuac dcnotcnt applicatas, erit 

 d\—d.xV{~-if-^'^^-i-uu-i). Atque dz—dxV{~^^ 

 -i-uu-i}. Hic fi loco // fubftituatur quaecunque fun 

 Tom. ir. H dlio 



au 



Vox 



