„CTceffus. arcıus defcenfu toto defcriptä fupra arcum afcenfü fubfequente

. deferiptim, ad penduli longitudinem duplicatam.

Defignet BC arcum defcenfu defcriptum, C a arcum afcenfüdeferiptum, 8& Aa differentiam arcuum:& ftantibus. quz mPropolitione XXV. conftrudta& demonftrata funt, erit vis quacorpus ofcillans urgetur in loco quovis D, ad um refiftentig utarcus CD ad’arcum C 0, qui femiflis eft differentie ilius Aa. Ide-oque vis qua corpus ofcillans urgetur in Cycloidis principio. feupun&o altillimo, id eft vis gravitatis, erit ad refiftentiam ut ar-cus ‚Cycloidis inter. pund&um.illud füpremum& pundum infi-mum C ad arcum CO; ideft(fi arcus duplicentur‘) ut Cycloidistotius arcus,feu dupla penduli longitudo,ad arcum Aa. Q,. E.D.

Prop- XXIX. Prob. VILPofito quod. corpus in Cycloide ofcillans refiftitur in duplicata ra-

#ione welocitatis: invenire refiftentiam in locis fingnlis. ı

Sit Ba( Fig. Prop. XXV.)arcus ofcillatione integra defcriptus,

fitque C infimum Cycloidis pund&um,&€ Z femiflisarcus Cycloi-

dis totius, longitudini Penduli zqualis;& queratur refiftentia cor-*poris in loco quovis WE

D. Secetur reca infi-

hita 0Q in pundis 0,/C,P,Q ca lege ut(fierigantur perpendi-cula OK, CI, PT,OE, centroque 0 8Afymptotis 0 K; 0Q deferibatur Hyper-bola TTG E{ecans'; Bat;perpendicula CT, PI; Q Ein T, I18&-E,& per pundum I agaturK F occurrens Alymptoto 0 K in K,& perpendiculisıC T 800 E

in L8& F) fuerit area Hyperbolica P IE Q ad aream HyperbolicamPITC

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