1ſitione XXV conſtructa & demonſtrata ſunt, erit vis qua corpus
olcnlans urgetur in loco quovis D,ad vim reſiſtentiæ ut arcus
CDad arcum CO,qui ſemiſſis eſt differentiæ illius Aa.Ideoque
vis qua corpus oſcillans urgetur in Cycloidis principio ſeu puncto
altiſſimo, id eſt, vis gravitatis, erit ad reſiſtentiam ut arcus Cy
cloidis inter punctum illud ſupremum & punctum infimum Cad
arcum CO; id eſt (ſi arcus duplicentur) ut Cycloidis totius arcus,
ſeu dupla penduli longitudo, ad arcum Aa. que E. D.
olcnlans urgetur in loco quovis D,ad vim reſiſtentiæ ut arcus
CDad arcum CO,qui ſemiſſis eſt differentiæ illius Aa.Ideoque
vis qua corpus oſcillans urgetur in Cycloidis principio ſeu puncto
altiſſimo, id eſt, vis gravitatis, erit ad reſiſtentiam ut arcus Cy
cloidis inter punctum illud ſupremum & punctum infimum Cad
arcum CO; id eſt (ſi arcus duplicentur) ut Cycloidis totius arcus,
ſeu dupla penduli longitudo, ad arcum Aa. que E. D.
LIBER
SECUNDUS.
SECUNDUS.
PROPOSITIO XXIX. PROBLEMA VI.
Poſito quod Corpori in Cycloide oſcillanti reſiſtitur in duplicata ra
tione velocitatis: invenire reſiſtentiam in locis ſingulis.
tione velocitatis: invenire reſiſtentiam in locis ſingulis.
Sit Ba(Fig. Prop. XXV) arcus oſcillatione integra deſcriptus,
ſitque Cinfimum Cycloidis punctum, & CZſemiſſis arcus Cycloi
dis totius, longitudini Penduli æqualis; & quæratur reſiſtentia cor
177[Figure 177]
poris in loco quovis D.Secetur recta infinita OQin punctis O,
C, P, Q,ea lege, ut (ſi erigantur perpendicula OK, CT, PI, QE,
centroque O& Aſymptotis OK, OQdeſcribatur Hyperbola TIGE
ſecans perpendicula CT, PI, QEin T, I& E,& per punctum I
agatur KFparallela Aſymptoto OQoccurrens Aſymptoto OKin
K,& perpendiculis CT& QEin L& F) fuerit area Hyperboliea
PIEQad aream Hyperbolicam PITCut arcus BCdeſcenſu cor
poris deſcriptus ad arcum Caaſcenſu deſcriptum, & area IEFad
ſitque Cinfimum Cycloidis punctum, & CZſemiſſis arcus Cycloi
dis totius, longitudini Penduli æqualis; & quæratur reſiſtentia cor
177[Figure 177]poris in loco quovis D.Secetur recta infinita OQin punctis O,
C, P, Q,ea lege, ut (ſi erigantur perpendicula OK, CT, PI, QE,
centroque O& Aſymptotis OK, OQdeſcribatur Hyperbola TIGE
ſecans perpendicula CT, PI, QEin T, I& E,& per punctum I
agatur KFparallela Aſymptoto OQoccurrens Aſymptoto OKin
K,& perpendiculis CT& QEin L& F) fuerit area Hyperboliea
PIEQad aream Hyperbolicam PITCut arcus BCdeſcenſu cor
poris deſcriptus ad arcum Caaſcenſu deſcriptum, & area IEFad
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