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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRTNOIPLA MATHIEMAEICA.
Corol. 2. FC, cum tempora periodica sint in ratione compolita ex
l  L H
racione radiorum directe ee ratione relociratum inverse, vires cen. Latuve
tripetx lune reciproce ut quadrata temporum periodicorum appli-
caca ad circulorum radios; hoc elt, in ratione compolita ex ratione
radiorum directe ex ratione duplicata temporum periodicorum in-
verlc.
Corob. 3. Inde E tempora periodica aequentur ec propterea ve-
locirates sine ut radii; crunt etiam vires centripetae ut radii: ec
COntra.
Cor. 4. Si ex tempora periodica ec relocitates sint in ratione sub-
duplicata radtiorum; aequales crunt vires centripetae intor (c: ec
COnEra.
Corot. 5. Si tempora periodica sint ut radii ex propeerca veloci
cates aequales; vires centripetae crune reciproce uc radii: ee contra.
Corol. 6. Si tempora periodica line in ratione sesquiplicata radio-
rum ex propterca velocitates reciproce in radiorum rarione lubdu-
Plicata; rires centripecx crune reciproce ut quadrata radiorum:
ec contra.
Corol. 7. FC universalicer, si tempus periodicum sE ut Radii R
Potestas qualibet Ae, ec propterea velocitas reciproce ut Radii
Potestas R; erie ris centripeta reciproce ut Radii porectas Rn:
EE COMEIA.
Corol. 8. Fadem omnia de temporibus, velociratibus, ee viribus, qui-
bus corpora limiles figurarum quarumcunque limilium, centraque
in Rguris illis similiter posita habentium, parres describune conse-
quuntur ex Demonstratione praecedentium ad hosce casus applicata.
Applicatur aurem substicuendo equabilem arcarum deseriptionem
pro requabilimocu, ee distantias corporum a ceneris pro ractiis ulur-
pando.
Corol. 9. Fx eadem demonstratione consequitur eciam; quod ax-
cus, quem corpus in circulo data ri centripeta uniformiter revolven-
do tempore quoris describie, medius est proxortionalis inter dia-
metrum circulis ei descentum corporis eadem data ri eodemque rem.
Pore cadendo confectum.
Scholium.
Calus Corollarii sexri obtinet in corporibus caelestibus, (uE SeOr-
sum collegerunt etiam nostrates Wrennus, Foohius ee FLatlaus) ec
propterca quae spectant ad rim ceneripetam decrescentem in dupli-
caea racione distantiarum a ceneris, decreri Fusius in sequeneibus
EXPONCTE.
POTTO