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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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11
PHTLOSODTLE NATVRALIS
De Moro latera recta principalia sunt aequalia relocitas corporis est reciproce
Conronum uc perpendiculum demissum ab umbilico ad tansentem.
Corol. 6. In Parabola, velocitas est reciproce in subduplicata ra-
cione distantiae corporis ab umbilico fgurae; in Fllipsi magis varia-
cur, in LExperbola minus, quam in hiac racione. Nam (per Corol.
2. L Cm. XIV.) perpendiculum demissum ab umbilico ad tangentem
Parabolae est in subduplicata ratione distantix. In FIpperbola per-
pendiculum minus variatur, in FIlipsi maois.
Corol. 7. In Parabola, relocitas. corporis ad quamris ab umbili-
codictanciam, est ad relocitatem corporis revolventis in Circulo
2d eandem a centro dictantiam, in (ubduplicata ratione numeri bi-
narii ad unitatem; in Ellipsi minor est, in FIyperbola major quam
in hac ratione. Nam per hujus Corollarium secundum, velocitas
in vertice Parabolae est in hac ratione, ec per Corollaria (exta hu-
jus e Propolitionis quartae, serratur eadem proportio in omnibus
distantiis. Hlinc etiam in Parabola relocitas ubique aequalis est ve-
locicati corporis revolventis in Circulo ad dimidiam distantiam, in
Fllipsi minor est, in HIyperbola major.
Corol. 8. Velocitas srrantis in Sectione quaris Conica est ad ve-
locitacem grrancis in Circulo in dictantia dimidii lateris recti princi-
palis Sectionis, uc distantia illa ad perpendiculum ab umbilico in
cangentem Sectionis demissum. Patet per Corollarium quincum.
Corol. 9. Inde cum (per Corol. 6. ProD. IV.) velocitas srrantis
in hoc Circulo sic ad relocitatem grrantis in Circulo quovis alio
reciproce in lubduplicara ratione dictanciarum; het ex equo velo-
cicas orrantis in Conica sectione ad velocitatem grrantis in Circulo
in eadem dictantia, ut media proporcionalis inter distantiam illam
communem ex semislem principalis lateris recti sectionis, ad per-
pendiculum ab umbilico communi in tangentem sectionis de-
mistum.
PROPOSITIO ZVII PROBLEMA. IX
Posito quod vis centripeta sit reciproce proportionalis quadrato distan-
stantiae locorum a centro, 5 quod vis illius quantitas absoluta sit
coenita; requiritur Linea quam corpus describit, de loco dato, cum
data velocitate, secundum datam rectam ecrediens.
Vis centripeta cendens ad punctum S ea sic qua corpus p in Or-
bita quaris data pq Grretur, ec cognoscatur hujus relocitas in loco p.
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