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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PHILOSOPHLAE NATVRALIS
Scholium.
SX AC
Fadem ratione qua prodiie densiras Medii uE B L  = in C0.
rollario primo, si relictentia ponatur ut relocitatis V dignitas quae-
libet V prodibit densicas Medii ut
R
=X AC
EF Propterea (i Curra inveniri potest ca lege ut data fuerit ratio
R
 n ac
t
AL.
vel 7 + = n 20 Y + OQI: COrpUS move.
bicur in hac Curra in unitormi Medio cum resistentia qua sIE uE
relocicaris dignitas V. Sed redeamus ad Curras simpliciores.
Ouoniam mocus non tit in P’arabola nisi in Medio non resisten-
te, in Fyperbolis rero hic delcripeis tic per relistentiam perpetuam;
perspicuum est quod Linca, quam projectile in Medio uniformiter
resiltence describits propius accedit ad IIyperbolas halce quam ad
Parabolam. Fs utique linca illa EIyperbolici generis, lcd quae
circa verricem magis dictat ab Asympeotis; in parcibus a vertice
remotioribus provius ad iplas accedit quam pro ratione IIyper-
bolarum quas hic descripsi. Tanca vero non est inter has ec illam
difterentia, quin illius loco possine hae in rebus practicis non in-
commode acthiberi. Fc uciliores Forlan Fucurx sunt hx, quam
EIyperbola magis accurata et simul magis compolita. Ip (X vero
in usum SC deduCenEUr.
Compleatur parallelogrammum XTOT, ec recta C. P tanget
Eyperbolam in G, ideoque densitas Medii in Cr es reciproce ut
tangens CT, ee relocitas ibidem ut V
vim gravicatis uc CZ ad 2nn + 2B CV.
n + 2
relistentia autem 2d
Proinde s corpus de loco A secundum rectam AFY projectum
describat Hyperbolam ACK, ec AFI producta Occurrat ACymp-
EOtO N X in FI, actaque AY eidem parallela occurrat alteri Asymp-
toco M X in P: erit Medii denscas in A reciproce ut ATI, et cor-
Poris velocitas ut y , dc relictencia ibidem ad Gravitatem ut
AIId
nn + 2n
in AL. Onde prodeunt sequentes ReguIX.
Rec. 1.
2AC
DE MOTD
LORPORVII