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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 49, page id 1040780814:0067
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l1D.
 ad PN
Um L
9c01
O2
ex 1
aquati
72BD4
BR
eAt ret
1. RIB
15 a CUI
PTOXIM
cum iII
FlipsI
F. ip
ectam
eripet
CiOn
LIB. I.
eE GTEOMLLRLCE ILLEMENT A.
GiOROLLARTUM 2.
AFllipsis focus s, ad gdem ceu centrum Vis alsu,, una cum
vertice Proximor maneat, alter vero focus F masS a On;
setur, _ tandem in intinitum abeat; siih, fit (se
corpus e eodem modo quo prius in peri ut ls
metro Rioura T P detinebitur a Vi centri.
Peta ads cendente, cujus cadem es qua
prius L Cx. Atqui in hoc casu FIlipsis mu-
tatur in Parabolam: Et isitur l ex Vis
centripetae cendentis ad umbilicum Para-
bolx, qua corpus in hujus tisura perime
tro detinetur; Ca cs, ut fit Ouadrato distan-
tix ab umbilico reciproce proportionalis.
COROLLARIOu:
DI returo  Plius Manentibus, FIlipss umbus acu e ad
distantiam plusquam infinitam ab- leor (cirrireisiui
Cat; (hoc eH, E a terso redeatver.
TuS Y, Faciatquo nunc vertices A e r1B
T inter focosSesF; cum prius fu  C11
erint Tocis et F inter vertices A 11I
_ T,) in quo casu F Iipsis mutatur R ic
in TIrperbolam; corpus eddem
Lesc Viscentripeta asitatum qua
Prius, (nempe ut Vis illa augeatur LiON
inratione qua uadratum diltantia
a centro diminuitur,) in perimetro hujus Fyperbola moreri perget.
GIOROLLARTOM qu
Ouod SI DMipSS Puperioris maneanE FoCUS F, erqu proximus ver-
tex a, dum interim Focus alter s, ad quem Vis asisitur, masis
magisque clonsatus, tandem in infinicum abcat, (hoc elt, l Lllipsis
rertatur in Parabolam:) Vis centrivetas
quae dixisitur ad punctum s intinite di
Ctans, sire secundum rectas Parabola axi
AF DarallelaS, quaque ursetur corpus in
verimetromotum, cradet aequabilis: Nam
distantia a centro intinite dissito, quarum 
incerralla sunt finita, aquales funt. Adeo.
queV is, qua es reciproce ut Ouadratum
illius distantia, aquabilis est. Ft c con
verso, corpus quol arsetur a Vi xquabili
tendente ad centrum intinite distitum, quaque proinde dirisitur
secundum rectas data cuidam paraHlelas, motu luo describet Para-
bolam, cujus axis praedictae rectae parallelus CHt. Atque hoc cst ce.
lebre Calilaei Theorema de Projecti semita.
(111
CiOROF