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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 50, page id 1040780814:0068
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LLDLRONOMLA PAESTCA
CiOROLLABTOM 5.
(scil. contrum ad quod
Vis dirisitur) ad distan.
tiam abeat plusquam in-
Ainitam, ut in Corol. 3.
foco F contisit; tum Hl.
lipsis vertetur in IIyper-
bolam, e corpus detine.
bitur in perimetro figu-
ex sc mutata, per Vim
quae secundum rectas Se
quidem dirisitur, e quae Ouadrato distantix loci à centro s est
reciproce proportionalis; sed qua respectu puncti s est centrifusa,
quia Curra AP CA versus illud conrexa.
Sicut FMipsis deseribitur a corpore quod ursetur a Vi ad Focorum
alterutrum (quia internum) cendente, d secundum legem Provosi-
tionis prxecedentis asente; ex Fyperbola, dum Vis centripeta ejus.
dem Legis ad focum internum rendit, vel dum dicta Vis contri.
veta mutatur in contrifugam tendentem à foco exteriore: Ita Para
Bola, inter sectiones dictas quasi intermedia, naturam utriusque
etiam hic participat; describiturque urgente Vi centripeta ejusdem
Legis ad Focum internum tendente, (ut in utraque pracedentium,)
e etiam urgente Vi centripeta ad focum alterum, vel contrifyoz,
illo altero tendente, (ad morem FIlipsis _ Fyperbolae respectire;
prout nimirum focus ilte alter ad partes Currae caras vel conrexas
Politus censetur: Potest namque urrolibet modo considerari, cum sit
intinite dissitus.
CiOROL L APTUMI 6.
Ex hac Propositione cum suis Corollariis sequitur, quod Ai COrpuS
quodris secundum lineam quamvis rectam eR quacunque cum
Velocitate exeat de loco quolibet e, de simul urseatur a Vi contri-
peta, qux t reciproce proportionalis Ouadrato distantia loci d
centros, extra praedictam rectam sito; movebitur hoc corpus in ali-
qua Sectionum conicarum, umbilicum habente in centro ad quod
Tis tendit. Nam in nullam Lineam praeter Rectam e coni Sectiones
poterit (per motum alterutrius foci in axe eore producto) praece.
dentis Propositionis F llipsis mutari. FF Sectionis hujus latus rectum
principale (ad axem majorem pertinens) tire L, ex iptius Proposi.
tionis demonstratione (in qua ostensum est L. X B R = BD9) est tertia
proportionalis ip(IS BR e BD natcentibus.
Reliquis ut in Corollario pracedente manentibus, sI FOcUS S