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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 292, page id 1040780814:0310
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292
auferatur Vis, qua est reciproce in ejuldem triplicata ratione; LCI
quetur Vis, qua urgente corpus describet Flliphn cujus apsides re.
crediuntur: Differentia enim Virium R=Cg =R= PQ est in hoc casu
A cub.
necatira; ee proinde e minor quam e, sire angulus A XL qua AXL.
minOr.
CiOROLLARTLM 2.
Atque hinc rursus sequitur quod si in orbe, a circulari non mut
tum abludente, Vis centripeta in receltu a centro decrescat magis
(hire minor (H) quam pro ratione duplicata distantia auctae; orbis
apsides morebuntur in consequentia. Sit enim immota FNipsiS AL. P
orbis descriptus a corpore, quod urgetur a Vi ad centrum r ten
dente, cujus tumma aptis a duplo magis distat a centro x quam ima
P; non quod talis orbis ad circularem accedat, sed hanc rationem
majoris perspicuitatis et tantum exempli gratid ponimus. Suppona.
mus Vim centripetam, qua corpus in P ursC.
tur, esse partium 400, e Vis, qua in a urse-
Tur, erit 100, _ in locis intermediis proDOr-
tionaliter; illa nempe Vis, qud ursente Cor.
pus Fllipsin immobilem a LP describeret,
Ec. reciproca duplicata dictantix a centro. Si
jam praeter hanc Vim, corpus in P urgeatur
alia Vi qua sit ex. er. ut 64 e in a Viqua
Tit ut 8, _ in locis intermediis proportiona.
liter; nempe st hac Vis superaddita inverse
ut cubus distantia a centro; in hoc casu (por
PExC. COrOL.) aptides in consequentia feren-
tur. Vorum Vis tota in e Tire ex binis composita cA ut 464, _ V18
in a ut 108, _ in locis intermediis proportionaliter; hoc eAt, in
receltu a centro Vis centripeta minuitur magis quam pro ratione
duplicata distantia auctae: nam R ea minveretur in illa ratione
dictantix duplicata tantum, Vis in A FOret ut TF6. Ft liCet requi
ratur ut Vis nora, superaddita priori illi qua est inverse ut qua-
dratum distantix, sit ubique praecise licut cubus dicta dictantix in-
verse, ut orbis ellipticus circa centrum Virium in consequentia re-
vOlVatuT: EE tamen FllipES haec a Circulo non mulcum abludat 8
Vis talis integra corpus urseat, qua in recestu à centro minuitur
masis quam quadratum distantia corporis d centro ausetur; orbis
hujus apsides in consequentia morebuntur. NTam quoniam, in orbe
fere circulari, distantia à centro non multum ditterunt; Vis illa
(cujus superadditione fit ut intesra Vis, qud urgetur corpus, minua-
tur magis quam quadratum distantia à centro ausetur) minuitur
in ratione quae non multum distert ab inversa triplicata distantia.
Sequitur etiam, si in orbe, circulari proximo, Vis centripeta de
crescat minus quam pro ratione duplicata distantia aucta, (HOC
elt major sit quam pro dicta ratione,) orbis apsides moreri in ante-
cedentia. Nam eddem manente Vi in e d an qua corpus t. liptia
immobi
ib.
ASTRONOMLL PAXSTCA
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