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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 30, page id 1040780814:0048
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C
TADLRONOMTA PALSICA
Fiat figura mr c e similis figurX X CD; unC _ C H est etiam re-
Etuta nascens: Adeoque CH e D ad G H SCuL arCUS F D ad arcum
MH. FF (per prX CCd.) C E CAtad EF
UE MHg ad Mt F g: Ft isItUT, CX X
quo, cD cA ad E F SICUL (FD L MH9
adMM RMEg; hOc CA, SICUE TD X MH
ad MF q, Sive LiCUt) TD X MH X S T
ad MFg = ST. Porro, ob similitudi.
nem ASUFAFLIM TOD, MGH, arCUS
TD, M _ sunt similes; id eAt, 8 X
BM :: YD. MH: OndC M H ~ S Y
= FD = SM. Posito erso hoc illive
lOCO, Crit CD. PF:: (FD9 X SM.
MFG X ST::)
TDG MEg
SL
SM. Sed sI
pra fuit ostensum Vires Centripetas
Corporum T _ M eAe ipLS CD, P F proportionales. FF igitur Vis
Centripeta corporis in F R Gyrantis eA ad Vim Centripetam corporis
sgrantis in m a sieut:
5Y
ag. MF
EM. Et (propter motum in utroque
circulo aequabilem) TD, M F, cum simul describantur, candem ha-
bent rationem cum simul descripris quolibet tempore. Ouare Vis
Centriveta corporis srrantis in Y R Cs ad Vim Cencripetam orran-
tis in m a sicut Ouadratum arcus quolibet tempore in T e descripti
applicatum ad radium s r ad Ouadratum arcis eodem tempore in
ni a descripti applicatum ad sMr radium.
Porro, si pradicta corpora ad centrum s alligata concipiantur per
Fila, quorum interrentu in praedictis circulis detinentur; Vis cadem,
qud tenditur silum, qua, in filo corpus trahente considerata, dicta cA
Vis Centripeta, si in corpore filum trahente consideretur, dicetur
Vis Centrifusa: Lademque proinde vera lunt de ViCentritusa, qua
de Centripeta sunt demonstrata. Oua crant demonstranda.
GOROLLARTOM L.
TTinc sequitur, quod s corpus agitatum eam per Vim Centripetam,
qua in circulo retinetur, demittatur versus centrum; ita ut Vis hac
in descensu neque auseatur neque minuatur, sed eadem maneat, e
praeter impulsum prius imprestum, norum e aqualem corpori per-
petuo superaddat, (ut fit in Galilaeana hypotheti Graritatis:) Ouo
tempore dictum corpus in circulo describeret arcum quemlibet, de
Scentu suo versus centrum percurret rectam aequalem orta, si qua-
deatum dicti arcus ad circuli diametrum applicetur. Nam ex Prop.
naC ZXV. patet istud ipso casis initioheri; e in praesenti descentis
hypochesi Spatia percursa sunt in duplicata ratione Pemporum; e,
cum circulus aequabiliter describatur, arcuum descriptorum Oua-
drata sunt etiam in duplicata ratione Temporum, quibus deseribun.
EUE: Atque Ouadratorum horum applicatio ad circuli diametrum
(quippe conttamtem) rationem hanc non mutat. Patet isitur istud
perpetuo
D.
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