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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 51, page id 1040780814:0069
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ib
S locu
AIIOS
entritus
lFOCOTUI
PrOPOn
Peta eju
IS Cent
Tta Para
utriusqu
ejusde
dentium
crifued.
spectire
Conrer
i cum
A COrpI
ad quo
Propo
est Ter
PR
LIb. B
_E GTEOMEZRTOA F LEMEN FA.
PROEOdLLIaC
ra plura revolvantut eaca cenlan commune, eos Vie
quod Duadrata Temporum periodicorum in Fllipsibus sunt ut Cubi
transversorum aurum.
in quibus superior constructio manere lupponatur. Flarum latera
recta, AVOL _ I, (per COrOI. 6. Propositionis pracedentis,) aequantur
BD9 BdG
RBG respectire; cocuntibus nempe B_ e, item B _ p. Sed eB CAt
ad rb (cum timul generentur) ut Vis centripeta in e ad Vim centri-
petam in p; hoc est, ex hypothesi, ut 5pg ad SPg: Erisitur L.. 1::
BD9 ba.
l5pg. Seq::) BDGESEg.
BagrSeg. FF BDLSP CA
ad b a  sp ut iplorum sc
misses; hoc cA, ut arex à
corporibus ea p limulde
Scriptx: Ft isitur L. e B
TunEuE Ouadrata arearum
quas corpora, radiis ad
commune centrum S du.
eis, eodemtempore delcri
bunt; hoc est, dictx area
Cmul descripex Punt in
Subduplicata ratione laterum rectorum. Cumque inteoia LNipsium
arex sint ut harum particula simul descripex, dueta in respectira
tempora periodica; erunt arex illa intezrae inter se in ratione com-
posita ex ratione Cubduplicata laterum rectorum, et ratione tem
Dorum periodicorum. POrrO, (per PrOP. CXeT. Lib. 4. Gregorii à
510. Fincentio,) FIlipAIS ACTY eA ad asLy ut ATKGY ad
atre p: Adeoque etiam rectangula sub axibus flliplium tunt in
ratione compolita ex ratione subduplicata laterum rectorum, e ra
tione temporum periodicorum; hoc cR, ut L. 2 tempus periodicum
e quadrando terminos inde relultantes, hiet ar Cubus ad at Cu-
bum ut Ouadratum Temporis periodici in FIlips a P Fad Ouadra-
cum Temporis periodici in FMipsi a p t. Ouod erat demonstrandum.
CiOROLLARTOM L
Sint dux quaeris Orbitae P F, apt circa communem Focum B,
in a Pxad V:  tempus periodicum in a p F. POTrO, exnatura F IIPHS,
Eex est media seometrica inter L e AY, e cy inter I _ at; sive
CX = L. E x A F3, 88γ = 12 x a FE. VndO L EL A T3. I= ~ a F 2:: (CZX AZ.
Pxab.LEntelus peoue a eI.  uipus peroent
in a pF. AppCaCGatS au L. 2, _ consequentes ad l2
duoniam Circulus ett Llliplis lpoeico; nempeubt Locus ulerque
cum