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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
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2
ASTRONOMFA PAZSICA
cum contro coincidit, ee axis major aequalis cuiris diametro; patet
axium: Aclcose  asco ilorus Duadrata fuerint agualta,
Temporum periodicorum Cubi, ip laque proinde Tempora periodica,
xquabuntur: hoc es, cum idem est centrum Virium, Tempora DC.
riodica in Fillipsibus eadem crunt atque in Circulis, quorum diame.
tri aquantur majoribus axibus PIliptium.
COROLL ARTUM 2
Fx demonstratione Propolitionis patet, quod Orbium quorum.
cunque a corporibus circa commune centrum revolutis, et d Vi
centripeta, qua est reciproce in duplicata ratione distantix a centro,
asitatis, descriptorum latera recta sunt in duplicata ratione arca
rum quas corpora, radiis ad centrum ductis, eodem tempore deseri.
bunt: Hloc enim ostentum est universaliter de quibutris Orbibus
sive Fllipticis, sire Parabolicis, sire Hyperbolicis, antequam ad FiI.
lipses ratiocinatio eAt restricta; in quibus solis Tempus periodicum
locum habet.
PROPOSTTIO ZLI
mente eadem lese ristentiocta, duo quod corporum
 circa commune centrum revolventium,  elocitates in quibu-
vis punctis sunt inter se in ratione composita ex ratione sub dupli-
cata laterum rectorum principalium, pertinentium ad Lincas quas
describunt, e ratione inversa perpendiculorum à communi centro
demissorum in rectas tancentes ad puncta ubi versantur corpora.
Rerolrantur corpora P ex p circa commune centrum s’in Lineis
quibulris eB, Pb. Duoniam corpora, ex hypotheti, arsentur à Vicen
cripeta, quadrato distantia loci à centro reciproce proportionali;
erunt (per Corol. 6. PrOP. XXXIX.) Lineae lxe Sectiones coni, quarum
Focus cAs. Vocentur illarum
latera recta principalia L.  1.
AD S deMICLANEU SN, Sn
normales in rectas PR, Pr IM
e eptansentes. Dico velo.
citatem corporis PeAe ad ve.
locitatem corporis pin rati-
one compolita ex ratione L=
ad 12, e ratione Sn ad SN
sire ut L. 2 x 5 n ad 12 x S N.
Sumantur areus eB, Pb c0.
dem minimo tempore de
Scripti; e per B ducatur BX
ad R P Parallela, e BD ad SP
normalis; simileque tiat ad B. Velocitates in P e p sunt ut nascentes
arcuS PB, PB; quipre rix simul pereursa: hoc est, ut hisce aequa-
circa idem centrum revolventtum esse ut Cubos trantvertorum
Ouadrata Temporum periodicorum corporum in Fllipsi e Circulo
les
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