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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
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Lib. IV.
eE GEOMEXRLCA F, LEMEN TA.
ponatur Flipsis alp circa immotum umibilicum + modo superius
descripto revolvens; e quantitates datae c e r eandem habeant
rationem quam anculi aX I ∞ ATL; si altitudo corporis revolven.
tis, sive distantia a centro, vocetur a: Frit Vis centripeta
pus in Fillixsi modili re volvi potest, ut = 4 = R LCq - l g
A9
sum, urcente hujusmodi ri centripeta, in P. Iipsi mobili feretur corpus
Cum Vis, qua corpus in FMips immobili AL. P revolri Potest, sit
(PeT PFOD. XXXIX. Lib. T.) reciproce ut quadratum distantia a centro
sive altitudinis a; exponatur Vis Haec per , e Vis in apside a erit
a
AFg. Vis autem, qua corpus in circulo ad distantiam ra ea cum
relocicate rerolvi ponet, quam corpus in FIliph revolvens habet in
a, CA (PeT PFaC. Lem.) ad Vim, qud corpuS
in Fllips revolrens urgetur in a, ut semi-
latus rectum FIlipseos ad semidiametrum
R X F
circulis sire ut R ad a r; adcoque ratet à T cub
Cum autem (per COrOl. 2. PrOP. IV.) disse
rentia Virium in punctis a e a sic ad Vim
LXFG
praedictam in circulo, ips a F cut aequalem.
UtCg = Fg ad F9: erit ilta difterentia Vi
rium aequalis RrGq = RXFq
A F cub. : e (Per PrOP.
IV.) disferentia Virium in aliis quibusvis
punctis aequialtis (ubi nempe altitudo est indecerminata 1) est ad
differentiam Virium in apside a (ubi altitudo cAt TA) Sicut cubuS
ipsius r a ad a cob; adeoque in quavis alcicudine vale bit R , 6g - R , F q
A cub.
Si isitur ad Vim =2, qua corpus revolvi potest in Fllipsi immobili
AEP, addatur dicta disterentia Q . CG L R 2F 9.
Eq + RXG g = RXFq
a cub.; componetur Vis tOLa
Acub.  qud corpus in FMlips mobili at p eodem tem-
pore revolvi potest. D. F. D.
GOROLLARTUM. F.
Einc s Vi centripeta, qua es in reciproca duplicata ratione di
Santix à CentrO, qua Corpus in FHlipsi immota revolritur, superad
datur alia qualibet Vis qua est ut cubus distantia rCCIpFOCO; COr
pus deseribet F.llixsin cujus apsides in consequentia feruntur. Nam
quia disterentia, quae cAt ut Cq - R LF g
A cab in hoc casu est polutira, a
excedit F; hoc cA, angulus a TY excedit ansulum ATL; unde (per
Corol. T. PrOp. IV.) apsides vel feruntur in consequentia, vel feruntur
in antecedentia celeritate majore quam dupla ejus qud corpus L in
orbe immobili in consequentia fertur: verum cum ultimum hoc
in nullo corporum Caelectium locum habeat, ab hoc casu abstra-
himuo. ACE d Vi, quae est recipioce in duplicata ratione distanciae,
auteratur
A clb.
Mia cor.
 vicis.