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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 53, page id 1040780814:0071
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Ina
eeC
periocte
IIPOTAY
im dialea
aequali
Quorul
d Centr
ionc aic
oredes
Orbibu
um ad
corporum
in quibu
subdup
neas qui
ni cent
Orpora.
dVicet
quart
la(cento
CC aqu
L ib. I.
eE CTFOM L + L +OEL. H, L F M F B L R.
LeSPR, Or rectR. LMLo, ob triangula rectangula BD X, SNP haben
tia ansutos B2D, StA aGlates DoPle ParallelaS B X, NP; ClE SH.
SD:: BB, BX; ex ideo B X vel huic aequalisPR=
BL
SH. FC, Propter
similes rationes, pr - SPXb
Su. Sed SDFBD, Sp B a sunt inter (C UE
eorum semistes, nempe rrilinea SPB, Sp B; hoc est. sicutarex a corpori.
busp _p Simul descripta, quae rurtus (ex COr. 2. PFOD. PPaeC.) Cune in
Tubduplicata ratione laterum rectorum F. _ I; SIre SICuF L 3 ad lJ. FF
isitur Px cA ad pr, sire Velocitas corporis in e ad Velocitatem COr-
poris in p sicut s ad :: L. = = Sn. PExSN: hoc CA, in ratione com-
Dolita ex ratione subduplicata laterum rectorum ad Figuras PB, pB
Dertinentium, e ratione inversa perpendiculorum à centro virium
S in tangentes demittorum. Ouod erat demonstrandum.
GOROLL ARTOM T.
Hinc Velocitates corporum, in maximis de mimmis ab I
communi, circa quem orrantur, distantiis, funt in ratione compolta
ex Tubduplicata ratione laterum rectorum, et ratione inversa distan-
ciarum a dicto communi umbilico. Nam, in maxima vel minima
distantia ab umbilico, perpendicularis in tansentem est ipsa dictantia.
Si dictantix la à centro tuerint aquales, Velocitates, in ilto temporis
articulo, crunt in subduplicata ratione laterum rectorum; alter d isd
dictantiarum inversa in rationem aequalitatis mutata. EE A Agu
rarum altera t Circulus, erit Velocitas in Sectione conica, in Maxi.
ma vel minima ab umbilico distantia, ad velocitatem in Circulo in
subduplicata ratione lateris recti sectionis ad distantiam duxlicatam.
GiOROT L ARTUM 2.
Tneadem figura, _ etiam diversis, quarum lateta LCCCa LunE X qua
lia, Velocitas corporis est reciproce ut perpendiculum demistum ab
umbilico, sive virium centro, ad tansentem: NTam subduplicata ra-
tio laterum rectorum est in hoc catu ratio aequalitatis. Adeoque
Velocitates corporis in Fllipli srrantis, in maxima e minima ab um-
bilico dictantia, Punt inverse ut distantia. Nam, in hoc casu, distan.
cix sunc ipsa perpendicula in tangentes Orbitam.
CIOROLLARTUM 3.
verticibus principalibus a _ P, C Contro
vicium s spectati, sunt in reciproca dupli-
Cata ratione distantiarum S A, S P. Suman-
tur enim ad vertices a d Parcusminimi
Aa P P, d Corporo circas reroluto aqua-
libus temporibus minimis deseripti; e
JUnSanEUE S a, S P. FrUnE COrpOrIS OTUS
Cx S apparentes, ansuli ASa, PS P. AnSUI
lorum ASa, PSP ratIO COMPONIEUF CX Fa-
de
ulocus apparentes Corpolio i Mblla