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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 286, page id 1040780814:0304
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ASER ON OMTE PAYSTCA
b. IV.
in OrDe GMICSCOntO A L F, PORCCITCS THECCIMC agua a PeC
in orbe revolvente aIp
Per centrum r in plano AF. Y agatur Temper XV ipsi TL aequalis,
angulumquo AYY anSUIO A PE DeTPCTLO PEODORTIONAICHI CMICICIS,
hoc est. ut hic angulus AYY Sit ad correspondentem A l L U auLI
quiris A FV ad TUILII AYL. Adeoque arCa, quan LV MOCU angularI
circa T sic lata describit, provortionasl ai alca Gnam FY describit.
SIE AVE CF Curra quam punctum I, modo iaI eXDOHEO WOTUM, COn
inoit. AF quoniam una cum L rerolritur corpuS quod MI.CCE d̀ V
centripeta ad contrum Y Tendente, area A LL A (PCL L1OP. XI. L ID. T. P
est tempori provortionalis; quare e ared PL lpO Cam pro
portionalis erit: sed e in plano immobiss cou, Codem nempe
in quo corpus i cirea r revolritur; hoc cl, Parcu 1 Ci Mocs
ut in plano immobili per Y traducto perpetuo reMatu, l aas
It
eto descriplas
colacla
286
a Tla, ddic
valcS.
emporibus proportio
FPrOP. XIT. LD. L. MaMMCICum Cl quod COrDUIS, CO.
in curra linea AL. CH, Gualu Punetum delcribit. Datur autem haeC
linea curra AIF CH, quippe ex data linea a 2. P a modo constanti ∞ dato
senita: quaeratur isitur (per COr. Prop. XXXMI. L ib. T.) lex Vis centri.
peta, qua corpus in illa rerolri potsit. Fiat ansulus a ra angulo
T.T, rectaque ra rectae x A aequalis; et isitur ansulus a r angulo
aTF aqualis erit. Describatur jam firura a lx similis e aequalis
AL T: adeoque punctum l cA in perimetro fisura iph a L. P a Cimilis
ex aequalis circa r revolrentis. Corpus ergo una cum llatum, et fgu-
xam immotam APF. CFr describens, describit etiam perimetrum a l pa
Orbis ipsi aLP ACmilis circa r revolrentis; ita ut eodem tempore
deseribatur areus a l in Orbe revolrente a lpa, quo similis e aequalis
AT. in aT. Pa Orbe quiescente ab alio corpore deseriptus est. In
venta erso est lex Vis centripeta qua sita. O. F. F.
sente juctae quantitatis Vi centripeta, revolri possit una cum puncto
lROOdL+1+V. LAL.
Herentia virium centripetarum, Guidus eot pus in dide qud
escente es corpus aliud in eodem d revolvente aequaliter
Nanen
moveri possunt, modo Prop. praec. indicato, est in triplicata ratione
communis titudinis inverse.
lib. I
Mai
virium
n trip
lerenria
pibus
dem m
pum p
Sun
minin
TL, PI
In ret
UE CiC
Porum
tium
Suune
lecune
Vero,
cundur
lormai
persis
8, qui
T, b7
Darum
Mento
LIB IY2
ad m
doris
nex
dem
PuSI
qua
de
i
Por
SUIa
AS CO1
umP
plus
a