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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 608, page id 1815201908:0665
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nte.
B 142. suius
i
6C
AI Y PE R BOL 11
eROPOSITIO CALIS
Ecex parabolaDPE hyperbolamveprius, de per punctum incerlectio.
LniS D, agaEuT AD EI linca, Parallela alimproro B C: deinde quaeuis
recta portatur LK; parallela AB occurrei D HI lineae in II, hyperbo.
lae in F.
Demonstratio.
 Eecangulum TRFT adFIRF.
L compoticam habecaracionem
exratione IK ad TTKS X ex rA
tioHC R II ad R F. Icd raTIOHR
ad FR B duplicaca cA rationis
IK ad TIK. Igicur rectangulum
IKII ad TIKE, rectangulum.
compolicam habet racionem ex
licara rarione Il ad lR: ergo extriplicaca ratto.
eai
dTK ad IIK: sunc enim rectansula L.LL, e FIK F incer se relinca LR, et LK.
Dico LKH rectangulum ad rectangulum HIILF, criplicatam habere
rationem lius, quam haber linca LIX ac LL LE.
ratio
ne TK ad TIK. Ouod turc demonstrandum.
ad F.
Gorollarii
ie manifectum estrationem TK ad KF, esse criplicatam eius, quam habet
l
7l
PROPOSITIOCL
Eperbolam AB, incer asimprocos angulum rectum continences
punctum diameterponatur FIFL, Occurtens parabola inHI, ex quo de-
micracur IIC aequica LF hyperbola occurrens in B: per B autem
acta F B OCCUTAE PaLabOla in D. denique ex D parallela ad P. F, demir.
Dico lesmencum CK B C Guacteplum esse Scgmenti BOIM.
i
Demonstratio.
Donatur Tnx, Equidistans FP.
quoniam IIC, D X aequidistan
E L normalirer ad F C poG, linex
ITO, DK ordinarim Polca sunead
axem HK: vnde GB, GTL, RD in
cconcinua luntanalogia: suncaurem
e GB, IM FIC: proportioualesi la
cio igicur DK ad FTC, certiX ad
HIC ad TMI, id cA, TM a BC: quia cGB, TNI, HIC
politam, secer in A Parabola F AD, habens axem alympEOTON FC.
Cumatur aurem seomencum hyperbolicum quodcumque A I, e per L
EaTUF DI, _ DK hyperbolam secerin C.
EXI. de
unc continux: Sed racionis DR ad FTCi, auplicata quoque eAt FaTIO FF R ad FG.
parabola. id estS BC ad CK. ratioigitur BC ad CK, Quadruplicaca eAt rationis TMI ad BC
Buius.
tirag tov. WOal.
rogression
17Mth.
SEr44. 2deoque ex lexmenrum BC C. K, quadruplum eAt sesmenti IM B C. Quoderac de.
la