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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1095, page id 1815201908:1152
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6D
CONOTDES HXDERBOLLCYM.
PROPOSTTIO
Tcertangulum pet aRem AB C ad conibalim BD C rectum, lumpeis-
que in commuserlectione BC punctis C_ L, CrIGANEUEGL, I. I
quae aequidiltene laceri AB: de ductis CD, L. HI ordinatim ad BC RanE
lectiones secundum lineas F. G D Xc IL FI.
Dicorationem Colidi A D F. F ad Tolidum AFTTK criplicatam esse ra-
tionis DF ad FIK.
Demonstratio.
Olida ADE F, A FT TK sunc ad a pyramides
sibi inseripeas ve 4. 2d3. ergo e candem n2-
bencracionem quam prramides. Se d hxe compo-
siram habenc ex ratione criansulorum parabolis
DFP, FIIK in Scripcorum, (hoc est ex racione
biplarum parabolarum D F L, TTTK) X exraciO-
ne alcitudinum BG, B L. eroo Colida ADF F,
AHTIK racionem habenc compolicam ex raclo-
ne parabolarum D F F, FTTK, _ ex racione alti-
tudinum BG, BL. Ced racio parabolarum com-
ponitur exracione alcicudinum CF, TL, (hoc cA
exracione (2C 3dT C) _ exrarione batumDV,
TTK, seu D G, FI L. racio ivicur solidoru ADR F,
AFITR componitur ex racionibus BC, ad BL,
_GC ad L. C, e GD ad L FT. sed rariOnES
BG ad BL, C Cad I. C, componuncrationem
rectanguli BC. C, ad rectangulum BL C, hoc cH
racionem quadrari DC ad TTL, hoc estracio-
nem duplicacam D C+ ad TTL. eroo racio Coli-
aOrUI ADF V, ATITK compolIca CA Cx 12-
tione duplicaca rationis D C+ ad FTI, e ex ratio-
ne DO adFTL. hoc est rario solidorum criplicata est rationis D C ad HIL, RuC
DEAdHK. Ouod erat demonstrandum.
PRO POSITIO CCI.
Ecetur irerum Conus per axem lectione recta ad balim exhibente
D triangulum ABC, e punctis I e D in communi incerlectione a(-
Tumpris eriganeur L. L, DE, parallelE AB, _ POLitis L. K, DC ordinacim
ad AC, hanc sectlones parabolicae per IL. I _ FDC. Denique planum
SdcH perB, de tectam C F occurrens parabola HIIK sccundum rectam
1095
36. hu
d. Pa
VC
LML
Dico parabolam FC. C ad MLI llabee aupcala cilo Laltbel
Demon-
quam habet F C ad NM.
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