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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1016, page id 1815201908:1073
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 25 lines, status machine
# Lines: 25 recognised, mean confidence 0.86
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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1016
VN GVL A CXL INDRTC A:
Demonstratio.
Emonstrat Archimedes libro primo de sphaera et cylindeo propositione decima.
quinca, cujusque coniisolcelii superticiem ad bauim suam eam habere rationem
quam lacus coni ad radium circuli baleos, hoc est in calu nostro, ve est AB linea ad
lineam AF. Cum auFeM BOnaCUE C K ad KL, eandem habere rationem quam H2-
bec DF ad F B: isicur Criam CAE C K AdRMI, VEDF Ad F A, SEVE R MI ad ML;
sic F A, ad AB, quemadmodum exelemenris pacet. (Cd VE RNX adM F, icacrian-
culum KM V ad triangulum LM N, cum eorum commmunis alcieudO GE MVT. er-
BOcrianguLuM RM N, Cs ad CrIANGUIUM LMN, VE F A ad AB, hoc est rebasis
coni A F. C ad reliquam coni luxertciem. Ouoderac demonstrandum.
P K O P OSITIO LXXX.
1dl
DOnacurrursum exlindrirnguta L. 1O, sed cuius alciendo H L par sie
diaeero G L: (CECFUT VerO CONUS ABC, sectione O P O, BaSI AF. C
Parallela, ee dividatur M L. in R, ve divila estin BF in P. cum per pun-
cum R sectio AaE R SV qux a quidister plano N MIK.
Dico spatium MIR SNY aequale esse quadrato sub linea quae media
eA proporrionalis inteF MIR _t MIE, RV Cimul Cumptas, eo prortus
modo quo spatium superficici conicae duobus perimerris parallelis AF. C,
OP O incercepcum aequale cR circulo cuiusrndius est medius incer P L
vel AO, ee lineas AF, O F simul LumPEAS.
.5191I1.
Demon-