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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 965, page id 1815201908:1022
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
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VNGVLA, CYLINDAICA.
PR OPOSIT1O XIII.
Olica ascudines haberes veram
que balim parallelam similem simili-
EerG POlcam, eam inter Ce lOrrinnEEFA-
tionem quae ex basibus e alcirudinibus
compolica est.
Demonstratio.
I masnicuames parallelepipedales Fuerine
velprismaca, lam per elemenca constac hu-
ius propolicionis reriras. Quod (alcera (ic p2-
rallelepipedum vel prilina, ve AL: alCCTA verO
curuilinea DFTL; vel E veraque sic curvilinca,
per inscripriones prilmacum SCMPEF CONEINUa-
eas concluderur propolicum ca discurrendi
Formâ, qua Duclides vrieur in elemeneo duo-
decimo. Ouem discurlum cgo ad alia prope.
rans Formandum relinquo Lectori.
PR OPOSIL
965
X
0
YNgutam LB, CD, cuius inbali diameter e lecet aliquod pla-
nuntaxi aequallistans P. FC FI Faciens it plano ABD, sectionem
E F parallelam LB; quod deinde sccerur plane scco ud planum
E FC, diuisa denique bitariam recta P. F in N, agatur planum per N e
axem cxlindri, ad quem ongula percince, occurrens plano IK L. secundû
communem incerlectionem OK, per quam hac lectio PK O paralle-
la plano ABD.
Dico Fructum cylindricum FTK LF
aequale esse Frusto F. PH OF.
deonporatio.
VCANEUT PK, KO rectae Cubrendenes
AECUS PR. RO, qui quoniam luncaequa
LesMer e, vepore equales arcubus F B, BF,
cruire quoque linexe PR, RO aquales. sune
quoque celangula aequalia et similia TPO
O, cum linCX P N, N F, hoc eA PO, O
adcoguil , l aequales sinc. Pgieur py
LAIHdeS IORP, OORL aequales CunE.
Ruccus Tegmentis PR, K Q inscribi ponu
inscripea rni prilmata, alcert Mipcis crunca
qualia quod cum tempet nen poisie, contcat
Ecomencu IPKOa sCOMENEOOKL Q estex.
quale. adiectoigieur comuni solido F. IKOF,
CTIE EOCUM EPKOF, COTI FIKL F xqua-
lc. Duodtuir demonttrandum.
criansula maxima ve prius: crunchec aqualia
incer le, ex per ca que pauls ance praemisimus,
AEX CorSII.
216. progres
  s s   sHHrgh r  s   ess s  sss   rpe to