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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1150, page id 1815201908:1207
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QYADRATVRA CIF
dinc L, Factum est xequale olido ex DC FFI in B P O B, minus est solido exB Bd R
in T, ac proinde e balis eius minor elt plato SBdR. licigicur basis illa rectitineum
1150
PNM O, hoc ek solido quod ACex DC FFL in se ducto subalterne. Fecimus ergo
gisod erac poltulacum.
_ DCFA in F, POB, una cum DCFCMPNMO. Cuncque Colidi ex SV BR
in T, Parres due, nimirum BF Bd in l, e BdLC I L, aequales lolidis Fi R B II
in F NATB, _ DCFFI inFP OB. Erit quoque solidi ex S E B R in Prehduum.
BdZ C. Ouoniam isiCUT EOCUM S F B R ductuI in F, _QUATIE F E B FT In B N M B,
nempe 91q HC ex SC. X R in alcicuMIHCM L, eequale ei quod AE CX DCFFI in
PROPOSIFIO LXX
TUIdeM Dosicis: Oportent Tolido quod scex seomeneo varabolico FTIHI
Linse ducto subalcerne, hoc est ducto in segmentu FNMFI, extribere
aquale solidum exlindricum cuius balis sic Termentum aliquod circula-
re, alcicudo rero Y, cadem nempe que luperiori propolicione repercatuie.
Constructio ex demonstratio.
DEanU CFHD, hOC CAPTKO.
ductu in PNM O, aequacur pl2.
no SC X R ducto in olcicudinemF.
per praecedent. ee quia scomencum
PTKO reduximus aad rectilineu,
etiam Colidum quod Ac ex PIKO
in FPOMI redactum est ad paralle-
lepipedum. Fiac igicur ips aequale
parallelexipedum cuius alcicudo AC
T, balis vero rectilineum, exempli
Bratia CBdX. Rurtum quia B re
duximus ad rectilincum porrionem
Parabolicam FPKII, Colidum quo-
QUC nACUM Ex EPOHIIn FIKHI.
redactum est ad parallelexipedum.
Fiac igicur ipsi xquale parallelepi-
Dedum cuius alcicudo (c P, basis re-
ro rectilincum BEr d. Fria igicue
Colida, qux nimir HUINECx SCZK
in Y, Cx CBdX in P, ex BE n d in
Tihoc est Colidum quod producieur
ex Tegmenco circulati EOTO SR NE
in alciebaem T, aquacurertouS IOHaIS GUEHUNE Ex PIR O In PNMO, ex PIKO
In FPOHT. ex FPOAm ENM EI. Acqui solidum ex PIK O in PNM O, cum Coli-
dn. PTKO in FPOMIThoc eA Tolidum ex P eK O FNMH) vua cum Colido ex
C DmOn- FPOHT In FNMEI, aequancur esolidoquod producieur ex FIKHI, in sc ducto
racur ex subalcerne sive in planum FNMHI. ergo sesmencum cylindritorme quod sc ex
1tta 2.2
1a2.
orquar. SR x E in alcicudinem Y ducto, aequarur solido quod sic ex segnenco parabolico
FIKHI in se duao subalcemS. exhibuimuS erso quod pecebatuI.