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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 40, page id 1815201908:0097
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L IN E A R V X
Lortacu numeruSIOO. Cx.
Posicus; diuilus in quotuis
parces; verbi gracia in AC
CD, DB. ACqUC AC PaF-
Ctu LO: CD, ParcIu 30.
relidul Pacclun
iubetur linsulas parces mul
ciplicare per lciplas: produ:
cene lx mulciplicaciones
cressummas; quarum prima
400. Secudla 900. FCTEIA 2500
Parres continebie. Vlcerius
iuberur AC, mulciplicare
per numerum C B. hoc cA
20. per 80. & cmeroit lum
ma1500. guxe bislumpta, ex-
crescic ad summam 3200.
Denique hoc Facco, ctiam
numerum CD ducere in
DB. X exlurser Cumm a 1500.
lam, cuius summa elt 10600. quam Cicomerra discursu propolicionis iam polux, ola
mulciplicatione numeri 100. per 100. tactam illico manitestam habebir, scilicet
10000.
SITIO LXIL.
VI Fuerie AB linca, divitave-
cunque punctis C D.
Dico rectangulum sub AB, _
comboia ca HODB, Ia Cum sectanoulo (ub CD, _ COmPOTITA CX
ACDB; aquale esse rectangulis BC A, DBC, ADB, C AD, simul
Cumpris.
900
2500
3000
3200
10000
qux es sumpea efficie numeruim 3000. canem collioir haec producta in vnam mas-
PROPC
Demonstratio.
21. Sccundi. Z EClatiSutu LUPeL AID, d CopOliTa Ex AC DB, aquale a cA rectangulis
AB, DB A; id CM CCMAANS ACB, ADB, una cum quadratis A C, DB;
id es xquale rectangulis C DB, ACDB, DCA, BD CA, una cum quadraris
AC, D B. Rursum rectangulum super C D, d Composica ex ACD B, equale cAt
rectangulis AC D, CD B: igicur rectangulum super AB, _ COmPOLITa CK ACDB,
una cumrectangulo super CD, e composita ex AC D B, aequale est rectangulis,
CDB, ACDB, DCA, B DCA, ACD, CDB, una cum quadraris AC, DB.
Icerum rectangulum B C A, xequalc est rectangulis DC A, BDC A; icem DBC
rectangulum, aquale est rectansulo BDC, vna cum quadraco DB: icem ADB
rectangilum, aequale est rectangulis CDB, ACD B; denique rectangulum,
CAD, aequale est rectangnlo ACD, vna cum quadrato AC; igitur rectangula
BCA, DBC, ADB, C AD, aqualia lunc rectanigulo (ub AB, _ COmpolICA ex
ACDB, rna cum rectangulo lub. CD, ex compolica ex AC D B. Ound crat de-
monstraudu.
PROPOSATIO La
ectangulum, aqualeherectangulo BF. C.
Lclatu D cat icumsdeC B Aelumin L. Mulaerc, Vt AL.L
Con
e ui  ei pii u et  pr iu p u e u      u  it  i   te pti     t   t         . 1  p   u 1e   pr  u. t  11