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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 29, page id 1815201908:0086
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# After the first blank line: the recognised lines in reading order, one per line.

d
1.
c.
Det
iis
2,
U.
3
F.
1C
c-
1M
1I.
1
3
et
d
C
POT F NTI A.
Dico quadeata AB, B C Simul TuMPTA, X qua-
lia esse quadraris AD, DB bis CumPcis.
Demonstratio.
DEmictatur ex B linea BF, normalis ad Balim A C
ec BF quidem r. cadac extra triangulum AB C:
Ouoniamisitur B P. normalis, cadic extra criangulum
ABC Formans angulum AF. B rectum, parec angulos
BAF, BDF, BC P acuros esse; quare AB quadratum
superaca quadraca AD, D B, Eectangulo AD P bis sum.
PCO. _ BC b quadracum ab iildem deticie rectanoulo
C D F, id est AD E bis sumpeo: addendo igitur ad qua-
deacum BC, excessum quo AB quadeacuM, (UIPCTAE
quadrata AD, DB, sieve AB, B C quadrara simul Cumpra
aequalia sine quadratis AD, DB bis sumpeis.
Sic iam FB normalis, eadem eum latere BC,
adeoque angulus ACB rectus; guadratum AB.
superac c quadrata AD, DB, rectangulO ADC
bis lumpro. 1d est quadrarum AB, eA aequale
quadracis AD, D B, ex D C quadraco bis sumpto:
sed BC quadeatum, deticie da quadrato B D
quadrato DC; igicur si quadrarum DC, id est
dimidium excectus quo AB quadeatum (uperAE
quadraca AD, DB, addacur quadeaco BC; PATCEI
AB, BC quadraca, xequari quadracis AD; DB
bissumpcis.
Cadat BF normalis, inter BC et BD lincas:
Ouoniam anguli AF. B, CP B TunC rectI, (CrUNE
AB, BC quadraca, aequalia quadraco B s bis
sumpeo: vna cum quadracis AB, F C: sed A F
FC quadrata, c dupla CuNE QUadTAEOTUM AD,
DE; ioicur quadeaca AB, BC, aequalia Cune.
quadratis BF, AD, DF bislumpris: est aucem
BD quadratum bis sumpeum, aquale quadraris
DE. B F bis Cumpris; ioicur quadcaca AB, B C Simul
sumpea, sunc aequalia qadracis AD, VB bis
sumpeis. Ouod ceat demonstrandum. I. 10
Est haec Pappi Lib. 7. PrOp. 122.
P R OF O SPF IO XB.
Sco ABC, triangulum isolceles, _ ex C, alceru-
sroansulorum aqualium, ductanormalis CD,
ad lacus oppolicum
Dicoquadrata cria laterum crianguli, ABC ae qua
ri quadraco AD semel: quadrato DB bis, _ DC
Quadracorer CuMPTO.
1
Demonstratio.
Voniam angulus EDR per constructionem rectus Cl
Lerit C B quadratum, aquale quadraris CD, DB: (cd AB
linea ex constructione est aequalis linex CB; igitur et quadea-
cum AB, aequale est quadraris CD, BD. Rurtum quadra
rum A C, aequale esAt quacratits C. D. D A. 1Bicur cria lacerum
(2C 1. p
213. Secum.
b12. Sccun-
C2bid
d13. Secum.
it