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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 293, page id 1815201908:0350
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=350
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.86
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# After the first blank line: the recognised lines in reading order, one per line.

r
E. L L. I P S L3.
293
t_E C C, BC aequales, e anguli ad Ci aequalesadeoqueredi. Cum ervot uas
AD, C B, (qua per r9. huius lunc parallela) bitariam ex ad angulos rectos iccel, dAIs
est. secancur igitur ab axe bitariam recte AD, CB excrema coniuracarum aequa-
lium connectences. Fodem modo ostendemus religuas duas AC, BD ab aXC FTY
bisecari. constar erso reritas propolicionis.
PR O POSITIO XCV
Ilinex qua extrema coniugatarum connectune, ab axibus secentur
bitariam:
Dico diametrosillaseseincer se aequales.
Demonstratio.
DOnacur eadem fgura guXe priuis, sinEque AD, CB, AC linex, exrrema coniuxa.
carum connectentes in Fet _ K bitariam ex ad rectos divila axibus TTI, F C. di-
coAB, CD, diamecros coniugaras elle inter se aequales: cum enim AD, C B pei
29. huius sinc parallelae ee ex hypochesi ab axc in F d Cbilecentur, arieuli ad F recti
sunc, de lacera duo AF, F P aqualia Cune laceribus DF, F B; reliqua igicur lacera
AF, F D quoqueinter se aqualia. similicer ostendam C P; P B ae quales. vnde _ COTE
diamerri AB, CD aequales. Quod Fuic demonstrandum.
Corollarium.
Ine pacexlinens, quxe inaqualium coniugaearum excrema coniurigune, nunqua
ab axibus auc alia quauis diameero bitariam es ad FCCOS LCCaFI.
PROPOSITIO XCVI
Inearum que exerema coniugatarum guatumurs contungune; illa
aIa CICQIa Coniugatas aequales connectens, axemminorem le
cari minima, quae maiorem.
Lbonstabteo
RTNC AC, bD atCG. CIHBLCOS,AB C
coniusaca vero aequales. FC, FII
iunetaquo FII maiori axi occurrac in
R: e HC minori in L. dico FTC li
neam maximam esse illarum qua cu
inscunque coninsacionis exrrema con.
iungune, e FFF minimam. Fiac enim
juxuis alia dismerrorum coniugatio
MR. NO. quarum exrrema iunsane
MIN, NR, quibus in O ex S bilectis
ducancurper centrum ZOP, VSI.
Duoniam ergo FC, TTI sunt coniuga:
+x, sectores EFBHI, aP IIC Caquan;
cur. Eroob scomenca FBII; IIC C ∞
qualla linc. Ouare, eumi axes BD, AC
etiam bilccentc rectas FII, IICi, quae
aequales coniusatasiungunE, CrUnEaKES
ipsid in R de L, proporcionalicer lecti, L. et Le1N
Ergo c rectangulum BR D aequalc est
quadrato L HI. simili plane discursu ostendemus rectangulum PO L aequari qua-
araro NS. Deinde quia Esectores M F. N, FPHI aequaneur, adeoque B lesmenta = Coroll. 46.
0
nus
2 46. Buins.
B 60. hroilis.
C9+. huins
53. huint
74. hain
LL L Ll1B60. Lotorrio