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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 151, page id 1815201908:0208
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.84
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

P
19
A
plane
1ac
1d
rion
neu
raliu
iam
B
E F OMIE T R IC A.
AB ad B C, HOC Cs VE P MI ad FTN, HOC CALDEOMBdMN, hoc es (quia O AN.
ETMN Cmili CCAngula) vE OM ad NET, hoc est denique M ML ud ON.
primo igicur au Hem; BK est ad CK, hoC eC MIL au NNS, vE M ad
ONV: rectangula eeu M I, NVP, proporrionalia habenelatera. Duare cum LInE X
Deinde dicta rectangulLBIPTEMIENCa sinE coTUI, que Circa diameerum lunE.
Lrgo lingula quadracis lingulis daca lerieia aequantur. ergo et progcessio cora cori a 13. primi.
progrestioni aequalis erie; ex quo eriam secundum pacec. Cum enim quadraca exhy-
Dochesi sinc in racione concinua, eriam complemenea illis xqualia, in ContinUR CruNE
analogia: qux cranc demonstranda.
aequiangula crunclimilia; quoderac primum.
C1. VI.
eR OPOSIFIO
idem velicis Anc AXBaqualis teset Lactonis AB ad C D, de ex puncto nnins
X, ductanormalis X Y Cccerlincas PL, GK, in TXV.
Dico rectangulum sub BK V X, cori complementorum seriei MI,
NL, _C. Xquari.
Veacur enim AR Per Banitum V Parallela aB. Isirur rectanoula c VI, A V
icemque rectangula MZ, a MI, X qualia sunE incer sC. Pgitur tiguTa MO IBV
fGUEA M P A X V aequalis elt. quare communi addico rectangulo LT, crunE re-
etanguta ZI, AT equalia. Acqui rectanoulum Z I est rectangulum lub ZB, id cst
BK, _ sub Z. O, id est V X; rectangulum vero A T seriei quadeacorum, sest àe qua-
lc. ergo rectangulum sub BKV Y, Scrici quadracorum, hoc est per peacedencem
serici complemencorum cA aquale. Duoderat demonstrandum.
PROPOS1L1O CLVII.
IIdem poscis, quae supra,
Dicoea quae circa diamerrum lunt rectangula PG, HIO, _c. eNC (1-
milia incer se e continue proxortionalia; rectangulum vero (ub AB et
VV, coricorum progressioni cslexqualc.
E. Prim
8ba
Demonstrulio.
morato.
P PMCRad MO, sivC HN, sic G P est ad ON, ob crianguioruni OMP.
MON, Similicudinem: quare cum rectangula PO, FTO, et lacera habeahe
propolcionalia, ee angulos xquales, crune similia; ac proinde e rellqua omnia eo
dem discuriu MMMaerune: quod fuieprimum. Deinde eum similia Unc dicta rectan-
sula, erunc in adpicacahomologorum laterum PMI, FIN, XxC. tarione. Ouare cumt
e quadraca line in coluem lalerum rarione duplicara, callet Checinutorum
ac quadracols proporcio. Acqui hxc ex hypochesi sunc in concinua analogia, crgo
de illa; quodcactum. Deniq; rectangulu a M, XquacUE CFECtarBuIOM X. AUCA. Ba.
alt.0