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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 87, page id 1815201908:0144
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=144
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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 0.81
# 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.

duo
ECTAN
EL
CaTA
nua
can.
Ira-
180
FF.
esse
EEd
180
14-
1.
est
et.
F,
n.
E F OM E FRIC A.
Dicorectanculum AE, ad F. B rectangulum, candem habere rario-
netu, quam habecreccangulum CF ad tD scctangulum.
Demonstratio.
Ario rectanguli AF ad F. B rectangulutr, eAt ex  quam habet A ad B; sed B A a 2. Sendt.
Lad B, ica ponitur C adt D, ersorectangulum A F 2d F B; est H C adD: Scd
rectanoulum C F, ad FD rectangulum, eriam est velinea b C ad B, igieur rectang- b ibid
lum AF, ad F. B rectangulum, eandem habet cacionem, quam habet C E ad F D
rectaneulum. OuoddemonAtrare oporrebac.
P R OP OS TFIO
DOnanEUEtres HMCx A, B, C, e aliX EreS D, L, F. retat primae, quam
secunda, suam analo slam licer diyet lam ContinuenE.
Dico etiam rectangula AD, BBs ob A110MH~ B ouC
CF esse in concinua analosia.
Demonstratio.
Lsicat ca luctornous l e  d D au L. Boporco gu quorecan B B
ex F. 2d rectangulum sub C ee F compolira ex racionibus B ad C, hoc est A ad
B, _ exratione B ad F; hoc est D ad F; inde racio rectanguli lib B _ F, ad
rectangulum C P; componirur exyldem, ex quibus racio rectanguli (ub A de D, 2d
rectangulum sub B ex E est compolica: Junie cum proporciones exijidem racioni:
buscomposica exdem linc, erunt rectansula AD, DP, C F in concinus analogias
Duod erat demonsteandum.
H HOIMIDO A d D, ad rectanontuim suB B et R HABCE C FATIONeM EOHiDO-C23. SexIt.
RO POS
TIC
ine loa aueasualou lelses continue proporrionalium A B,
DAC, AD, AE, AF; GFL, IIT, KFE, LFE, MHI.
Dicorectaneuta ABCHL, ACIH, ADKHL, AE LH, AFM H esse
alconrinua analogia.
demonstratio.
Eccangulum enim sub AB G FT; ad rectangulum sub AC YFT racionem habet
compolicam ex racione AB ad AC, _ racione C TT ad IFI: ex rectanoulum
ACIFI, daCcaneu LKMCactorre habel compolcam exracionibus AC d
AD, e IIL a XCI. C MMEABAdACS HC AC. ad AD; _ ve
GTI ad TFI, hic LH ad RHLSM TacOreCtanguIOruM ACIFL _ ADR H; ex
cur rectangula ABCH, ACIFL, ADRHL in concinua analosia: idemque  le.
quis eodem alcurtu ollendetur.
Iiidem EacionibuS COPONIEUE, CX GuBuS TCCLAISMIOTUM ABC HL; ACTFI: Cuncist.
Corot