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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 84, page id 1815201908:0141
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=141
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.85
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

84
LLk1.ddCeC0
de DH de F F eAt vE D alt L; C150IL a C, veD ad F. Fodem discurlu eric P ad
C. Me L al 1. Macaccemoatum.
ve AB ad BC, sC DF ad F F. acqui rectangulum AB ad BC, est vE A ad C.
ROPOSITIOL
Lrectangula AB, BO, CB, GH, _c. rectangulis DE, F. F, F L, IK
Dico veram que lacerum letiem A, B, C, G, HI; _D, E, F, L, KL, E pO-
nantur esse continuae proportionales, esse quoque continuas ciuldem ra
C E
Demonstratio.
DEF PFACCHEMEM CNA ad C, VE D ad F: quia aurem eam A, B, C, quam D, F, SF,
Llune concinux proportionales ex datis, eric tam ratio A ad C, (id cst D ad F,)
rationis A ad B duplicaca; quam racio D ad E (id eA A ad C) duplicaca AIE ra-
cionis D ad P. Duare re A ad B, Sc D ad E; _ B ad C, ve F 2d F, exc. Cuncigi.
Eur A, B, C, C FBB _ D, L F, I, K concinux cuuldem proporrionis. Ouod erat de-
monstrandUm.
P R O P OSIFIO LI.
prima A ad securdam B, eamdem habeat rationem; quam cerria
Dico eria rectans und ex hilce Facta, ese in conrinuata proportionei
Demonstratio.
Diireula linguns ataITA HHE:
rionis.
DC ad quatcat.
nembe cccatigua AB, BC e CD.
danigulum AB, C ad rectangulum BC; re A ad a C, sed eriam rectangu.
SC; 2d CD Tob eandemracionem) estve B ad D. cumigitur Sc ratiO A
ad C eadem cum racione B ad D; cam quoque rationem habec rectangulum A B,
ad BC, quam habet BC 3d CD rectangulum: sune igitur in continuata ratione,
dutac demontel attcc.
LCOIOSITIC
ma A ad securtca eandem habeat Laclonem, qualtunta
quarcam , Hacque ve prima A ad cercIam C, ica cerCIa C ad
m F:
Bicorectangula exisesConuta, et
le in concinuaca racione; nemve rectangula
AB, BC, CID, DF.
Demonstratio.
Ectaisca HB dd BC seltansulum, habee
camracionem,  quam A ad C; ledracio Aad C.
cadem