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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 80, page id 1815201908:0137
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=137
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
# Lines: 46 recognised, mean confidence 0.86
# 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.

PR OG R E SSION F S
nam AD 2d CE. eandem habec rationem, quam AIICa A F ad C F. Sed quam
parionem habet D A 2d C L. Candem ex constructionc habet AC da CD, puu
ounin Farionem abet cota A F ad rocam CF, eandem habet A C abtala ad CH
atq. Omh. Lblaca. elore Al cocaad. C. licocam lic quoque a CS celiqua adtelqua Be.
Ouarelecta B adiuncta elllinca Bfi, guae Faciat A F, C F, B F in concinua pro-
porcionesquod PeleDatur.
aliter.
e
eto lineis conveniae lublu als allatur sux inomnipe
DaEI IBIEUE SNE CKCCHUS A B, BC: AaE A F. MMctenca dacorum excelluum, ipBI-
Que AF, AB inveniacurcercia proportionalis concina L D AD abi
reproblema. Cum enim ex constructione A F sIC ad AB, ve AB ad AD, cric di-
videndo AF ad EB, vi AB ad BD: e componendo AB eric ad B R, hoc eA
BC, ve AD ad BD; d Permurando AB ad Ad, ve BC ad BD; e dividon-
do AB ad BD veB C ad C Di componendoigicur AD, BD, CD sunc concinux.
Fecimus ergo quod percbatur.
PR OPOSITIO
X L l
vntixc conctru
onere guancitacis locum habeac:
Acam magnicudinem AP. Semet sectam in C, propotuone mdioris
inaqualicaris, ica in duobus aliis punctis B ee D Subeluidere, ve qua-
CHOF ParceS AB, BC, C D, D F. Sinc in concinua proporrione; qua dimi-
diaca sic racionis AC ad C F, ex prima divissone Orta.
Constructio es demonstratio.
DEx quadragesmam huius Addatur F. F, vE AF, C F, R F sint PFOPOOCS cum
incer AF, C L media ponaour Btis incer C Fi quoque e FF, media D F. Dico
Factum quod pecebatur. Cum enim incerrres continuas AF, C. F, P. F modix Anc BF.
D F, Patec exelementis omnes AF, BF, CF, DF, BF, elle concinue proporcion-
lcs. Quareeriam AB, BC, C. D. D F, luncb concinua. de quidem in rarione A F ad
BF, quxe ex constructione dimidiara est rarionis AF 2d CF, hoc eA AC cad C. F.
Factum igicur est quodporcbatur.
aliter.
NEer AC, C F invencam mediam F ET ita diuide, vE FC sic ad OFT, vE A C ad
FFI, (CU F H ad C F: Rancque C B. CD ipSIS F G, OFI aquales. Dico Factum
quodpecitur. cum enim siE A C 2d F HI, ve F C ad GHI, id eAt BL ad CD, erie
quoque AC ad BD (qua ex constructione aqualis est F FI) veBL a C V. a 
nucando AC ad B C ve BD ad C D: et dividendo AB ad B C, IL B Cad C D.
Suncigitur AB, BC, C D eres continux proporcionales inracione BC 2d C D. Si
milicer cum FFI (ic 2d C F, ex constructione De FC ad C FI, cric quoque B D ad
=L Ve BC ad CD, ac permurando converrendo BD ad CD, ve C F. A LI.
lacoque dividendo B C eAt ad CD, ve CB ad BF. Sune igicur ces Conmva
_L, CD, DE, inrarione B C ad CD: ac proinde omnes quaruor sune convina
oporcionales in rarione BC. ad C D, id est FC ad C. H, id eAt AC ad F HI, qua
et e . . a 1 1  1e 1 1 1 1 .  . 1  e.  1  e 1 1e  1   A.  1  11B. 11t 1 e 1. 1 u  1 t. .   e    e 1 u 1  1e 1. 1 1. .  . 11