# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0138
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0138?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 81, page id 1815201908:0138
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=138
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000138.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.74
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

icur
B1
Dro
pil
cdi.
den.
IUX.
12.
m.
BF.
012.
E a
CP
tum
erit
Det
.
dP.
et
_L D ME FRACA.
ecltuetione dimnidiara est rarionis A C ae CB; tormus eteo quod lverat pro-
POLCum C.
it
Cordnarium.
Asc problemare licebie praxim delumere, non lorum lubdiuidendi duas in
quacuor concinuas, sederiam in sex concuas; imo quoruis datas in duplo plures
Concinuas, ec quidem in rarione dimidiara eius, in qua iplae exiltun.
Ed1
VIEAB, BC, CD in cBriL A
Ocinua artalo eid; deinde Foces
eut quapiam linea FO in B, ve
s
3F
FF ad F C, eandem habcacrationem, quam A B ad BC
Dicotoctateulu BC FB, aquale elle duobus ABFC  LFC
rectangulis.
Demonstratio.
Vaienim heve AB ad BC, lta FB 2d F C, Rectansylum BC DF + quale eA a1s. SenI.
rectansulo AB P C. Similicer quia ve B C gu C V, ica Fi, H est ad BB Ca
rectangulum BC FC =quale rectangulo CD F. F. duo 18IC BC F FBC F CY FC-, B 1. Socudi
clangula id csb rectanoulum B C. F C, aequalia sune duobus BBC, CD F B ren
ctangulis. Quo derat ollendendum.
R
1c0 m M210ch ilum
Y fuerinc quocuis contimix proporrionales AB, CB, DB, EB, _C.
D Dicorectangula ABE FG CBDF, DBCD, E B. AC eNe inteT Ce
aequalia. Hloc est rectangula sub linois seriei AB, CB, DB, _c. e (ubKe
Siduis FF, DE; CD, AC eseinter. se aequalio; modo rerrograde con-
IUASAREUL.
Demonstratio.
Voniam est ve A B ad e CB, siC DE ad FF, rectaneutum ABK F aquacur CI. Huius
Ldrectansulo C BD P. similicer quia ve CB ad DB, ica C D est ad DF, CxIF L 16. Sexil.
rectangulum CBDE, aquale rectansulo D BCD. rurlys quoniam DB est c, ad e1. Hmins.
E.B vc AC ad C D, rectangulum D BC D equale cric ip A BB AC, xequalia fUNE
sicuromnia incer se. Ouod erar demonstrandum.
ldem pontto.
Root
AL. tV
Dicorectansula EB AC, DBCD, CBD F. ette inter le xqualia.
monset atloi
Vitemm CB ad DB. IaC BdOF: COMC BDF aequa-Eibid.
ClFSFCCanO D B CD. Sed curtum ve D B ad P B, SiC AC ad h C D, quarC  I. Huim-
ant ectansulum DBCD, xequalo cric rectangulo R B A C; oRenlum aurem fuic
canoulum CBD F, elle rectanoulo DB CD eequalC, quare d haC duo FB AF
u CBDP. proindecsuc omintairla inter se crunr aqualia. OVOd etaE demonctran.
dum.
Edet