# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0142
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0142?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 85, page id 1815201908:0142
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=142
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000142.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.82
# 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.

ad
sipe
M Ed
Est
dF,
IC rd.
acigi.
C den
onei
0A
B,
ne,
C
2d
s.
et
GE OMF TR IC A.
eadem ek, cum ratione C ad P ex constructione, igiturratio rectanouli AB, 2d
BC, cadem elt cum Fattone Cad L. lca guantre A Cn alt B, Ha C alt B, CM
permucando A ad C; vE B ad eSCHS AB a BC, CMLaCO B a
D: Sed rectangulum BC ad CD; etiam eAt a ve B adt D; ergo racio AB rectanoui 
ad rectangulum BC, cademmen Cumracione ecation BC, 2aC Drccanouta.
eu adcemeaaudde et a e cacequa enC alte vide cclaalio
ectanguli C D, ad DL. seclansulum, eadem elt cum racione rectanguli B C, 2d
CD rectangulum; quocirea in concinua analogia sune rectangula AB, B C, C D,
DE, cum unc inratione A ad C. Constacigitur vericas propolicionis.
R OPOSEFIO
C, tres in continua rarione. Sincq D, F, F, in eadem vel di
tinuata ratione.
BICb rectansula CD, CE, C F, item BI, BF, BF: ILEM AD, AF,
ese incona alaZCa.
Celangulum CD est ad rectangulum CF, ve D ee C CCclat- b1. Sent
Suru CM Ad rectangulum C I, VE F, ad F: Sed D, F, F ex hypochesi sunc conci-
Demonst
nux proporcionalesiereo aTeaa CD; C L. CF lunein concinua analovia. L0-
demmodo probancur B D; B F, B E rectangula, item AD, AP, A F esse concinue
proportionalia. Duod crac demonstrandum.
aetstetL
Ic A prima ad B secundam, ve C terria ad D, quartan.
Dico quadracum capetu, ccansulum lub secunda ee rerria, et
Quad uu   upe edo
Demonstratio.
Acio quadrati A, ad rectangulum CB, Ccomponirur exracione A ad B (LL CM C2) Senri.
C ad D,) e exracione A ad C. Se lalto eclatsu BC, dd D quadrarum,
compolica elt exiildem rarionibus: nam ratio recranguli BC, ad D quadracum,
componitur exratione B dd. HC et A ad, C; ee ex ratione CadD, hoc ell A
fauaum D. Ouoderac demonstrandum.
ad B: erso luneeres concinuae quancirales, quadrarum A, recrangulum B C, et
eROPOSLTIO L.
Inetres linex AB, BC, C D in continua analogia.
Dico AB quadcacum primae, rectangulum ABC, lub prima ee
de Cellas delilee Dquadracum cerrix, esse in concinuara leric ciuldem
lacionis AB ad BC.
Secunda; quadrarum B C sub lecunda; rectangulum B CD Cub sccunda
Demon-