# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0943
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0943?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 886, page id 1815201908:0943
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=943
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000943.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 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.
# 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.

223. hucus.
006
PR OPORPIONALITATES
Demonstratio.
Voniam proporrionales
 bC in con
tinvaca rarione constiturx
MM godC A a dt B, veC ad
D.d inderredoveD adc ic
Bad A. Scd quoniam A, B, C
Acis duabus rarionibus duas altas tactoes exhibere quae communes
habeant cum rarionibus datis denominatores.
TUNE CONTINUIX VE A ad C, ita per C OrOIL. rB. huius, est rario A P ad B A, FacIONC, ergo
ve A ad C, ita quoque est rario AB ad D C. rationem. Ouod erat demonstrandum.
BellNCB.
R OPOSIFLO XXIV.
2. 35.
AEE SinE dux quaenis ratiOneS AB,
CD oporceat exhribere duasracio.
nes illis proportionales quxe denomina.
corestrabeane cordem. Aac ve D ad C
ita B ad L. eric ergo aratio AB ad C D
rationem, DE A ad F. ponacur deinde
quaenis F. Dico quodrationeS AF, FF
CTUME, QUR REQUIFUNEUE. MAM BFaTIO AK
ad F, racionesisitur AB ad C D, Feduletx lunc ad rationes que communes sorrian.
Constructio es demonstratio.
 uto..
eA ad F F FarIONEM DE A ad F; sed rario quoque AB ad C D rarionem eA VE A
cur denominatores. Ouoderat Caciendum.
PR OPOSLLIO ZXV.
Vaspationes exhibere qua calam incer Sc rarionem continoane.
Constructio es demonstratio.
Aca sic racio AB, ex quaeuis ponacur e.
dicotactum esse quod pecitur, nam ratio
AC ad BC, est ve A adB, per secundam
huus; eodem modo racio C B ad C A, est
D ad P. Cric ergo ex constr. rario AC ad D Frationem, ve racio AC ad BC. sed
ratio A C ad B C, est DE A ad B. igITUFa TALIO AC ad DF, est ve A ad B: exti-
ve A ad B per Seprimam huius.
Si veroperancurrationes quarum antece.
dens vel consequens commune non sic, in data racione exhiberi: Hat ve B ad C, ita
buimusixicur duasrationes, qua au . 
1