# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1009
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1009?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 952, page id 1815201908:1009
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1009
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.83
# 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.

PR OPORTLONALLTATES
Scholion.
e
An Mareriam vlcerius non prosequor, cum ex is quae iam dixcho
ciencer indta
ccum formari queat qua rasione in vlteriore terminorum numero sit procedendum.
5 IF1O
C
1dsiX e2) CCd.d EISES  1S
L. X 1
DG ad HI; sic aurem ratio A ad B, dupTICALA LaTIONIS L ad F.
Dico A cum F, ad B cum D duplicacam gu quehabers rationent
eius quam lade P. cum C a L e.
Demonstr
10
II A ad B eandem rarionem habuerie quam C ad D, de P ad F, quaM
iam A3
10d1-
atio.
nis quam habec F. ad F, ee quia
O, racio cadem eAt cun
A 2d B, cric e C 20
ratio duplicaca
15 F. 2c
ia vero el
Ve E ad F, ita C ad HI, _ PCF.
mucando
ad C, hic F ac
TT, CPIEVEF, cum C, 2d F, SIC L
cum FI ad F, ee perucando re
cum FI. limilicer elre Aad B,
AC A cum C, ad B cum D: est
autem Aad R aaem duplidara ex hyportrehrarionis F ad F, quare eriam duplicaca
cricracio A cum C, adB cum D eius quam habec E cum C. ad F cuin FY. Quod
tuic demonctrandum.
Scholion.
DNous hic processimus in duplicata ratione, cum opus fueris, de quavis alia mulsiplicata rario
ne intellisi debet, modo eadem servetur hypothesis.
PROPOSTTIO CLXZ.
VP racio AB ad C D, sic duplicata E F ad CHI. e diviix AB, C. D in
OI_ I, propgetionales exhribeane AI, IB ip sis CKE, KED, de Cunili-
cer E F, C HI diuita in L. de M consticuanE P L, L F ip (IS CMI, M IIPrO
portionales:
Dicorarionem ALad C. KE duplicaram quoque ese eius rarionis quam
Haber RL. ad GMI.
EeN HIETIDEBEIF)
MMIHCCEZBe et VErCA
AC. Baris De Flau
B
L
 nid hvC Lil Co, C Mt HI
Voniam ponuneur proxortionates cam AF, TB ipLS CK, R D quam EL, LF
LiptiS C A MHI: iBICUEVE AY cum YB ad AL. ica CA C K cum KD ad CH,
rnde
Demonstrario
E ad F, sIC F cum C, ad F
d