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# Title: Où il répond à plusieurs difficultez qui luy ont esté proposées sur la Dioptrique, la Geometrie, & sur plusieurs autres sujets (shelfmark Leibn. Marg. 43:3)
# Folio 264, page id 82327652X:0292
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=82327652X&page=292
# Source image: https://digitale-sammlungen.gwlb.de/content/82327652X/jpgs/default/00000292.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.87
# 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.

264
L TTRF 
MI N X NT O. Cum aurem eX constructiOne SIE VE D N ad
NS, ita HI N ad NI L, _ ita N O adN V; ErGO CTIEDED Nad
NTS ita lumma rectaM M N, NO, ad summam rectarum
IN ec N V. Estaucem eliam VE D N ad NS, ita M R ad
R P; FrOOVELAMMIaTCCLaruM M N, NO, ad summam recta-
rum IN, NIV, ita rectAMR ad R P. Estaucem recta M R
major Cunma rectdrum M N, NO; Ergo recta PR est major
summa rectarum IN, NV V. Superest probandum rectam
RFI, ese m
jorem recta FIV, quo peracto constabielum.
mam rectarum P R, R II esse majorem summâ rectarum
INT, NTTT. IncrianguIONFIR, Ouadracum R FI XquatuF
quadraris FTPT, NI R, mulctaris rectangulo subS N in NR,
bis, ex Fuclide; Cum autem sIc ex constructione vE M N
radius, sive NTFI ipSixqualis, ad D NF, ita NY R ad NO; ve
auTeM D N ad NFS, ita NO ad NV; ErgO ex aquaCriEvE
FINTad NS, ita N R adNYV. Rectangulum ergo TubFI N
in N V aquale est rectangulo (ub N S in N I; Ideoque
rectangulum (ub FI N in NV, bis, aequacur rectangulo lub
ITS in N R bis. Ouare quadrarum LIR aquatur quadraris
TIN, N R, mulctaris rectangulo HI N, NV, bis. Ouadra-
cum verO N R probacum cst majus esse quadraco NV:
Ergo quadracum EI R majus est quadraris FINF, NV, mul-
ctaris rectangulo FI N, N V bis; Sed quadrata LI NT, NV
mulctara rectanouloFI N, NV bis, aequalia lune ex Fuclide,
quadraco rectae TIV; Ergo quadracum II R quadratOFI V
majus est; Ideoque recta II R, major recta FIV; quod (e-
cundo loco tuie probandum,
Duod(i DuDCEU R CUMaTuE
ex parre semidiamerri A BY,
liceE reCtR MR, R HIAnEin
directum, e rectam lincam
consticuane, re in secunda A-
sura (demonstratio enim est
generalis in quolibet casu)
idem continget; HIoc eAtre-
ctarum PR, UFICumma, eriv
Major.
8I
S
Me