# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/82327652X:0338
# Permalink to this reading: https://leibnizlegible.com/page/82327652X:0338?run=74
# 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 310, page id 82327652X:0338
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=82327652X&page=338
# Source image: https://digitale-sammlungen.gwlb.de/content/82327652X/jpgs/default/00000338.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.92
# 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.

BTC
E T TR FS
natam B C, major eric proportio C D ad DI, quam
quadrari B C ad quadratum OF, quia punctum O est exrra
Ellipsim. Sed proprer similicudinem criangulorum, ve BC
quadracum ad OT quadrarum, ita C F quadrarum ad Y E,
quadrarum. Majorisitur eric proporrio CD ad DI. quam
quadrari C F ad quadracum IF. Cum aurem punctum B
detur, dacur applicara B C; Ergo punctum C. Dacur etiam
C D. Sic igieur C D aequalis D daER. PONAEUT C E CNC A.
Ponatur C I ese E. ErgO D, ad D - E habebic majorem
proporcionem quam Ag ad A g + Eg - A in E bis. FC du-
cendo inter se medias e exrremas, D in ag F D in E9 = D in
A in F bis, majus exie quam D in A g. (= A q in F. AdX-
quencur igitur juxca superiorem mechodum. Demprisica-
que communibus, D in Fg = D in a in F bis, adaequabitur
=a g in F. Auc quod idem est D in Eg T ag in F. Adxqua-
bicur D in A in E bis. Omnia dividaneur per F.
ErgoDineF ag adxquabitur D in a bis. Elidatur D in F.
Ergo a g aquabitur D in a bis. Ideoque a ae quabitur D bis.
Ergo C F probanimus duplam iplius c D quod nullo modo
ita se haber; Sed semper Fallic icta mechodus.
e
Application du mesme raisonnement à l’Fsyperbole
es à toutes les autres lignes courbes.
IEdara Ayperbole B D e, cuius verrex D, diameter D
DC, e punctum in ca darum B; Ad quod ducenda est
recta B e, cansenshyperbolen, e in puncto e, cum diame-
eroconcurrens; Freo lumendo quodliber punctum in recta
BE, e ab eo ducendo ordinatam o r, a puncto aucem R
ordinacam B C, major erit proporrio cD ad DF, quam qua-
drari B C ad quadracum o x, quia punctum o est exrrahy.
perbolen. Sed proprer similicudinem criangulorum, ve BC
quadrarum 2d 0 r quadratum, ita C E quadracum ad YF
quadrarum; Major igirur erit proporcio c D ad Dr quam
CF2dF E, cum aurem punctum B derur, darur applicate