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# Title: LBr. 56 · Bernoulli, Jac.
# Folio 3v, page id DE-611-HS-958800:0006
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958800&page=6
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958800/jpgs/default/00000006.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 144, 2026-09-10T03:13:18Z — 23 lines, status machine
# Lines: 23 recognised, mean confidence 0.90
# 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.

portiones ABCD, BCF ad circumseripla rectangula MD, NF eandem
ubique rationem habere, quam vocabo ; simulque 1G. LH longitudinibus
DC, FC proportionales esse. Etenim posito AD =a, DC - b,
BF-y, FC=X, manifertum,
AD9. BF9:: Tril. ABCD in DC. Tril: DCF in FC.
aa. yy:
abb.
Q
id est: ea yy:: abb. xxy; adeoque bby=x; e propterea curvam
ABC esse Parabolicam: sicut etiam si desuderaretur, ut trilinea
ista ducta in distantias controrum gravitatis se haberent, ut
(ubi vel Biquadrata ordinatarum, ADC foret linea recta, vel
paraboloidica ejus generis, cujus natura exprimitur per is.
ax. At in altero casu, ubi praeter trabis pondus etiam an
nexi oneris D habenda ratio est, non apparet, quo pacto ex-
resolutione proportionis hujus aa yy:: abb 1.
e
natura quaesitae curvae elici possit; quia nunc litera 2, quae e
ipsa incognita est, non utr antea evanescit: quin imo ex hoc
ipso non obscune consiao, quaesitam figuram talem non esse
qualis supponitur, id est, cujus portiones ad circumscripta
rectangula ubique eandem rationem habeant. Quare
suspicor, Amplissime Vir, latere huc sublimioris cujurdam