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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 520, page id 175905688X:0542
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=542
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000542.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.76
# 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.

52O TIEMR. VAN TIEURAET EP. DE TR ANSMUT. QC.
enim eam pro libitu assumere) ad MI L∞Z, Critque ZDV = a X L ; a a
Id quod arguit, lineam (5HIIA L. esse P’arabolam, cujus vertex
eAt in a, existente A A ∞ = a, e latere recto ∞ = a. ac proinde
lonsitudo linex currae ABC D P cAt V -  a, existente
AF∞V.
Similiter Si locoy y ∞ = Ponatur haec requatio y + ∞ =, auE
a
de
∞ =, auE y3 ∞ =, aeque sic porro in infinitum: inrenietur
Semper superticies AOFTLKL F ejus naturxe uc quadrari potti,
ac proinde omnes hae curra in rectam lunt permutabiles.
Sivero ABC DF. Sic Parabola, cujus axis AG, _ latus re-
43
ctum va: invenietur M  ∞
a de ejus quadratum x 
adde quadratum CNI, ee habebitur
b 
UE CM = ad C OV
+ XC
2+ 
e 4
4X
2+
X
a
x
4+. Cut
lic cognita aliqua linea, puta a,
ad NI ID Z: erieque Z∞ V 4 X x - F aa, de linCA O FTIKL IIy-
perbola, cujus axis linea AC, cenerum punctum A, lacus re-
ctum ∞ : a, de transverlum ∞ 2 a.
Ouodipsum docet, lonsicudinem curra Parabolicae inveniri
non posse, quin sinul inveniatur quadratura HIyperbola, e vi-
ceversa.