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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 175, page id 175905688X:0197
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=197
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000197.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.80
# 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.

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GOMMLENZARLL LA SM LL.
175
Secta AB bitariam in F, pOnO A F vel F B ∞a, F C ∞y,
CD ∞x: erieque AC ∞ a L y, _ C B ∞ a - . CUM iBIEuF
ejulmodi sic relario punctorum currae A D B ad puncta rectae
AB, ucrectangulum (ub C D de R aequetur rectangulo sub A C,
CB: erica a = py ∞ kx. Oux aequatio ad omnia veriusque li-
nex puncta reterri porest, quandoquidem pec x duae GuanLIEaLCS
indeterminatae existune, qua ad omnes lineas F C, C. D appli-
cari pollunt. Excepris punctis F_ F, quo casu quancitas y nul-
la eAt, _ P F EquatuT =~. quod Sc de duobus praecedentibus
Problematis estincelligendum. Caeterum cum in aequatione in-
venta a a - y y ∞ R x Una quanTIEatum incogNItaruM y ad-
Scendat ad quadratum, indicio est, lineam curram esse primi ge-
neris. Ouam aliam non esse, quam Parabolam, demonstravit
Pappuslococitato.
Non alicer concludes, aequatione existente x y ∞ a b, vel
X y ∞by - ax, lineam curram, quae hanc aequationem produxit,
esle primi generis: cum tantum alcendat ad rectansulum dua-
rum quanciatum indeterminatarum x ex y. FR aurem curra illa
linea Flyperbola. Ouod Facile incellisetur, si in prima ae qua-
tione, ubi x y  ab, concipiamus ab consticuere rectansulum
aliquod parallelogrannum AB C D, cujus unum latus AB (IE a,
ec alterum BC sit b; atque per punctum C Circa A(yMPTOEOS
DA, AB Hyperbolen describamus C P; ac denique à quovis in
Ca pUI-