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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 292, page id 175906937X:0316
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=316
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000316.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
# Lines: 29 recognised, mean confidence 0.86
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

292
E L E H. C U R Y A R U M
∞N = a, ec A C ∞ V X X. +. y9, aEBC D V XX = 2 a. X + a. 4 + yy;
SIEGUC A C =- A D ∞ BC: aequatio crie
VXX -F yy = b ∞ V XX = 2 a x F a a + yy, Factaque operatio-
ne conrenienti, ut veraque aequationis pars à signo radicali libe-
retur, e transpoliris transponendis, crie
4bbyy ∞ 4 aa ∞ x - +bb~ ∞ - + a3 X F 4. bb a X F a + - 2 bb a a F a
Uinde Facta dirisione per 4a a = + bb habebitur 3677
aa = bB ∞ X X
a x -F = aa = = bb. Deinde asumpeo juxta Regulam v ~ N = = a,
erie x ∞ v. F = a, ideoque substicuco hoc ralore in locum ip(IuISX,
atque ejusdem quadrato loco xx, expunctisque us quae le inri-
L18. L
cem destruune, crie
13
aa = b8 ∞ VV = = bb. Dui quidem calus etE
Theorematis 12mi hujus libri, ac proinde LOcus quaesitus erie
Hyperbola. Cumque rallumpea lic Prox = =a, ( ab A versuSF.
sumatur A HI∞ = a, erit, juxta Regulam, FIcentrum, ee Cemi-
diameter tranversa (puta HIC ob una, e EI E. ab altera Parte,)
∞ V = bb, id eA, = b; ita ut diameter erantrerta F C (quae qui-
dem, ob applicatam C. P. ad diametrum FI F pervendicularem,
crancrerlus quoque aXis Cst,) sic ∞ b. Ratio autem transverla
diametri ad parametrum, seu quadratieran (ver sa ad quadratum
lecundae diametri, erit uE bb ad a a - b b. Unde per ea quae libri
primi capiribus secundo e ultimo expolica sunt IIyperbolam
aplam delcribere haud difficile erit. P orro cum quadratum semi-
diame.