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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 133, page id 175905688X:0155
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=155
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000155.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.78
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

4.71
1AI
1600.
A
lumm
ecen
ide ten
1VY
et2 L. 22 1. 1 2. 0i
ac per consequeno
bbbb
255.
Dec LbbrrFDe.bDdc Lbbrr.
+bv.
bv
Ouocirca habebimus
 
bb e
Tsinc mulciplicando per crucem, ut in Fractionibus, d auterendo
utrinque producta aequalia, habebitur
2ef 7bc5 -  8bb et f 4b3 e3 - 4b3 V eCb+ vC ∞O.
V - 4bD = 6bb  b4
Duam aequarionem si ciridamus per ee-Lbe, orietur
2 et -5b e3 + 3 bb ec -- 3bbve = b3 v∞O:
2C per conlequens
bv b3
et 5b e3  L3bb ee - L b3 c ∞ b3 v - L 3bb ev. L3 bec v L e3 V.
ac demum 2e+ f - 5b e3 + 3b2 e2 + b3 e
b3 + 3b2 c. + 3be c- L e3 dV.
Vbisi inlocum e substicuatur Y, acque ex hac lumma deinde au-
2b73 +. y4
teraturlinea AL ∞ y, relinquetur L. ND 63- F 3bby + 3byy f p2
ut supra. Vbi nocandum, lineam hanc curram non aliam esse
quam typerbolam, supra a nobis constructam.
A D B A C L N A MI 75 de 76.
Emonstranda hic est opcratio, quam hxc Geometria nOs
docet, cum radicem incornitam alicujus aequationis multi-
plicare rolumus per certam aliquat QuanCIEATCI aNE numeruIM
COGHIEIIM. PEOPOnaEUE~QuaLIOX 3 CX   t a X m b3∞ O, CU-
jus radicem incoenitam x per lineam h mulciplicare oporteat.
Supponatury w xh, et Hiet = ∞ x, ideoque = ∞ X =, nec nOn 
13
∞x 3. Proinde (i substituamus in xguatione prxecedente lOcOx,
e  loco x2, itemque, l0c0 r3, erir sequens xquatio