# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175905688X:0145
# Permalink to this reading: https://leibnizlegible.com/page/175905688X:0145?run=74
# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 123, page id 175905688X:0145
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=145
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000145.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.77
# 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.

N O Y s B R E Y E S.
129
quod cum quidem tractio, (ur supra nocavimus) (i alia quam 
M
Eueric, cransmutanda sic in Fractionem ubi habeatur L. Cuxpo-
nendo scilicet m esse ad p, sicut denominator alterius tractionis
ad ejusdem numeratorem: quoniam in hac Methodo requiritur.
uEm iplius m Sit denominator tractionis ipsi x adhaerentis. Vbi
quidem, in calu, quo haberi ponimus m, non autem Fractionem,
quae ipsix adhaereat, supponere oporter p∞m, ita uc habeamus
P x non alius raloris quam x2. Ouod cognolcendis centris, la-
ceribu (que rectis atque tranrersis inserrire porerit.
Adpleniorem rero incellectum, decur in sequente tgura linca
AB, ec puncta in ea A ec B; oporceacque invenire punctum,
e
cl, nheca
 
uncot
ti
de
t
Co
dede
07
aC
vanliei
eas
ccait
mon
ut D, a quo si ducantur linea AD, DB, ut ipla datam inter (c
obcineant rationem, hoc eA, ut A D sic ad D B, Sicutlinea PII
ad lineam MNI; quarum quidem P EI SIE major quatm MN.
Demictatur a puncto D super AB perpendicularis DC, d
TuPpONatT A B ∞ b, AG DX, GD ∞y, MN ∞f. Ouoniam
isitur rectus est angulus ACD, erit quadratum Cx AD aequalc
quadraris ex AO, OD, Simul Tunpeis, hoc est, D x= L yy. F0-
demmodo, cum GB sit b = x, erit quadratum ex D B aequale
quadraris ex BC, GD, hoc est, ∞y y L b b - 2 bx. F x 2. Jam ve-
rO, Cum AD sic ad DB, SICuL P HI ad M N, erit quoque quadra-
tUI Cx A D ad quadratum ex D B, SICUE qUadFATUM ex P HI ad
quadratum ex M N. POrrO tac, uc P HI ad M N, sic L. N ad PFI,
22
crit-