# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0164
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0164?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 82v, page id 00068201:0164
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 83r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=164
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000164.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.91
# 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.

Relenta X H positaquna radice vera, caeterisque falsis 
et vera minore omnibus falsis simul sumtis naecesse est omnes terminos
resse affirmativos excepto, uttimo siquidem Recnla vera est.
nam cum termu ultimus sit negativus secundus autem affirmatious
tunc si aliquis negativus inter eossinter ponitur, dabitur aliqua Etalis cujus omnes radices falsae
signorum
b + C+d
Hinc ergo sequitus si et sit minus quam  c+den
earum
tunc a in xcombinatione ejus esse minus quam combinationem
  aliquam
proxime altionem, veqs a n b+0 +d, esse minus quam
 omo. bc. Quod mihi non videtur semper verum, nec
demonstaabile; imi tentemus sergo sitaec a aequ
55
b + c + d = l ducatur in bt C fiet b2 + 2 bc = l b quod debet
esse minus quam bc Verum si l sit tam parvum,
contrarium utique eveniet
ut  b sit minus quam b
tuma Rem in numeris experiamur, sit.
invicem duc
X
+
c  et sit X 4
sint.
et in se
X+ 2 fiet
it caeterist
Retenta X positaque una radice vera catqu falsis
(cum una tantum cncontingere debeat mutatio, ncesse
est situe ultimusu terminus regatioue et secundus affirmativus)
si regula vera est, necesse est 
sed quoniam hac methodo rem prose
Quendo sero admodum ad 1 universa lem
dermonstrationem pervenicimus
s
inici dit mihi
methodus pu brevis et puldiia per quam
calculo experiemur, uttum.
regula
ita procedendo: