# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068197:0090
# Permalink to this reading: https://leibnizlegible.com/page/00068197:0090?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 45v, page id 00068197:0090
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=90
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000090.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
# Lines: 70 recognised, mean confidence 0.76
# 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.

Extrahenda est radix Tubica ex D 2+ Y3. multiplicetur per 2 divisorem, fit 18 + 1013
s extractio
ergo duccelit etiam in producto ex ambebus 2+ (abb - ac) = c
Nam esto O, aab + a4 ) ac) = f + 4 sac, eAt  sC aab-aa tac) = f - g lac Ergo erit
ea
oa
sit ac=  (ab act et Habemus 0 Op = ac. Hatemus
+ D = 2f  O = D = 29 1aC
es(aabF haad ac)
=  aam
3= aan aam + aan =aa b = C
3+36) (01)) 100)
f fit 2aab + 3aCf
=
dO+ O+ D + C D (O+D)
fC3f56+
C
aab
Bac
et ee -3ffg ac +d
aa vac
s
ac
cum .a2, 9
etanee
cun f -C, :9gc
et e3 = bb =C res salcedit
  bb - (3 = ff - C, :9)
Hinc sit. ff a Chaque + sC - set
quadratus opinia haberi possunt
in rationalitus idc et
pro eponatu l, e
itaque quotias succesit extractio
biromis erit 3 (b + vC)
en _e s, quadratus
Mirum
aab + ad saf sicibit pro eo ponere
pruo autem a semper esse, nam etsi daratur
aab taa dd et ddK = aac et firt aab + ad sac = _ aab + aa Vac
Quia ergo as 4c = 3AHg = a diferunt unitate seu
9C - 3affg disferunt unitate seu 9
ee
in
 i (aab = saC) eigubis est Sace si succedit etium jucaedet aab = aa iae)
39
propontur 1.
a
11
03
= 74G , 1 34 se 1 + (3 23 B)2 B + 3.3. (3
11 (3) 23 + ((3)2 + 33) 1 1 +(3)23 + (g3 qu (B2 + 23)
3((++)E3 + YB Y((+(3) 2.3 - r B. qu (32 + 2.3))
+21 = 1+ 3. 4 = 1 + A (3, 23) B qu (B2 + 2.3))
1+ 213) 1+ 3. 2.3 + 3. 213 + 9. 3(3 = 37 +30+3 = 37+ 12700
BC. (+ _213 = 1 +9003 1+ 60 2700
aab aa V(nab + aaV ac) = g eo yn cd posito co ria
acb
V- co + a
1cd
= 6+
= f
S
ac
et
pis
v +ae
Ld
124
304
f