# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0472
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0472?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 236v, page id 00068201:0472
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 235r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=472
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000472.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
# Lines: 88 recognised, mean confidence 0.83
# 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.

sit datum a Aad binomium
Datum sit atiuda Ponatur pro radice:
b + sC Unde extrahenda radix.
at d +  esc,
Unde exciletur binomium simile dato: + d3 + ec Nc
13dec + 3ed2
Jau S0 + ACCH +d = e
Unde extrahenda est radix
Jam it d.
bpy d+3dec. et 63C + 3ed71
ngi 3d Y3 + b C +, A3d - 3de addatu ad b. fet: 3d (0+ b  C + b p 4d Unde redet
bd oritur aequatio lubreo. Ordinaria, sed hac nihil ad rem. Parro Ponatur + ere inventa
in nimeris prope veris. Ponatur b foc.
sit pin s3 4b - c +  d + e se F d - etc, + d + etc  d
Unde paret origo regulae, nam 1b C pd - eC ,d - etCda pve
Y(3) b2c
d+ etc
tantum vero habeatur tamen quia eb, enor non est major, quam . h et d necessam
integer, hinc rece statum deleminatur mnerus, si quis est, qui satiffacit. sed difficultas de qu in eo consistit
sii facias: Quod ac nontus quidem vero propinquus haberi potest, tunc cum c. est quantitas negativa.. sit radix
C
d + es.c. Erit cubus. + d - ec f.c ()p d 6d ec + 94 (B,  ec +6e d-9 d’ec
-3déc 13de..
(A) 1B)
et (A; - (B 1 46 + 3d ec ubi notabile est idem prodive,
+ 3 d20 =2
ac si fecissemus A + B, posito a  non -C sed +C. Data est autem hec quantitas, adeoque et ejus
radix quae est d+ ec  vel d ec t. C. Cum quantitati si jam esset
Sit ergo propestita quantilas VO Z + Sr= g. exqua radix extrahenda est, et sit alia
+(2)Y + F.Y A9 exta itidem radix extrabenda est, manifestum est
sit s0= +XSq + H
27
du
17 + Sr. 4 + 1 2 - s2. 93 in 13 Y + tr  q + Y - s. 2+ qu
Jam  es 3d. A N 3d 55, 3d + 3Ecd, et (A) H d3 - 3 dec. Ergo 3d N + A⊓ 4d. sive d’p 2 Xd + A
Ausus: 3ese 3de + 3ec, et (H 1 H 3d2 C - eC unde 3eN- 1⊓ 4ec. Unde componendo:
+d+ 4ec p, +A +3d N. Ponatur jam CH 1. quod simper obtineri potest, erit  +C t A 41d 
1 +3C N
A =1 + 3 s
sive d + e _deH 4 d +e
6 sive  ~ de, A -1
4d + e
ex
Rectius faciemus Ape 1. et relinquemus C. et frei:
d- 3ec
4d + 4Cc  A. +dercr 3ad
Ergo A + N  d.3ec, + d’ +ec 1 2d2 - 2ec. Adeoque A+ Nd d- Dec
Eodem modo Bt - eC + 3d, ego BR1 + Np, 442
+ Sc. 1 d + esc.
b + 1+ d+ +- ec s+
-3dec 43ed2..
H f+gVc. et b +. dCr f +gc 1.
y +d V +h
y 42b
V X iaV
ad. td
+3f9C +39f..
(- cb1 r. eit CpY
ei = - b p 4
yi y Asd. quae aequatio divisibilis atrobi per y -b
18b3
Hini ad radiem inveniendam binomi A + B sC ita procedenus:
1I d’+ ec adeoque quaerendus est numerus cujus quadratum sit  13) A+ BE
fint A + Bc. eut 1C) A+ BC 
et quia 43- 3d ec p A
ideo cabus ejus est  d( A. Quaerendus ergo numerus d, cujus quadratum sit pH S A+ BC, et cujus cubus p A
Nempe d 13) A + Bc, et dp A. Ergo e sB A. dY A
 Ergo d p A. et dp
jam d y  A+BC. Jam quod est maius A diviso per D. erit etiam majus A diviso per id quod est
majus quam d,
ergo
dp
A
1(6) A78
.Et d d consistet inter hos lerminos: 
Et d consistet intra hos terminos 16 A+ 8C et s A
contenti esse doterminatione: dY sB A +Bc. et dHA.
 sed cum S0A+ BC est numerus tunc prossumus
1(62) 1+BC Jam ex numeris qui satisfacere possunt eligatur rursus
is, qui cujus cubus add octuplicatus ad ditus ad duplumf divisus, per ipsummet d dupliculum; des sgC s 3 s(-9c-f
sed fauliora addi possunt, necessario 4d H 4. contra necessario r per 2d. divisibilis, et producum divisionis duplicatum ma
denique necesse est
ut sit ut f + 8d, divisa per d., dent 9. Addi potest: 4d  3s 3 ( A+B quia supra 3dN + A,  4d3 sed rem
abovo repetamus
De exhathonbstutio
a +
B ed + cd
13b - sc