# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0335
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0335?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 168r, page id 00068198:0335
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=335
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000335.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 132 lines, status machine
# Lines: 132 recognised, mean confidence 0.85
# 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.

Absolvatur
ut in fine
10 VV + 17
et 2000+ 12 ita sunt explicanda, ut factum ex ipsis in se invicem
ductis fiat aequale quadrato, s idque scilicet ita ut 
ii
e
sitera v 50C+51e+52,: 160e46i e+62 (itu deni expksi
ic o
n inventa rationemoas quadrata aque
jam quod in viatulo lat
adhibetur in explicatione iphius v, vinculum nen
ita
1c aequ
+ 10. 51.5] +2.10. 51. 52C +. 52.52 : 608+612+62
oYBH12 aequ. 10.50 e+ +, 10.50. 51 e2 + 2. 10. 50.52 C
Hinc si 20vv + 22 explices e
modo solum  ex in aeq. 3
pri. 10 et 12 ponendo 20 et
+12. 61 + 12. 62d
et in se invicem duos valbres ducas, hominator
producti fit utique quadratus, quia in utroque valore moncintr producente nominator est idem. Tautum ergo superest ut
ex producto i Numeratorum fiat quodratus. Itaque unus numerator scilicet in valore 3 conparetur cum
+ 12. 60
A 20. 70 C +2. 70. 71C + 71. 31, in, 80C + B1C + 32; alter scil. in valore + comparetur cum 90. 90e + 2. 90.91 8+ 91.91, in, 30C + 81P + 82
 aeque
et 1080C1 +702. 81C +70. 82C
Hic 100 (Supponit +2. 70.71.98,. + 2.70. 7181.. + 2.70. 71. 82C
10 etc)
pro3 literis,
et 600ek
pro duabus
ad ser.
vandam
legem
sd moge
neorum
materia
em
EX1ZCt 13,
+
+ 71. 71.90. +71.71. 81. +71. 2182
aq. (9) compendio
100e+ 101 23 +102e +103 C +104
aequ. (M)
105o + 3. 105053 +2. v sost e .
+ 10. 51. 55. 4 2. 100st. s1 C 4 10. 52. 52
+17. 60. 4 12.6] . 12. 62
Ex aeg. 9. fit 80 = 100: 78 8 = 1: 71
per ( fit 703. 81+ 2(10. 80)15 70. 101
3
rere fit 13. 81 + 2. (71. 82)70 = 71. 103
4(5
n. 103 -2.70. 104, - 71
seu fit 70. 713. 101 + 2. 70 18- 793. 71. 103 +2. 71, 100
Ex e. multiplicando 70. 7(2. 82 +2,713. 7(. 81 4 78. 7(80= 70. 71. 102
per 20. 7 fit
104
vi
f= 7. 70. 104
100
(15)
a416
eodem modo ut in aeq. 7. pro 70, 71, ponemio q0
et faciendo
(1)P 200C+291 C t2orC + 2032+ 204
seu ex 17 per 15 fil(70. 109 ≠ 2. 78. 11. 103+ 7 p2. 100 = 20. 71. 102 +4,10.109
prodit 70. 104 +715 100 + 78.71.102 2703.71. 103+ 70.713101
inveniri pure imo tolli. Sed quia id prolixius, rem potios praestemus
per adjectum calculum DO ope duarum radicum aequalium.
2030  2905051 ( 4 2. 7050. 52e
422. 60 1 + 22.61.. +32. 62
obae q. g. patet forumlam 100C 410 B etc. habere duas
et ex 17 perch fit 703. 104 +270. 71. 101 (713 109 2 70. 71. 102 + (4 117. 100
si aeq. 19 et 19 invicem subtrahas redit aeque 16. siu sibi addus,
itaque ope Aeqq. 1b et 20 tolli poterr  71: 70
4q
1
+40. 51. 51 n +2 30 51. 51 C18a. 52. 5L
radices aequales (posito 100 = +) adeoque considerari posse ut
aequationem talium radicum. Hinc multiplicari posse progressione
chithmetica salva aequatione et fieri, s. 101 C3+ 2. 102C+ 3103C + 4. 107 -
et 4. 100 C+ 3. 101C+2. 102P + 1. 003=0 unde per ter minos summos
fit. _ L. oB 12. 4. 100. 102. + 3. 4. 100. 103C+ 4. 4. 100. 104
- 1. 3, 101. 101. = 1. 2. 101. 102. = 1. 1. 101. 103
et per terminos imos fit. 
5II
p 102. 103C f 1. 3. 105. 105C F 1. 4. 123 104
L + 1. 1. 101. 103C 4 1. 2. 102. 103C + l. 3. 103. 103=
=4. 4. 100. 104.. - 3. 4. 101. 104.. -2,4, 102. 104
pro ag(+) et (5) scribamus compendio 3oec+ 3) C + 30 et 40C+ aet
Exbeth pet 31. 42 -32. 41 in 31.40-305 = (2) 30. 42- 32.40, ut
itaque si hypothosin
tunc  ex p.
alibi calculavimus. est gutem 3249
assumamus Z2 =0 seu 408
fiet 31. 42 in 39, 41 = 302. 42.  seu fiet 31. 4f= 30. 42 et ex
+6 vel 7 fit  31: 30 = 42: 41 et explicando aeq. _ ex 4996.7.
1. 2. 102. 103f2. 4100(32. l.5. 103.
3. 4. 100. 103. 3. 4. 105. 1642 2. 4. lvetr. 24. 102. 10
4. 100. 103
= 1. 2. 101. (02. 1. 2. 102. 103 = 1. 3. 101101. 1.3. 14, 107
coparatis cum 4 et 5 fict
(121
= 1.2. 101. 102. 3,4. 101. 104) (113. 101. 107. 7. 7. 102. 11
adeoque destractis destruendis in aequo fit Et in hac
3.34.  novissima aeq. 13 p nova rursus institui potest explicatio
nam quia assumsimus 2 vel 40 =0 et 32 = 44. 100104 - 1. 1. 101. 103.
hins sit 4, 4. 100. 104= 1. 1. 101. 103 quem valorem ipsius 4. jaieq
(15) - 1. 1. 2. 2. 101. 102. 102. 103 NN
suubstituendo in aeg. 13. fiet:
= - 1. 1. 3,3, 101. 101, 103. 103
∞I. 1. 3. 3 101. 101. 103. 103
quae est aequatio identica, successit ergo hypothesis (10D sube
a P. 1. 2.2. 101, 102. 192.103
seu 14) adeoque non amplius est hypothesis sed necessaria veritas
Hinc quia calutus idem in comparando secundum eq. 9 esse debet
quia qui foret, si aequ (() fictitia esset veritas, et eo casu
4. 100. 10317 10
24100. 107 +1.3. 10, 10
Ex ro ( pripriiatali haius pogiun fit 8C- 10017 Et eodem modo fier
fit ergo 71. 703. 4. 100. 103 - 1. 2. 101. 104,:,-2. 4. 100. 102 + 13. Iaod fier
91. 903. 4. 200. 207. p. 2. 201793:: 2. 4. 200. 202 + 1. 3. 201. 201
et pierndo a et 80 = (00:70 209: 90 82 = 104: 718 seu per (14V
3= 101. 103: 4. 4. 100. 7(.  201. 203:, 4. 4. 200. 912. senique
81= 70. 101 -2. 71. 100, : 703290. 20] - 2.91. 200,:90 ((23
itaque absutrant denique ad instur (14)) scribatur 4. 4, 200, 209 = 1. 1. 201. 203
vatu itaque athibiti aeg4. (14D 23D, (191, ((21D, (22), et in is explicatis 7, est 
) per aeg9. 71 et 91 per aegq (17) et (17) et denique explicatis 100, 101, 102, 10) 104
ahselutus et noenientur 10, 51,52, 60, 61, 62di licet
Absol f
i