# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0410
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0410?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 207v, page id 00068196:0410
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 208r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=410
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000410.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 109 lines, status machine
# Lines: 109 recognised, mean confidence 0.80
# 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.

Loto X pinatur 7. in hoc catculo
10V + iea 20 20X F2Ia = 0 (50. 20X) + 11. 20a 1-0
X + 1t ax. + 12 aa = 0
2077+ 21: H + 22 aa =0
-20. 10 a)  21. 10a5
+10. 21H. 11. 21a =0
20. IH = 2IH a)
10. 20, + 11. 20(a)H +12 20a ( (3) Fu. Z2L11. 1a (+ 12. 22a4 4
20. 189-1. 10 (aY - 2210 a( , 20. 12 = 21. 12a 22. 12445
videamus an duo hi valores ipsius X coincidant, quando du ae aequationeshabent divisodm
communem. Sit 30H + 31a  et 407r4la multiplicantur hae duae aequationes pe
od  + 3051 ag + 31 s1a a  Eet e  40. 50 4 y +. 41 50, a9 + 41 514
50x. +51 a fiet 30. 50b + 31. 50aY
fiet 10 = 3050 11 = 31.50 42 =31.51 20 =2 4050 21 = 41. 50 27. = 41. 51
et fiet L. 31. 50. 40(G0) 
agato
210. 51. 30.60)
30.50, 41 (51) 7
= 31 (51, 40. 50
+ 31.81. 4060) a
3150. 
 31 (5)) 41.50)
= 31. 51. 1f0. 61)
I diso. ises X +21150 ile
quae binae aequationes
coincidunt inter se, quando
scilicet datur communis ouojor
utonque nempe 50 + si a
nam p duisa per 31. 40 - 30. Cx t oat 50X 1 51 a
 Hc nempe methodo etiam determinatur divisores communes, cujuscunque gradus
sunt hae duae aequationes 9X + Da =0 et 6X + 8a, debet esse utiue
ettque 3+ 2a -  communis aequationis divisor eutus  2
Si 10xX auat +2
hadem methodo  inter tollendum eit
o habeant dommune
mcoris sepressionabus
et habentur divisores communes aequationum
Prgamus in c 3, moste notae  sinistrae sunt dextrae sunt l. D in Hy
 2. 0 in a,
Tanxio cs aen. 3 A. 4
in aeg. e notae dextrae sunt 5. 2 in FY et 112 in a
+12. 20, 10. 22 - 11. 22012010 semp 1220, 10. 22 = 11. 72. 11. 20
posset etiam aliter RCsE +. E9. 12. 22.
ordinari sil pt
nabo baaa abab laba
baal abb
italim enunture ormis 20
qua 20 poni potest = 0. si aequatio
autera sit primi gradus, et fier
explicando
IL. 10- 20. 12 4 11, 22. 21. 10.
p0rg. 1 d H0. 21. 11. 22
+10.2t H. 1a Sc
-10. H. 21, 22
notarum aptem sinistrarm in 12. 20. 10. 22 sint tantum vata
parere, sed ex binionibus horum sequentium 1. 2 et 1. 2. et. 2. 15t. 31
seu exbinionibus ipsorum a, a, b, b et harum transposit onitns
quae sunt aa, bb ab, ba seu 1.2; 6. 2 2.1 2.l 125 24, 2 1; lo2
13 est -10. 22. I2. 10 + 10. 21. 1. 220 caeserae combinatione exeluduntur, eo ipso quod
iho gx gr ape o can maysuas 2 vurga
itaque hac jam videor ad clavem pervenisse harum variationum.
10γ3 + et aHY ,. 12 adY + 13a =0 (+10, 20N3 H. 2otX , 12. 2eX 1 15 
vel exquatuor pariparibus
seu =10. 21. 11.2 1) + 18.21,. 12. 234 =8
3D. 2281625)  du (∞. 23) 
Extense +10. 21. 11. 23 Y 4 10. 21. 12. 23a (5)
= 10, 21.21. 13 = 10. 21. 22 13 1
-201I. 1. 23 - 20 11 12.27
LeN  X
11021. 12. 23Y + 10. 27. 14 3a0
+10. 21. 12. 23H + 10. 2E, 12. 23 a 7 (6)
+20. 112. 13 +20. 150. 23 k) X. XVI -
Et explicate fie
Idem cum oimen Des si giuihiabet onemtinur, quod ex io sit
transpositione nitarum sinistrarum simplice, triplice, quintuplice, etc inimpari
opposit. Ain suu embro signum habet aliad membrum quaod exillosit
transpositione notarum sinisrarum duple quadmplice, sextuplice etc.
Ab solvatur adhuc tok p. Na FLa aX  13 ax rc
et 20d 21 Laax 3aX 124a 20
il Hotae aptro se haber ad V, ita notae retmo ad a, hinc in ullima ag. ubi
eornescit u ut a habent se eodem modo
is alterias
Hoc unius sequationis se habent.
  erm i utor ni  e  otalitu et iet pant
Deniqe onplipaitia. vtiam institui potest 1er efli 10. 21. 1 23,9 4 10. 21. B. 23a 20
oalisene cum coetti–
 21. ll. 23 10
1+..
nemp. 10. 11. 51. 24. 10. 22. 13. 24, et 1021. 11. 24 1023. 4. 24.
+10. 20. P: ad F 11. 20Y + 12. 20aH + 13. 20aa 120 +0. 23HH + 1. 23at +12. 23aa (+ 13. 23 a. X) 7= 0
20, seu 10, 21. H. 23
ti
10. 2. 11. 349 10. 2r. 13. 24, 10. 4. 11. 24, 13. 15447
veldemque ex dutibus parpat ponions
tronssi quo mo paria  essesil coltatata)
-29, 13 = 2. 13 - 32. 13
compendio 26. 10 + 2a 2o a 1 lona =  10. 29 hy + 11  ay + 12. 13   os
-20. 10. . a) 2 21. 10
unde
a - 12. 20
transpositiones quatuor, hinc patet rem non ab earum hanspositionoti
-10. 22. 22. 10 + 10. 21. 11. 22 =
20Y + 21 axy +224a) + 23a3 2 20 104 4qod v nu 25. a
2
citdibus teminer
aatefas
Ex functiim insino ))
.... 20. 12 14
. H. 13 Eit