# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0696
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0696?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 350v, page id 00068196:0696
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 351r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=696
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000696.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 106 lines, status machine
# Lines: 106 recognised, mean confidence 0.81
# 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.

itaque ex coefficiente ipsius m facto o in aequ. 24, fit it2. 71 2 = vel 123: 213, vel 223: 123) Ex duabus harum trium
id est 112: 212 =, vel 123. 223 vel 223: 123
et ex coefficiente ipsius l facto 0 in aeq. 24 fit 112: 212 = vel 113: 213 vel 213: 113
a44. jam sequitur tertia
et ex coefficiente ipsius n facto O in aequ 24 fit 113: 213 = vel 123. 223 vel 223: 1233
Ex his ita eligere poterimus, ut fiat 112: 212 =13: 213 = _B NX 223: 123 O, Unde 112 = 113. 212: 213
simili calculo institut ex coefficientibus in aeq. 29 nihilo aequatis
123 = 213. 213: 113
nihilo aequatis, eodem modo fiet 312. 212 = vel 323: 23 vel 223: 323 2 Ex duabus harum
(31 mo)
312: 212 = vel 313: 213 vel 213: 313
313: 213 = vel 323. 223 vrl 223. 323.
trium aequationum
jam sequitur tertia
Ex quibus eligere potrimus ut fiat 212: 32 = 313. 213 = 323 : 223 5 unde 3n = 212. 213: 313
ita in olectione priore, Doerunt prisa  nempe  12 respondent mediis nempe aB
postariore 31. postrema nempe a 2y respondent ... ..
. i. 
- 113. 123.213. ~ - 112.213
(21 ) 4, , 2. 22 22ZM + 113. 113. 123N, : 3=12
2069F - 12. 1(2. 123 = - 1(3,. 213. 225.
( 12. 119 20 m + 219, 13 7
309h= = 212, 212, 223. =313, 323.207
312. 312.323. =313. 213. 213.
312.-13
- 312.1212
g 313. 23. 213
.
. 1 23 m + 112. 213. 213L
susobs =32. 223 . - 112. 113. 213
aus 1  in 20n + 12 l5. 1B l
uo
11(3. 22
Valores ex 30 et 31, substituamus ipsarum 112, 123, 312, 323 unde
seu fiet 100f = + 212. 223. 12 m
= 213. 213.22)
+123. 213
+323. 213
=22. 223. 23 = 312.313. 21313.)-313. 223
312.313,325. 313,41713313. 233
n : + 113, 212
ita patet omnia evanescere, idem enim in caeterarum iteratum valoribus continget.
= 212, 212, 223
21
Et tagus . 169 -- 112. 127. 123. = 1(3. 22. 213. 31) -13. 229
F113 (212: 213) 223 (213: 115) 212 M + 213. 113. 21,
100f = LHZ _ 212(2I. 213) M
9
Itaque non licet aequationes 24 et 29 divellere  in tres alias unamquamque. sed paulo prolixiore
calculo utendum, et coincidentiemus aequationes 24 et 29. vel ponendo, esse
aZm= + 6N et 5m = 4 l+tin, fiet m - Z1Fon,: E L 7 l + tin,: D
fiat 8 = d, et fiet 2l + hn = Zl+ 6n seu F (9 -7) l + - t) n = 0 et ut
evanescant l et , fiet Y-2 =0 et 6 -t = 0 seu fiet
Harum trium aequationum ope quaeratur. 21Z, 213, 223
= 212 (112. 123. 123-313, 313. 323)
223 (H2, 12. 123- 313. 312. 323)
1
f= 2 et 8 2 ut G - 8
Ex his aequse unam consiieemus nempe cum  = B, fa sit 212, 213, 213; X, y, Z fiet
+212, 213, 223 (123-423)
a 212. 243.223 (112-812)
 0
compendio 1201XXZ + 1102 X2Z + 110OXlaX + 1001 aa Z = 0 = 9- 5
+
2210 XXy + 2120Xyy + 2100aaX + 2090aa =9= 8-2
3021 99Z + 3012y77 + 3010 aay + 3001 aa z= 0= 5- 6
=Yy = 22IOXXG + 2100a aX + 2010 aayC3: 2120x
= 3011y2Z + 3001 aa z + 5010 aay 3 : 30217
quos dues valores aquande ipsius gu aequando fiet y = (2100. 3021 Z + 2120. 300, ) aax Z:
: +tE2IOXX + 2010aa uti notandum temper qudivabre eX a piontere
-301277 = 301044
ubi notandum semper
posse permutari simul
X, Linitiat, antepenultima, notam
2
3 inital, ultinam notam
compendio y= E)  C ex 2m: a  12. 3o)  XZ
 Sed sumamus prius aequs 2 et 3 pro tollenda y, et compondio scribamus: 1
12 27 + Byy + nay + 124450 et 20yy +21 ay + 22 aa 20
fiet - 10. 20yy = 11. 20 ay + 12. 20aa = 10. 21ay+ 1022 aa, seu erit
Alitor 10. 109y +. 101ay + L II. Vaa = L. 11. 11 a a = 12 a a seu y =  - = 11 a t a 4u 12,:10
fiet
seu a y = (10. 22 = 12. 20) a :, 11. 20- 10.21.
= (pari jurC) = L 2a + a Y + 21 - 22, fr: 20 
fiet 21. 20 - 2 10. 21 - 20 ( 112 - 12) - 10 ft2-22),
 C202 10. 21 + 11.25-2. 10. 1120.25 -a 721Z 422 - 2. 10. 20p11. 21 - 4 11. 12
FII, 2F = 4112. 22
2. 22 4. 1V21
Senz. 10. 22 + 220 2. 12. 20 = 10. 11. 20,2] = 10. 201+161222 4. 12. 22)
4. 10311. 28.21. 22 = 4. 10. 11. 19. 20.21CC 7,10. 711. 20. 21, 10. 20,. 12. 22)
ext
4. 10, 22 22 + 4. 12. 12. 20 )3. 10. 20,17. 22 4 10. 11. 20. 212
Et divisie omnibus per 4 et ordinatis fit =10. 112. 26. 22 - 4. 10. 12. 20, 21
0
18. 23 10. 22
=4.10.12. 20.22. +10, 113 20.22,  103.11. 20.21. 32
10, 12. 2021
10. 11. 12, 20,21
seu (2) (10.22 - 12. 28) + 18. 2D (1. 22 + n. 21) = 10. 11. 20. 21 (182 22 + 12. 20) =0
12.209
12 = 2100aAX
1 = 2210Xx + 2oaa
20 = 30212 2= 30122Z + 3010aa 22 = 3001 2a 7
10 = 2120
Unde fiet:
voc