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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
# Folio 8v, page id 00068241:0016
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 7r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
# Lines: 65 recognised, mean confidence 0.89
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sed ut tollamus ol
 omnino X
Attollemus ad quadrato quadratum
multiplicando aequationem
10 + IX + I2 X + 13X per b+ mx
et 20 + 21X +22 X per a fbXtex
et..
10l + ulx + 12 l X + 13l X
+ 10mX + um X + 12m X + 13 m X
20a + 2IaX + 22 aX
+20bX + 21bX + 22bX
+20CX + 21 CX + 22CX
a aequ = 10l: 20 per 1 C aequ. - 13m: 22. per 5 d g- _l- 10m -
baeq. 11. 20l - 10. 20m + 10. 21 l, : 20. pur 2 b aequ. - 13. 22 l - 12. 22m + 13, 21m,: 22. 2 per 4
fiet:  + 10. 21. 22 - 11. 20. 220 + 13. 2022, l aequ. 13. 28.21 - 12. 2022 + 10. 20. 227m
e
ubi possumus diminuere calculum faciendo vel l aequ. 20. vel m aequ. 22. quorum posterius
eligere placet, itaque sit m aequ. 22. fiet: l aequ 13.2021 - 12. 20. 22 + 10. 20. 22 22
2 10, 21. = 11. 20.4 13, 20.20
10. 22= 112= 13. 20202
(-11. 13. 2021. 22
Superest aequatio 3. nempe 12l + 1 m + 22 a +21 b + 20C aequ. N
=13. 13. 2821
ubi pro l. m. a. b. c. substituendo valores repertos tollendoque fractiones,
fiet: 12. 13. 2020 21 12. 12. 20. 20. 22 + 10. 12. 20. 20. 22
+ 12. 13. 20. 20. 20. 21. 22 = 12. 12. 20. 20. 20. 22. 22 + 10. 12. 20.20. 22. 22.22
= 10. 11. 20. 21. 22. 22. 22 - 11. 11. 20.20. 22. 22. 22 F 11. 13, 20.2020.22. 22
= 10. 13, 20, 30. 21. 22. 21 f 10. 12.20.20. 22. 22.21 =10. 10. 20. 22. 22. 2. 12
(13. 13. 20. 20.20. 21. 21) + (3. 13, 20.20.20.21. 22 = 10. 13. 20. 2021. 22. 22
= 10, 12, 20. 21. 21. 22.21 + 11. 12. 20, 20.21. 22. 22F12. 13. 20. 20.20. 21. 22)
F10. 13. 20. 21. 21. 2122- 11. 1320. 20. 21. 21. 22 13. 13. 20. 20. 20. 21. 21
= 10. 13. 20221. 22.22 + 11. 13. 20. 20. 20. 22. 22 = 13. 13. 20. 26. 20. 20.22
Unde sam sublatis tollendis omnia possunt dividi per 20. 22. Et quidem de 20
poterat praecaveri, jam qua a aequ - 10l: 20. et l in suo valore continet 20 poterat
omitti. At de 22 non potuit quidem tali calculo praecaveri, at poluit tamen
praevideri per generalem naturam regulis mutantarum liberarim. itaque fiet
213. 13, 20. 20. 20 + 12. 13. 20.20. 21
410. 19. 21. 21. 21
1B. 10. 22, 22. 22
Calculus est probus, nam sequente
1r. 133 20. 20. 22
= 11. 13, 20, 21. 21
= 11. 11. 2 20, 22. 22
scheda alia via eundem reperi - 10.12. 21.21. 22
F 10. 11. 21, 22.22
+ 11.12]20.21. 22
(3)10. 13)
aequ. N.
si sigua omnia mutentur hec regula obsera.
l ubicurque et est impori gradu il
est ubi pari ibi est 4
ticum
diatum cogniturum (10. 11. 12. 15) ibi est.
pidetur et sposse hoc aequatio D deduci ex aequ. (11) et (17) utiprima pagina ex
aequationis X aquis a 10 + IIX + 12X aequ. N. et 20 +21 X aequ. 
factum est: 10. 21. 21 = 1120. 21 + 12. 20.20 pro 20 in qua al aequ. N. 
in Ex qua ultima aequatione ut fiat aequ. D. pro 10, 11 12. ponamue 20, 21, 82.
pro 2d, ponamus 13.2020-1120. 22 4 10. 21. 22  (3. 20. 21-12202248.2
et pro21 ponamus 13. 20. 1 - 12. 20. 22410. 2222
et per aequ. 0 etit baequ. - 13. 13. 20. 21 + 12. 13. 20.22 - 10. 13. 2022, 1012. 21. 23 ̸ 11. 12. 20.22 1213 2522og ui aequatione 4  pro 10, 11, 12. ponatur 10.21, 11. 21 +12. 21, et fiet:
et C aequ. D. - 13.
landem:
+(2)1v. 12)
bitur:
aequ. N