Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 7r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.84.

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1. Maji 1711
2. Esto sequatio: bX + 1 = gy. quaeritur ejus solutio in integris, porito b est
3. numerum datum, x et y quaesitos, y autem minorem quam b. Detitur autem
4. solutio ea lege, ut dissimulentur factores numeri dati b.
5. Solutio.
6. Cum petatur y esse minorem quam b.
7. ponatur b - Z = y
8. ergo b0- 2bZ +Z8 = ye = bX +
9. Unde bx = b ∞bZ + 72
10. et X = b 2 -2 bZ + Z 2- 1, =b
11. Proinde si Z sit unitas, evanescent + 2 2
12. Atgs ita habetur solutio in integris, quantuscunqu detur D 2 b. Dummodo
13. major quam 2. erit enim b - Z = b - 1 = y
14. C
15. atque ita bX +1 = bZ- 2b. + 1 = 9Z
16. Cujus V. b. 1 = y. a. C. f.
17. Si vero Z assumatur majoi unitate, tunc quoque b datus debet esse majoi
18. ternano, et (ut habeatui solutio in intepris) Z ea cautione sumendum
19. est, ut ejus quadratu unitate minutu (22- 1) dividi possit sine
20. fractione per b.
21. Cstob = 8. Z = 3. erit b - Z = 8 - 3 = 5 = y
22. b= 2bZ + Z Z = ∞5 = yZ
23. b2
24. ZbZ
25. 22
26. 24 =3 =X
27. Hic assumpsimus Z= 3. quia Z 2 - 1 =9 - 1 = 8 dividi potest per b = 8
28. esto rursus b =b. Z = 5. etit b - 2 = 8 - 5 = y = 3
29. 26Z + 221 =
30. Hic Z= 1= 25 1 = 24
31. dividi potest pb = B
32. =X
33. vertatui

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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 7r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0009?run=74