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Leibniz-Handschriften zur Mathematik LH 35, 3 B 11, fol. 9v

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: 0.90.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 10r); this page is its left half.

The machine reads it as

  1. in progreff Exprissione Denaria 2 - 1 p dibic habet ultimam notam 3, ergo
  2. si per 31 exacte diviti potest, habebit quotiens ultimam notam 3
  3. In Expressione Novenaria 2 -1 habet ultimam notam 0, et 31 novenarie est
  4. 34. Ergo 2 -1 divis. per 31. dabit quotientem cujus ultima nota novenarie est o
  5. Ergo idem quoliens devarid expressus habet ultimam notam 3, et novenarie expressus
  6. habet altimam notam. 0. seu idem numerus quotiers q est ex + 3
  7. et
  8. Denarie sit 2 = t = 3, et 2 - 1, : 9t -. M3 Fiel
  9. D
  10. Resid 3y = h
  11. Rurgus a Resid .. h3 = Ergo h = 6
  12. Rursus Rosid. nA62 = 7 Ergo . H63- 7 seu
  13. K5B dinidi potest per 8. Cergont i. k dividi potest per 8. Barsus t63 = 0
  14. Ergo fit 220 - 1=.. Y63
  15. sed 3s duidi potest peqe B, s
  16. sinos esis
  17. seu. K 63 exacte dividi potest per 7 sed 63 exacte dividi potest, per 7. Ergo rk poterit
  18. urgo et K poterit pacte dividi per 7, sed ilam spacte dividi potest per 8. Ergo _ K = 6 nam monersus
  19. numerus qui tam per 7 quam ser B dividi exacte potest necessario terminatur per 6
  20. Burjus nR63 divisus per 6 relinquet 3. Ergo. K60 exacte dividi potest, u 6.
  21. Ergo et iK exacte dividi potest per 6. Hinc quia.. K exacte dividi potest per 6,7, 8
  22. Sequitur quod exacte dividi possit per productum ex 3,7, 8, seu per 168
  23. in expressione octonaria 2 1 habet ultimam notam 7. Et
  24. 1+ 31 ex primitur per 37. Ergo si dividas 2 - 1 per 31, qua
  25. quotiens octonarie expressus habet ultimam notam 1
  26. in expressione septenaria 2-1 habet ultimam notam 0, et
  27. et 31 exprimitur per 43. Eq quod si 23 - dividatur per 31, quotiens
  28. septenarie exprossus habet ultimam notam o
  29. in expressione seraria 20-1 habet ultimam notam 3, eti
  30. 31 exprimitur per SI. Ergo quo si 370- 1 dividas per 31, quotiens
  31. senane expressas habebit altimam notam, 3
  32. Ia expressione quinaria 230 - 1 habet ultima ia ) 99
  33. si 31 dividas per 4, umerum periddi, restat 7, sed 3tia nota periodi est 4). Ergo si 230-
  34. dividas per 31 quotiens quinanie expressus est 4
  35. itaque si 2 = 1 dividas per 31, quotiens sit 4, et 9 per 10 divisus
  36. do
  37. relinquet 3, per 9 divisus relinquel 0, per 8 divisus reliciquet 7, per 7 divisus
  38. relinquet 0, per 6 divisus relinquet 3, per 5 divisus relinquet 4
  39. - 30 -1 = bxt3~ cg 9c Y Xb + 3 = 9c = Bd +7 = 7ex = 6f + 3-59+ 4
  40. Ergo divisibile per 3. 1t d per 7 et e per 9 et f pM Z e per 3 (1 tandem = 31K

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 11, fol. 9v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068261:0018?run=74