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Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 4r

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: 0.96.

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. 3v); this page is its right half.

The machine reads it as

  1. etiam ad majus minurque pertinens,
  2. nempe ut a, b, f, etc. sint hoc locoquan-
  3. titates positiva necessania est, alioqui
  4. si frat a + b = m non sequitur m eose
  5. majus quam a vel b, ant haic erse par-
  6. tes ipsous m, et si sint membra formu-
  7. lae aqualis ipsi m; nam fieri potert,
  8. ut b suerli gratia) sit revera quanti-
  9. tas negativa aequalis ipsi = d
  10. porito d esse positinam et tunc
  11. a existente positiua pro a + b = m,
  12. fieret a - d = m unde patet a fore
  13. majus quam m, tantum abert, ut pos
  14. sit erse ejum pars
  15. (27). Eteor. Pars est minor toto, vel to-
  16. tum est majus sua parte.
  17. Sit a + b = f, erit a minus quam
  18. f. Nam a aequale est ipri a (per 3)
  19. jam quod aequale ipri a est minus
  20. quam a + b seu quan f. (per 26). Crga
  21. a est minus quam f. 4. c: D
  22. suno, vel ae
  23. (28) Defin. Honogenea conpa-
  24. sunt,
  25. rabilia quorum uniuc quantitas
  26. ab alterius couantitate semel aut
  27. sapius subtrali potest, ut subtra
  28. ctum relinquat nitie aut aliquid
  29. se minus.
  30. tanc
  31. 29) Escor. Duo homogenea cunt aequalia,
  32. si alterum altero nec minus sit nec
  33. majus.
  34. (ex hypoth.)
  35. Nam homogenea sunt, (ergo (per 24)
  36. quantitas unins eorum ab alterius
  37. quantitate semel sbtracta aut reliu-
  38. quit nihil, quo facto erunt aequalia
  39. per u) aut relinqurit aliquid
  40. Se rursus minus vel majus) et id et tunc partiejus a quo subtractio
  41. cujs quantita subtrabitur est facta est, aequale erit, ad (vid. 11.) adeoque
  42. (per 26) erit minus. LE.D.
  43. monuc (per 26) . E. d.
  44. (30) Heor.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 4r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0007?run=73