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Ad majorem Dei gloriam. Theorema Arithmeticum, fol. 7

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: 0.93.

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

The machine reads it as

  1. Non ergo possibile est inrenire rres numeros primos incer
  2. se, quorum differencix, quadrari, ec differentix quadtato
  3. rum, quadrari.
  4. Sed Aa, b, c, tuerine assignati non primi, accipiatur eorum
  5. maxima communis mensura: gux profecto difterentiarum
  6. a = b, b = C, a =- C, COMMUNIS mentura eA quadratorum,
  7. iplaque quadratus numerus est. Ideo enim a, b, non lunt
  8. primi, quia a, relolutus in primos, re hac hpg, ec brelolutus
  9. in primos, re tiac hps, habent aliquem componentem com-
  10. munem, putahp: ec differentia a - b, est hp g -- hp5: Ouxe
  11. non porest esse quadratus, nisi ec hp, SEquadtatUS, e 9 - 5,
  12. sIE quadracus: alcerum enim sinc alrero non (ufficit. FC CirO
  13. iplorum a, b, c, communis maxima mentura quadeatus, qux
  14. dicaeur h2.
  15. Ec dividaneur a, b, c, per h2, ve hanc primi numeril, m,
  16. n: ec differentia, quadeari a = b, b = c, a = c, dividantur
  17. Per h2, VE Aant l = m, m - n, l = n, paricer quadrari nu-
  18. Mmeri: item a2, b2, c2, diridantur per h4, ve tiane quadraci
  19. l2, m 2, n 2: e differentia quadratorum, quadraci a 2 - b2,
  20. b2 = C2, a2 = c2, diridantur per h4, Ve Aanc l2 = M 2,
  21. m 2= n 2, l2 = n 2, quadraci numeri.
  22. Sed hujusmodi priminumeri l, m, n, alsignari non possunt,
  23. ve ostenlum est: ergo nullomodo poruerunt astignaria, b, c5
  24. quorum differentix a b, b - c, a = c, quadrati; e quorum
  25. differentiae quadratorum a 2 = b2, b2 = C2, a 2 = C2, qu2-
  26. drati. OMare, ec.
  27. LVAN ZDM sic erronea propositi nostri Problematis allata
  28. solutio, quaesiti tres quadrati sequentes indicabunt.
  29. 52357727962243 35097474586243 5755474489249.
  30. Latera 2288168
  31. 1873432
  32. 2399057
  33. Intervallum primi es secundi quadrati est 1725965337600.
  34. cujus quadrata radix est 1313760.
  35. intervallum secundi es tercii quadrati est 2245727030625,
  36. cujus radix 1498575.

Cite

Ad majorem Dei gloriam. Theorema Arithmeticum, fol. 7. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/827668708:0009?run=74