Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ad majorem Dei gloriam. Theorema Arithmeticum, fol. 3

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: 0.69.

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

The machine reads it as

  1. bensoben sobesobe ddben
  2. 110 le 6(06106e 6 606O
  3. st os os cto e e
  4. 65
  5. 60 1000 soet den8060 30610de
  6. 6c660606C(6106l0 no 0eeo
  7. l e use esg esg als ess uls eo es ess e ess ils e ese els ess ala plo ese els es d
  8. e
  9. ese
  10. D(O esu Ces∞ (D C)C ((C) () (3 ((C (e)C (0)D (0(∞) (D sC )) C(C) Cet
  11. a
  12. e
  13. C6 4
  14. ose 6 6 6 e e6e 66 6 6 622 6
  15. 6090
  16. ARITIIMETTOOM
  17. Macese
  18. on est posibile, tres inaquales numeros assi-
  19. enare: quorum differentia, tres quadrati;
  20. eg differentiae quadratorum, tres quadrati.
  21. s
  22. e
  23. ne
  24. OSSTBTLE CA enim, duos inaquales nume
  25. 10s allignare, quorum differentia quadrato.
  26. cum, quadracus: ec primum duos, quorum
  27. differentia quadratorum quadratus impai.
  28. ADumatur enim quodcumque Lacusa: e du-
  29. plum lacus 2 a: ex augeatur rnicare, ve hat 2 a F r. APumatux
  30. ejuldem laceris rriansulus a 2F a (2): e quadruplus criangu
  31. LuS2a2F2a: d mulciplicetur per quemdam imparem nume-
  32. rum b, ve Aac 2 a 2 b F2 a b, numerus minor: qui augeatur iplo
  33. impare b, ve frac 2 a 2b F 2 ab Fb, numerus major. FcaTuman-
  34. cur duorum hujusmodi numerorum quadract, 4 a 4 b 2 + 8 a
  35. b2 + 4a 2b2, minor quadratuS; ec 4 a 4 b 2 F8a 3b 2 + 8 a
  36. 2b2t 4 ab 2Fb2, major quadratus: quorum differentia + a
  37. 2b2+ 4 ab 2 + b2, quadratus a radice 2 a b t b: quxe producieur
  38. ex 2 a FF, in b.
  39. Irem possibile est duos assignare numeros, quorum difte-
  40. rentia quadtacorum quadracus PaI.
  41. ANumatur enim quodcumque lacus a: ejusque quadratus
  42. a 2: Qui vnITaTe MINUAEIT, VE AAC a 2 = f: de per quemeum
  43. que numerum b, mulciplicetur; ve fiac productus a 2 b - b.
  44. ex minor numerus: cui addaTUF 2b, PaF, ve AaE majOF nu-
  45. merus a 2b F b. Ouorum AanC quodraEt, a A6Z = 2 a 2 b 2 1
  46. r
  47. A
  48. D
  49. 2
  50. e
  51. A

Cite

Ad majorem Dei gloriam. Theorema Arithmeticum, fol. 3. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/827668708:0005?run=74