Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 46

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: 0.81.

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

The machine reads it as

  1. +6
  2. P R L N C E P L A
  3. veniat Z ∞ 5. Sic e Situerit Z3 ∞ 125, erit, extraet d utrinque radi-
  4. cecubica, Z ∞ 5. Fadem ratione, (i habeatur ZZWaa- ]- 2 ab. f- bb:
  5. extraeta uerobique radice quadrata, tiet Z ∞a J b. Nec aliter HEA
  6. fueriE ZLWAA L bc- L 2aVbC, erit enim Z∞a L Vbc. Non secus LIEX
  7. Eequetur = + a L V = aa L bb, erit X ∞ V -: a L V = a a- bb
  8. Elis subiunse lequens exemplum, in quo omnes praecedentes
  9. modireductiOniS (IHLOCCUTTUNE. PFOPONAtUF N22 L 3aa, 22 3a_
  10. a2Z
  11. DV.
  12. :quiaisitur eorum, quae aequalia lune, ae qualia quoque
  13. sune quadrata, tec, multiplicando utram que parrem in le quadrate,
  14. 202
  15. 124- 9a+ aZZ
  16. A. Z2
  17. D
  18. . Addatur jam verinque p21 - 9 at
  19. e Tub-
  20. crabiatur cransterendo scilicet ipsas in alteram partem sub
  21. a22
  22. 121- 544
  23. 2Z2 ∞V =. Ouo tacto, multiplicetuF rIESUS uEraque
  24. pars aequationis in se quadrate, ux cranescat sigrum radicale; Ha-
  25. bebiturque = Z +-
  26. a24 aa2t
  27. 24 - 94+
  28. bb D
  29. . EIbI CIUErInqUC dematuE
  30. 27, 2c reliqua partes omnes addendo ac subtrahendo ex una
  31. parce in alteram transterantur, quod tic mutatis tancum signis, crie
  32. a2+ aa 2+ 09+
  33. 6b ∞
  34. . Porroue deleantur tractiones, reducantur
  35. omnestermini ad communem denominatorem 4bb: quo pera-
  36. cto, Puerinque per cundem mulciplicetur, ipsum nempe deno-
  37. minatorem omierendo, obtinebitur 4 ab Z7- 4 a aZ + ∞9 a+ bb.
  38. Dividatur jam ubique pera, hoc est, a ubique deleatur fcque
  39. 4bZ+ 4 a Z+ ∞ 9 a b b: quo Facto, diridatur uEraque ParS Per
  40. 4b = 4 a ut habeatur quantitas Z + ex una parte Cola, crieque
  41. 2+∞ Da3bb
  42. ab - 4a bi (iverobique extrahatur radix quadrata, habe-
  43. e
  44. BITIE ZZ D = abV,
  45. : d Si denuo utrinque extrahatur radix
  46. quadraca, invenietur Z ∞V Z ab V
  47. E quibus patet, reductionem per additionem ee luberactio
  48. n
  49. Pag. 6.

Cite

Ps. 2, fol. 46. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0070?run=74