Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 425

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: 0.84.

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

The machine reads it as

  1. primana, e in iplis Reliduis si auterantur Subquintana, led e in Ouadraris si au
  2. ferantur Subsecundana; Irem in Tonanis I auterantur Subprimana, _ in ipsis RC
  3. liduis h auferantur Subnonana, sed et in Cubis li auterantur. Sublecundana, e
  4. Ouadraris Ei anterantur Subtertiana: Trem in Oetaranis si auterantur Subsexrana
  5. e Sexranis si auferantur Suboctarana, sed e in Decimanis li altetattu Sugum-
  6. cana, ec in Ouincanis Rauserantur Subdecimana: et sic alibi ur ex tabella patet.
  7. PFOP. CXXNIIT. TNEENETORUM.
  8. Sed _ etiam alias idem aliquando accidie, puca in Super solidis s auterantur Sub.
  9. PROP. CXXXITI
  10. Theorema.
  11. CTexponalue Lelus Flmanorum mulctara serie Secundanorum; Re-
  12. siduorum Ouadrata, Cubin Biguadrata, erc. ad seriem squalium, Fa-
  13. tionem habebunt cognitam.
  14. Pata
  15. Ouadrata
  16. 20
  17. 2bD.
  18. _c. usc
  19. Relidua
  20. dc. usque ac
  21. DD-
  22. ZAD 5
  23. Cubi.
  24. a D = 3a D + 3a D -
  25. pe
  26. 83D3 = 3UD 3b3D -B
  27. BB - 30D F 3B51- ∞
  28. AD - 3 AD f 3AD - 3AD
  29. +3 = 20
  30. C3D3 = 3c4D 2 = 363D -c
  31. ecc. ulque ad
  32. 4X5X6X7 840 140
  33. 30 273 4X5 6x7 140
  34. Ft sic deinceps; continue mulciplicando Numeratores per numeros quadratos.
  35. et denominatores per binos continue sequentes Arichmence proportionales.
  36. 2LL. CaAaIV.
  37. Corollarium.
  38. Deoque; Si series Aiqualium mulctata serie Primanorum respective du
  39. catur in seriem Primanorum: Rectanculorum (aut ipsis aequalium, vel
  40. etiam proportionalium, Quadratorum aut frurarum quarumvis similium)
  41. accreratum, ad accrecatum totidem aequatium, rationem habebunt coenitam.
  42. Aque idem acvidet si Duadrara seriei illius in Quadrata hujus: Lt Cube
  43. illius in Cubos hujus, C3c. respective durantur.
  44. Nempe cadtem prodibune rationes quae in PrOP. praced. Nam si ducatur
  45. D - a 9: D - a: = D - 2a D. + a C: D - a: = D - 3 a D. + 3 a D - a
  46. Fet a D - a
  47. ec.
  48. M a2
  49. in a
  50. a D = 3 a B + 3a D = a
  51. ec
  52. aD - 2 a D + a
  53. ec.

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 425. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0445?run=74