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. 390

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: 0.92.

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

The machine reads it as

  1. ARLTAMETICA
  2. erop. LIF.
  3. inchoatarum; (puta VO, VF, Y2, Y3, _C. YCO, VCF, VC2, YC3, _c.
  4. V990, rgqF, Ygq2, V9433ec.) Ouas appello series Subsecundano-
  5. rum, Subtertianorum, SubguarEanorum, etc.
  6. Exempli oratia. Si exponantur ejusmodi infinita numero Ouadrata Arichmetiee- pro-
  7. portionalia, lire juxta seriem Primanorum; quibus in Tabella altignatur ratio + ad 2.
  8. Forum Laceribus, (hoc elt, seriei Tubsecundanorum) conveniet ratio E ad L =
  9. (Tire 2 ad 3;) quia F, F3, 2, Tunc Arichmetice proportionalia.
  10. Trem, si supponantur ejulmodi intinii Cubi Arichmetice proporcionales, Cire
  11. juxta seriem Primanorum; quibus conrenit in Pabella, ratio F ad 2: IIlorum
  12. radicibus cubicis, (hoc elt seriei subterrianorum) conveniet ratio X ad F3 (vel
  13. 3 ad 4:) ec harum radicum quadraris, ratio + ad 23 (vel 3 ad 5:) Ouia Lcilicet
  14. F, F5, +3, 2. Tunc Arichmerice proporcionalia; sicur Onicas, radix, quadratum, e
  15. cubus, sunt Geometrice proportionalia.
  16. Ft pari modo, s intinira Biquadrata, Supersolica, dec. constitura intellisantur
  17. juxta leriem Primanorum, quibus convenit ratio F ad 2; eorum radicibus Biqua-
  18. dracicis, Supersolidalibus, ecc. conrenient rationes 4 ad 5, 5 ad 6, ecc. vel 1 ad F7
  19. Zad F= _C. quia nempe F, X2, +4, L3, 2; ieM I, L5, F5, L3, +8, 2; deC. fUINE
  20. Arichmetice proporcionalia. Adeoque.
  21. P ROP. LIV
  22. Theorema.
  23. F incelligatur series intinita quantitatum, a puncto seu o inchoata-
  24. Drum, et continue crelcentium pro ratione Radicum quadraricarum,
  25. cubicarum, biquadraticarum, etc. numerorum Arichmetice proportio-
  26. nalium; (quam appello seriem Subsecundanorum, Subtertianorum. Sub-
  27. quartanorum, 6c.) Frit corius ratio ad seriem cotidem maximx aequa-
  28. lium, ea qua sequitur in hac Tabella: Nempo
  29. Subsecundanorum
  30. Subterrianorum
  31. Subquartanorum
  32. Subguintanorum
  33. Sublextanorum
  34. Subtexcimanorum
  35. Suboctaranorum
  36. Subnonanorum
  37. Subdecimanorum
  38. Lit he dCinCePd.
  39. Patet ex praecedente.
  40. R O P. LV
  41. Corollarium.
  42. RBO Planum semi- parabolae (vel etiam Larabolae) est ad Paralleloeram-
  43. mum circumscriptum, ut 2 ad 3. ( consequenter ipsius complementum
  44. est ad idem L’aralleloerammum ut X ac 3.)
  45. Fst enim Planum Semipara-
  46. Bolae (aur etiam Parabolae) Sc.
  47. ries intinita sublecundanorum
  48. (Der 8 PFOD. COn. Sect.) Pa
  49. rallelosrammum autem leries
  50. coridem maximo aequalium: F r-
  51. 80 illud ad hoc uE L ad x3, vet
  52. ut 2 ad 3. (et, consequenter,
  53. ipsius complementum, nempe
  54. Eata) decamimi reliduum, uc
  55. PKOP.

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. 390. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0410?run=74