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. 399

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: 0.91.

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The machine reads it as

  1. PxOD.
  2. at.
  3. INFENLTORUS
  4. P ROP. LXXIV.
  5. Corollarium.
  6. Deoque, Dbi Mcereeatum Indicum serierum invicem respective mulcipti-
  7. catarum idem est, ibi es idem erit Index seriei productae.
  8. Frempli eracia. Si series Terrianorum in seriem Fercianorum, vel series se-
  9. cundanorum in seriem Guartanorum, vel series Primanorum in seriem Ouinca-
  10. norum, vel series Aigualium in seriem Sextanorum, respectire mulLplICeT:
  11. Prodibis series Sexcanorum. Duia nempe in lingulis aggregatum indieum est 6,
  12. (nam 3 f 3 = 2 F 4 = F + 5 = 0 +6=6.) Et Similicer i aliIS.
  13. PR OP. CXXV.
  14. Corellarium.
  15. CI AD B Paralletoerammi rectae omnes DB, in D B rectas Lrianeul.
  16. ADB (aeque alti) respective ducantur; rectaneula produca erunt se-
  17. ries Primanorum, (qualia sunt plana cunei P’arabo-
  18. lici, prop. 2Y. Con. Sect.) pro quibus si substituan
  19. tur totidem Quadrata (vel quaevis aliae fieurae
  20. planae similes) illis aequalia constituetur Pyrami-
  21. doeides Parabolicum: Et eorum Duadratorum (vet
  22. fieurarum similium) latera, vel mediae proportio-
  23. nales inter rectas sie multiplicatas, D consti-
  24. tuent Parabolam, vel Semiparabolam.
  25. (Incellige, A plana illa, vel medix proportionales
  26. quae SIC CErGUNE, SupPOnantur ad rectam aliquam
  27. ita ordinatim Dolica, ux tixurarum consticuendarum na
  28. cura postulat. Ouod et deinceps aliquories incelligen.
  29. dui
  30. Itam, cum rectae Parallelogramimi, sinc series Aqualium, (cujus O;)
  31. recta Prianguli, Teries Primanorum, (cujus index L:) producetur, multioliean-
  32. d0, series irem Primanorum (quid O = P = L,) qualia lunc plana cunei P’arabolici
  33. et Prramidoeidis Parabolici, (per PrOP. 9, II. Cion. Sect.) e mediae proporcio.
  34. pales (seu latera similium planorum) cxune series Subsecundanorum, (quippe ut
  35. Radices quacsariea Primanorum,) quales sunt parabolarum recta Pex PFOP. 8.
  36. Con. Sect.
  37. e ROP. LXXVL
  38. Corollarium.
  39. ADB Latducoani ecta D in
  40. rectas DB semiparabola aeque altae ADB
  41. respective ducantur, rectancula producta e-
  42. runt Series Subsecundanorum; 5 mediae pro-
  43. portionales, Series Subquartanorum, (quales
  44. sunt rectae Paraboloeidis Biquadratici DE.)
  45. Hoc est, Series Aqualium (cujus index 0
  46. in Seriem Sublecundanorum (cujus index Z) re
  47. Spectire ducta efticier Seriem item Sublecunda
  48. norum, (quia = f 0 == Z,) de mediae PrOpOr
  49. tionales (quippe sublecundanorum radićes qua.
  50. dralica) Crune Series Lubguartanorum.

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. 399. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0419?run=74