Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[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. 307

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.

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

The machine reads it as

  1. PFOP. IX.
  2. a O e L C 1, 5
  3. inter ipsas ordinatim. applicatas et verticem in-
  4. TCrCePEIS, P A, D A, _C.) aequalia quippe re-
  5. Ctansulis BPS, BDS, _C. Qua PrOPteI aqua-
  6. les PS, DS, ec. (in parallelogrammo APSS)
  7. Tune aeque alta, et propterea basibus (PB, DB,
  8. ec.) proportionalia.
  9. Adcoque ipsae ordinarim applicatae sune in
  10. subduplicata ratione Diametrorum intercepta-
  11. rum; nempe in subduplicata ratione Tuorum
  12. Quadratorum.
  13. Si isitur ordinatim applicatae quotlibet aequa-
  14. libus ab inricem distantiis CIANEUT; CrunE cacum quadrata in COn-
  15. tinua progrectione Arithmetica, (ut patet ex dictis ad PrOP. 2.)
  16. Constabit isituT (PeF PEOP. L.) Semiparabola planum (adeoque et
  17. torius Parabola) ex infinicis numero lateribus quadratorum Ariitime.
  18. tice proxortionalium.
  19. PROP. IX.
  20. De Converde, Cs Pyramidoerde Lalabolo.
  21. A
  22. A quadratis, ad communem axem ordinatim posicis, Formetur Py-
  23. ramidoeides Parabolicum (eo modo quo ProP. 5, 6. Formarimus Pyra-
  24. midem e Conum,) erit illud infinitorum numero planorum Rrittime
  25. tice pro portionalium aegregacum, (sicut Friansulum rectarum,) ab
  26. o incipiendo ex continue progrediendo ad butin usque
  27. TInc sequitur; Si ex omnium in Parabola ordinatim applicatarum
  28. Adeoque si Basis tigura lic conttructa in lemistem Alticudinis du-
  29. catur, prodibit corius figurae soliditas: (eodem argumento quo us
  30. Tumus de triansulo PFOP. 3.)
  31. Cumque idem (eodem argumento) raleat de circulis, aliitre Rou-
  32. ris planis similibus quibuscunque, (sunc enim ad inricem, ut diame
  33. Erorum, vel rectarum quarumlibet limiliter ductarum, quadrata;) erit
  34. univerlaliter Conoeides vel Pyramidoeides Parabolicum, quacunque bale,
  35. (sire etiam crectum sic, sive scalenum, sive etiam quocunque modo
  36. luxacum, per ea quae dicta TunC Pr. 4.) aequale basi in semissem altitu-
  37. dinis ductae; hoc ett, Semissis Prismatis (ul parallelogrammi Priansu
  38. lum) super eadem basi aeque. alti.
  39. Fsenim (ex dictis) Pyramidoeides Parabolicum (Fub quo et Conoei-
  40. des comprehiendo) Asoregacum planorum similium numero intinito-
  41. rum Ariclumerice proporcionalium (ab 0 continue proerediendo,)
  42. Circa

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. 307. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0327?run=74