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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. 394

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. AL L L L FT ME H FTCA
  2. P RO P. L XII.
  3. Corollarium.
  4. ATque exinde etiam patet methodus ad aequalie Cylindros e Prismata
  5. reducendi Conoeidé a C Pyramidoeidea omnia Paraboliea Parabo-
  6. locidica (non modo qualia memorantur prop. 50, ubi planorum ordinatim-
  7. applicata procedunt juxta rationem simplicis alicujus pocestatis, sed es) etiam
  8. quae aptantur ejusmodi Parabolocidibus, (qualia memorantur prop. 6L.) quo-
  9. rum ordinatim applicatae procedunt juxca rationem seriei alicujus potestatis
  10. composita.
  11. tirempli gracia. Si Parabolocidis ordinatim axplicarae sine in diametrorum ra
  12. tione lubiriplicatae duplicata, (vel suberiplicata duplicacae,) erit iltius planum re-
  13. ctarum series intinica in ratione radieum cubicarum secundanorum: d propterea
  14. Conocides vel Pyramidocides erir leries coridem planorum in carundem rectarum
  15. ratione duplicata, ideoque radicum cubicarum Ouartanorum; _E PTOPterCA (juXIA
  16. tabeltam PrOP. 50.) ad Cylindrum vel Prilma circum seriptum, ut 3 ad-
  17. Trem, si Parabolocidis ordinatim applicarae sine in diametrorum ratione subqua
  18. deuplicatae criplicata; crune plana Conocidis vel Pyramidocidis, in carundem dia
  19. metrorum rarione lubquadeuplicatx sexruplicata, (lire, quod rantundem valer, sub.
  20. suvlicatae criplicata,) ideoque Conocides vel Pyramidoeides illud (ex iltorum pla-
  21. norum serie contlatum) ad Cslindrum ret Prisma circumscripcum, uc + dd 20, ret
  22. 2ad 5.
  23. Et paricer in aliis juxta tenorem Pabellae.
  24. PROP. LXI
  25. Corollarium.
  26. Odem modo; Forundem Semi- Paraboloeidium complementis aptata Conoei-
  27. dea Pgramidoeidea, ad aequalia Cylindros e Prismata reduvuntur.
  28. Exempli Etacia. Si semi paraboloeidis complementum ordinacim applicatas ha.
  29. beac in diamerrorum rarione subduplicatae criplicata, erit planum illud rectarum
  30. series intinira in rarione radicum quadraricarum Cuborum sire Tercianorum, et
  31. proinde Conocides vel Pyramidocides buic aptatum, erie series coridem Plano.
  32. rum in carundem rectarum ratione duplicata, adeoque in diametrorum ratione
  33. subduplicatae sexuplicata (seu, quod cancundem ralet, in diametrorum ratione
  34. triplicata:) exic isitur ad Cylindrum vel Prisma circumleripium, ut 2 ad 8, vel X
  35. ad 4.
  36. Trem, si semi parabolocidis Complementum ordinarim applicatas habeat in dia.
  37. metrorum ratione Luberiplicarae quadcuplicata; erunt plana Conocidis vel Pyrami
  38. docidis in carundem diamerrorum racione subcriplicacae octuxlicata; et PrOpierea
  39. uc radices cribica octaranorum; adeoque Conocides rel Pyramidocides illud, ad
  40. Cylindrum vel Prisma circum (exipEum, ut 3 ad FF.
  41. Let Palitet de aliis judicandum est juxta Pabellam praemistam.
  42. I
  43. PxOD. L.
  44. C 11O L. LVL.
  45. Docuimas ssuur, quo do Parabolae dt Parabolocidea omnia cujuleunque se
  46. peris, e eorum Complementa, ad Parallelogramma: FL corundem Conocidea ee
  47. exramidocidea ad Cylindros e Prismata; reduci poltunt. Adeoque innumera PrO-
  48. blemata solrimus quae nemo (quancum scio) anrea lulcepie, nedum exequutus
  49. Placet autem adhuc ex Fabellis omnibus praecedentibus (ProP. 44, 54, 59.
  50. hocunirertale Theorema collivere, (quod quidem conrenit cum Regula PrOP.
  51. 4V.) Nempe
  52. eAOP

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. 394. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0414?run=74