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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. 411

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. lroP. Cit L1.
  2. jus index = 2; prodibie series Primanis recipro.
  3. Ca, Cujus index -- L = - 2 + F; nemPC =- 2
  4. minus = +
  5. Trem, S Series Primanis reciproca, cujus in-
  6. dex - 2, dividat seriem Secundanorum, cujus
  7. index 2; prodibit series Percianorum, cujus in-
  8. dex 3 = 2 7 T, nempe 2. minuS = L.
  9. Trem (i seriem Primanis reciprocam, cujus index =x, dividat series Secundano.
  10. rum, cujus index 2; prodibir leries Z ercianis reciproca, cujus index = 3
  11. 29 nempe == + mInUS 2.
  12. Arque idem concinget, in aliis quibutris hujusmodi seriebus. Adeoque constac
  13. Propolicum.
  14. PROP. CVT
  15. Corollarium.
  16. TprOPterCa; Si ad hujusmodi ficuram AD Bd3 (ex una parte in infi-
  17. nitum productam) juxta quameunque seriem reciprocam, aptetur (eo
  18. modo quo 9 Prop. Con. Sect. C alibi supra ostendi:) Pyramidoeides vel Co-
  19. noeides inversum, (seu potius Calatoeides:) habebit illud ad Cylindrum aut
  20. Prisma inscriptum (super eadem basi aeque altum) eam rationem, sive fini-
  21. tam sive infsinitum sive plusquam insinitam, quam praecedentia Theoremata do-
  22. cebuni.
  23. Puta si planum sic rectarum series Subtertianis reciproca, cS index -
  24. adeoque ratio quam habet ad parallelosrammum inscriptum (Per PTOP. 64, e
  25. 202) ut F ad 3 (= - 5 ] X) hoc cE, uI:
  26. ad 2: Colidum ex cocidem planis constans in
  27. rectarum carum ratione duplicara, erit series
  28. Ouadratis Tubtertianorum reciproca, cujus in-
  29. dex (Per PFOP. 106.)
  30. DluS =5, _ ratio illius Colidi ad inscriptum
  31. eslindrum vel prilma (Cuper eadem bali aque.
  32. alium ) uc 2 ad 5 =
  33. F E, vel uc 3 ad
  34. utrobique ratio tinita. Per prop. 64 X202.
  35. Si planum, sc Series Sublecundanis recipro-
  36. ea, cujus index - 3, adeoque ratio iptius ad
  37. Parallelogrammum inseriprum ut 12d= =
  38. Solidum ex cocidem planis in rectarum ratione duplicata coultans, erit series Oua-
  39. dratis Sublecundanorum reciproca, vel
  40. (quod cancundem valet) leries Prima-
  41. nis reciproca, cujus index - 3, vel-
  42. Ideoque ratio hujus folidi
  43. ad Cylindrum vel Prilma (super eadem
  44. basi aeque aleum) ut F ad = L F F =0
  45. (DeT PFOP, T03.) Nempe illic ratio tinita,
  46. hic simpliciter infinita.
  47. Si planum sic series Ouadraris Subter.
  48. tianorum reciproca, cujus index
  49. ejusque racio ad Parallelogrammum in-
  50. Seripeum ut F 2d3 =- 3 F F, vel ut 3
  51. ad T. (PeF PEOD. 102.) toluum ex planis cotidem in rectarum illarum duplicala
  52. ratione constans, erit series Bignadratis Subtertianorum reciproca, cujus index
  53. Ee propterea rario ipsius ad inseripcum Cylindrum vel Prisma su-
  54. per eadem tasi aeque alcum ut 2 ad = 3 f 1 = - 3, vel ut 3 ad = + (Dex PFOP.
  55. 204.) Nempe illic rario finica, hic plulquam intinita
  56. Si planum Cir series Primanis reciproca, cujus index = +, adeoque ratio quam
  57. habet ad Parallelogrammum inscripcum ut r ad - c F F = O: (per PFOP. 1O3.) 50-
  58. lidum ex planis in rectarum illarum ratione duplicata constans, erir leries dua-
  59. draris Primanorum (hoc elt, Secuncanis) recipioca, cujus index = 2, e proprerea
  60. ratio
  61. INETNETORUK
  62. Vet
  63. PTOP. 1O2,

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. 411. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0431?run=74