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. 373

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: 0.85.

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

The machine reads it as

  1. TFLN
  2. lFOD. XI.
  3. Cum enim (proptet aquates angulos) iplae
  4. reCta MT, M V, SC. GInC UL L, 2, 3, 4, ec
  5. (per constructionem Spiralis:) ec propterea Spi
  6. rales MIF, MT, _c. (iltis rectis contermi-
  7. nX) sinc in rectarum ratione duplicata (per
  8. DEOP. TT.) NEMPC UE X, 4, 9, T6, CC. erunE ipIa
  9. legmenta continua, ML, TY, _C. ut 2, 4
  10. 9= 4, 26 - 9, Ouod erat demonstrandum.
  11. SCHOL. ZVM
  12. Foca hac de longicudine linea Spiralis doctrina; continuis quatuordecim pro.
  13. policionibus jam cradica, est, apud Archimedem in libro de lineis Spiralibus, pe-
  14. nicus omitta: Neleio an ab alio quoxiam ex recentioribus tradica tuerit.
  15. e ROP. XIX.
  16. Lemma.
  17. tul
  18. T PrOBON selles Suantitatum in duplicata ratione Arithmetice.
  19. proportionalium, (sire juxta seriem numerorum quadraticorum.)
  20. continue crescentium, à puncto vel o inchoatarum, (Duta UE O, L,
  21. An 9, etC.) propolitum sic inguirere, quam habeat illa rationem ad se.
  22. riem totidem maxima aequalium:
  23. Fiac inrestisacio per modum inductionis, (ut in PTOP. L.) eritque
  24. 0 + X= Y
  25. + F = 21
  26. 0+ F + 4 +0=24
  27. O+ x + 4 =
  28. + + 4 + 4 = 1 2 = 3 f 15.
  29. 9+ 0+ 9+9- 36 18 5 1 15.
  30. 0 ++ + + +9 +26= 30
  31. 26+16 +16. + 56 +26 -808 2 5t 2.
  32. 0 +F + 4 +9 + 16 + 25 = 55
  33. 25 +25 + 25 + 25 =25 + 25 =450 3
  34. 0 f F f 4 + 9 = 16 F25 +36 = Or
  35. 5 + 2
  36. 36 + 36. + 36 + 36 + 36 + 36 + 36 = 352 30 = 3 + i.
  37. Et lic delnceps.
  38. Pacio proveniens est ubique major quam subcripla, seu J. Fxcestus aurem
  39. DErpCTLO dCCTELCIL DTOUL NIMETUS EETINOTUM AUIS CIIE, DUT 53 133. 183 213 263 35, _C
  40. aucto nimirum tractionis denominatore, sire consequente rationis, in lingulis Jo-
  41. eis numero senario, (uE Patet,) ut sic rationis provenientis excettus supra sub.
  42. rriptum, ea quam habet umicas ad sexcuptum numeri cerminorum pote 0. Ad.
  43. coque-
  44. PROP. XZ.
  45. Theorema.
  46. LPoponatur series quamicatum un duplicala satione Arithme
  47. rum) continue crescentium, a puncto vel o inchoatarum; ratio quam
  48. habet illa ad seriem totidem maximae aequalium, subtriplam supera-
  49. bic; exitque excessus, ea ratio quam habet unitas ad sextuplum nu-
  50. meri terminorum post o; sire, quam habet radix quadratica termini
  51. primi pott o, ad sexcuplum radicis quadraticae termini maximi.
  52. A42 3
  53. cice proportionalium (sire juxta seriem numerorum quadratico-
  54. Puta

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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. 373. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0393?run=74