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. 324

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.

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The machine reads it as

  1. DE SECPIONIDUS PFOPXXIV.
  2. Tum substituris (ob commodiorem calculum) idoneis symbolis, elto P a = p.
  3. P A = d. (ideoque per praeced. P L = pC = 2d.) PD = a X = VG = g. (CrSO
  4. DA = P A F DP = a f8.) PD =9. (ideoque D A = D A F PD = 4 + 5 +9.
  5. e DO = pG F PD = 2d
  6. Fric ixitur (Propier Pacabolam) P A. D A:: P ag. DO4. hoc cst d. d + 8
  7. g:: p
  8. S= 2p = D04.
  9. Trem (proprer similia criangula) PF. Pa:: DC. DO. hoc CA 2d. p: : 2 d F, 9.
  10. 2d di
  11. 2d
  12. Lp =DO. FI Cromendo quadlata) 44 L a dq + E p = D04
  13. a + 5Eq
  14. Fireo (mrinque dividendo per pe dt mulciplicando per 4 d2) 4 d + 4. ag + 9
  15. =4 a + 4a8 =4 dg. hoc est (Tublaris utrinque aequalibus) 9= 4 d e. Adeo-
  16. que inventa elt quanciras q. adeoque et puncta D, D, quibus Ordinacim appli.
  17. CantuT DO, DO. Vera isitur est propolitio.
  18. Illud Synthetice sie demonstrabimus, premendo Analyseos vestisia.
  19. Diametro AP ducatur parallela a ∞, per cujus punctum quodvis (intra pa-
  20. rabolam) ducatur recta n G diametro occurrens in C, ee parallela taneenti a F
  21. occurreni diametro in P. Dico an ejuldem Parabolx diametrum elte cique or-
  22. dinacim poni rC.
  23. Digmerro AP ordinatim applicetur à P, eique parallela dueatur xP diametro
  24. occurrens in p. Iic Funto (ymbola P a = p, P A = d. FC == a x = P P = 8
  25. Tum sumantur in diametro utrinque d puncto p, aequales rectae pD = (V 4 d e =)
  26. 2Vd 8. (hoc est, duplum media provorcionalis inter AP, a n, rectas.) acque
  27. punetis D, D, ordinatim. ponantur DO, DO, rectae x C Occurrentes in O, O;
  28. quae cum paralletae linc rectae p, Sicut recta DD (ex constructione) bilcca-
  29. tur in p, erit ideo e OO (propier parallelas) Bilecta iH H.
  30. Rectat ue ostendam rectam illam OO (bisectam in m) Parabola inseriptam
  31. este, (ut an recta bisecans sic diameter,) hoc ett, puncta OO este in Parabola
  32. Curra. Quod Ec probatuE.
  33. 2d. D = DC DD = 2d + 2Vde
  34. applicata puncto P, ad quadracum ordinacim applicacae pugclo D: hoc est d. d + 5
  35. +2Vde:: p
  36. Duncto D.
  37. 8
  38. ZYde
  39. d
  40. P. quod isiur est quadiacum ordinacim applicatae
  41. e1
  42. Sed e camcundem elt quadiacum recta DO. Nam (popter similia triangula)
  43. PF.
  44. Fst pA = P A + PP = d F f. DR = BA =B 18 16. DC = DF
  45. de

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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. 324. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0344?run=74