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. 333

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: 0.83.

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

The machine reads it as

  1. PFOP. XXXI.
  2. ON IC IS.
  3. P RO P. XXXI.
  4. De Fllipseos Diametris.
  5. T a puncto quoris a in F.Iip(eoS curra A an ducatur ad Centrum
  6. C recta a C; erit haec ejusdem FMlipseos diameter, cujus rertex
  7. an ejusque Ordinatim applicatae rectae ipsi a P, Ellipsn in puncto a
  8. contingenci, parallela.
  9. Fibet hanc propolicionem (ut prius prop. 24.) pri-
  10. mo Analycice eximinare, deinde et Synthetice demon-
  11. Strarc.
  12. Supponamus igicur rem este ut perhibetur; adeoque
  13. inscripiam quamlibet OO tanSeNE a F paralletam, 2
  14. recta aC (per contactum e cencrum cranleunte) bi-
  15. sectam in A. Sintque rectae OD, OD, a F, diametro
  16. AF. ordinatim applicatae, adeoque invicem parallela
  17. quibus etiam parallela ducatur se eidem diamerro in c
  18. Occurrens quae propterea (ob parallelas) bilecabie (ut
  19. OO in E, lic) DD in c. Denique recta OO, diame.
  20. ErO AF, (VErISque R opuS est productis,) Occurrat in
  21. C. (Salcem si Parallela sic, uE non pOlIE OCCUERerE; reS
  22. ipsa jam demonstrata est, PrOP. 29.
  23. Supponemus etiam imprasentiarum, rercieum A a (dia-
  24. merri AF,) verticem A propiorem, 2 remoriorem, Puncto R: Trem punctume
  25. intra puncta a C incidere: rectamque OO diametro A F producta exera F. Iip-
  26. TIm OcCurrere: Si aurem horum alicui concrarium concinsat, (quod quidem tieri
  27. Docclt) nihilo camen minus res succeder mutatis tancum aliquories lignis. + -
  28. quod operationis prosressum neuciquam curbabit
  29. Dieancur autem (ob commodiorem calculum) F. a = C, P. A = d A a = 1
  30. Ca (= + - 4) = ∞, C C. (= Zt - 4) = C, CD = 9, 2_ = dy 4. C =0726 - d =E
  31. C (=0 - 5
  32. Tum (per praeced.) EC. F. A: : Ba. F. F. hoc est 5. d: : v. = FF. EL
  33. (proprer parallelas, et similia triangula) C a. E9.:: C. F.. CF.. hoc est 0. 5:: c.
  34. E=CF. ELC4. C5:: F. a. Cc: : F F. CC. hoc elt, 0. 7: : e. = c,:: d 7d X
  35. A
  36. = d + de ca = 1 = , ideoque DA (= e A = C D) = d. + = 9, de
  37. D2 =∞ - = = g. EL rectanentum D A L D a =
  38. =0 dg + 205c9 + 05 v0 - 05 dc = s2 02
  39. 2x = 8 9 +2809+20809+2055
  40. 20 - 8 = E
  41. a d -69-2012 16
  42. de
  43. q
  44. +
  45. 2 xq
  46. (vel, Guia X = d = 26
  47. Cvel, quia 0 - 5 = 7, e
  48. Deinde, (quia, propter FIiplin, Ouadrata ordinarim applicacarum sunt rectan.
  49. gulis segmentorum diametri crantrerlae proportionalia) E A X E a = d N. D AXD2
  50. :: Fag = c. D09 = = dx - 89 + 207c9 + 5E6
  51. Trem

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. 333. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0353?run=74