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. 340

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: 0.90.

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The machine reads it as

  1. DE SECTTODEBUS PFOP.XXXV
  2. Inde sequitur; Ouadrata Ordinatim applicatarum Rectangulis Dia-
  3. metro intercepta e agoregato diametrorum trancrerla et intCrCCPLX
  4. comprehensis, esse proportionalia. Sunt enim ubique ut + ad l.
  5. Adeoque, Prout lonsins à rertice remoretur punctum applicatio.
  6. nis, ita semper auxeri Ordinatim applicatas. Nempe quia sic tam d
  7. quam t F a (diameter intercepta, et aggregatum tranlrerlae ex inter-
  8. CeptX) augentur, adeoque e eorum rectangula, et propterca quadrata
  9. Ordinatim applicatarum his rectangulis proportionalia, adeoque et
  10. ipsae Ordinatim applicatae.
  11. Et propterea; FIrverbolam ex earum linearum numero csse, quae A.
  12. suram non claudunt; Cum Ordinatim axplicarx (a verrice inchoan-
  13. d0) Derpetuo crescant, adeoque et crescat crurum diraricatio, qua
  14. idcirco nunquam lunt deinceps coitura.
  15. Ideoque C Fyperbolae diametrum quamlibet non nis in unico Ver-
  16. ticis puncto cidem Eyperbola occurrere; Duoniam nempe crelcen-
  17. tibus continuo Ordinatim applicatis Arverbola curra d dliametro ma-
  18. sis continuo resiliat, nunquam ideo deinceps coitura. Vertices enim
  19. Oppositi, quanquam in eadtem diametro, non tamen lunt in eadem
  20. yperbola, sed in OppOtis.
  21. PROP. XXXVI.
  22. De recta Fsyperbolam contingente.
  23. Ecta HEyperbolam continsens diametro produetae inter verticem
  24. ex CentrII OCCUrreT. Punctum rero concurlus sic inguiremus.
  25. SuDDONAtuE TaNGENS A F OCCUIETeNS, in F, diametro FI A producta, eique Or.
  26. dinatim applicata a FI. Supponatur etiam ubiris cidem diametro Ordinatim ap.
  27. Plicata DO, cansenti Occurrens in T. Sitque A VertEX, C centrum.
  28. Dicancur autem (ob commodiorem calculum) Ha =b, HI A = d, Aa = 1.
  29. (ideoque Ha = + F d, HIC = 35 F a,) FIF =f, HID = a, (ideoque DF =f + a
  30. DA = a = a, Da = 1 = d = a.)
  31. Tum (quia proxier Hyperbolam, quadrata Ordinacim. applicatarum sunt rectan.
  32. gulis AHa proporcionalia, ut modo ostentum cst) erit HI AX H a. D AXD2::
  33. 10g. D0g. hoc est, 1 a. + a. 14. + d + a = 1a = 2da:: B. 2d + d + a = 1at 2 da p
  34. 2d = 2
  35. FF (propter similia criangula) HF. Ha:: DF. DT. hoc cll, f. B: : f F a.
  36. = B = D T. ejusque quactracum
  37. he = DT9
  38. Tum

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. 340. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0360?run=74