Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 320

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: 0.84.

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The machine reads it as

  1. 320
  2. F L E NI. C U R Y A R A M
  3. haereat Fractio, crune lacera tranlversum et rectum sibi inricem
  4. aequalia. AC vero politis la sina qualibus, erit ratio lateris eran-
  5. verli ad rectum ut l ad g.
  6. Si enim descripea incelligatur praedicta FIrperbola per pun-
  7. ctum C in veraque diametro versus Z e versis B respectire; lup-
  8. ponatur que eandem secare rectam Z E, qua ducta lic ip(I AB ~-
  9. quidistans, ue de iplam B L, ad dictas diametros respectire ordi-
  10. natim applicatas, in puncto F: erit
  11. FX ∞ y + 5,
  12. C X ∞ y - f,
  13. FB∞X L f.
  14. C B∞N -f;
  15. ideoque rectangulum
  16. FZC ∞ yy - fF, de FBC ∞~N -ff.
  17. Cum autem lacere recto ipsi crantrerlo aequali existente re-
  18. per ropri Clangulum FX C = SIE ∞ quadratO ex Z F seu A B, hoc CA, X X;
  19. icemque rectangulum FB C (ic ∞ quadrato ex BF, hoc ell, yy:
  20. exit py = ff∞ Xa, hoc eAt, Yy ∞ X X L ff itemque
  21. X X - ff∞ yy, EIYCy y DXX -fs.
  22. Sed cum secus recto latere ips erantverso inaequali existente
  23. unius ad alterum ratio lit, ue l ad e; Cimiliter que etiam ratio re-
  24. ctanguli FX C ad quadratum X F, aut rectanguli FB C ad qua-
  25. dracum BF cadem sIC 2, quae trantrersi laceris ad rectum, hoc
  26. pruci hujus. est, eadem quxe lad8: exit ur lad 8, IFa yy = ff ad Xx; icemque
  27. uE l ad 8, Ita X X = fFad yy. hoc est, reduetâ proportione ad a-
  28. qualicatem, eric lX N ∞ 8yy -8FF, ut ec lyy ∞ 8XX sFf. unde
  29. Xe X
  30. dirilis omnibus pers, tc-- ∞yy- ff, hoc est, yy ∞
  31. e ∞ x x =ff. Ouod demonstrandum erat.
  32. X _ +ff.
  33. Ac si quantitacum incognitarum primo conceptarum un d ex
  34. aequatione sublatâ, aliaque in ejuldem locum juxta Regulam a(-
  35. Cumpea, aequatio (IF
  36. l2Z
  37. y
  38. IaX
  39. L
  40. + ff (id CA, ZZ-- ff ∞
  41. lXe X
  42. D. vel
  43. D XX -ff: auc Z auMPEa CxIF pIO y 86, vel PrOY 8 =, aUI
  44. 8. T. PrOy 8 = 8 6. Et quidem primo (iZ altumpea sic proy 8c, du-
  45. cenda est per punetum A recta A D ip(I B F. parallela _ ∞C; ita
  46. uc, (1Z Fuerit altumpea pro y -c, praedictum punctum D cadat
  47. ab eadem parte linea AB, qua dacus vel conceptus est angulus
  48. ABF. Sin contra Z fuerie allumpea pro y. +6, idem illud pun-
  49. ctum
  50. ni hujus.
  51. Per 10
  52. Casus 2dus,
  53. cum LocuS
  54. est H) per
  55. b0la.

Cite

Ps. 2, fol. 320. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0344?run=74