Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Ps. 1], fol. 137

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: 0.78.

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

The machine reads it as

  1. uation
  2. uM
  3. et
  4. 10, e
  5. Omne
  6. eTITUT.
  7. Fet
  8. qui
  9. sulin
  10. Xqual
  11. ention
  12. ellio
  13. sumpe
  14. I5 b ene
  15. arUI
  16. Itera
  17. tam le
  18. CaM.
  19. 0
  20. 11
  21. Ol
  22. N. O F A B R E Y F 5.
  23. tocum per 27, Orietur y3 = = cy7 L 3 d dy . - b3∞0. OUX
  24. aquatio quoque inrenietur, liprocedamus juxca hujus Geome-
  25. erix Mechodum: Subrogando nimirumr in xe quatione proxolica,
  26. quadratum ejusyy, ee iplius cubum y 3, in locum x, quadratix, de
  27. Cubix3: _ diridendo deinde sCCundUIM TerINUI PerZ, terrium
  28. perhujus quadracum 9, e quartum per iplius cubum 27. Fadem
  29. demonstratio locum obtinet, li in ae quatione radix incognica plu-
  30. res dimentionestrabuerit.
  31. AD P ACL N AM 79, ee sequentes.
  32. D ROPONAtIEK+ X L P ~2 F qX- r ~ O, dE SuPPOnatuF juXLZ
  33. Pexe Ccripeu hujuS GCOICETIK X ? f y X E y + =P-
  34. , O, ericquex = ; yy = =P3 2 = y x, ac proinde quadra-
  35. cum unius partis aequale quadrato parris alterius, hoc est, x +:
  36. 7Y X X F =y + pX + pyy = = PB∞
  37. 472 = 9V y y X de
  38. consequenter x + + y + + P x + = Pyy + = PP + 4 ∞
  39. Exr. ∞0. Ex qua aquatione (i collatur priima X + X - = p X X - = 9X
  40. r∞o, relinquetur = y+ F = P9 + pp. + r - 2 ∞0. Vn-
  41. demulciplicando torum per +y7, exlursetys L py t. L p2
  42. 9900. Ouod erat demonstrandum.
  43. F. Ar 73
  44. Fadem rarione demonstratio het secundum omnes rariationes
  45. lignorum ee =, atque obserrationes in hac Geometria expo-
  46. lcas. In cujus rei exemplum duorum adhuc lequentium casuum
  47. demonstrationem subjiciemus.
  48. Sit aequatio propolita x + X = p X - F q X = Y ∞ 0. Si er3O
  49. juxcatiane Geomeeriam luppoluerimus v + y x f = y - =p
  50. ∞0, habebimus x 2 - Lyy - = P∞ 2 = y x. Vnde d qua
  51. dratum unius partis aequale erit quadrato alterius partis, hoc eAt,
  52. ∞E f 99 N + =gt - px - = py y - + = PP ∞ Q - 4V - + y9 ∞ X
  53. Ec per consequens n + - Lg + P X X - = P y y + =pp. + 9V
  54. 2
  55. 30. E. qua si auteratur prima x + + = P X N L qN = Y ∞0.
  56. relin-

Cite

[Ps. 1], fol. 137. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175905688X:0159?run=74