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Leibniz-Handschriften zur Mathematik LH 35, 15, 2, fol. 5r

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: 0.79.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 4v); this page is its right half.

The machine reads it as

  1. A = 0. Et area =X n = hoc est
  2. Areu his casibus diversimodo extribetur, quatenus computatuur
  3. adiversis finibus, quorum assignatro per hos in ventos
  4. valores arearum facilis est.
  5. Exempl. 3. Sit ordinatim applicata a5
  6. 25 V= + Z2
  7. hoclest, perreductionem ad de bitam formam, vel
  8. a7
  9. b + Z2 Vel a5 4
  10. X1 + b = 2 et erit
  11. in prioris casu d = a 5. 0 = - 2. C = b. f. - 1. n = 1. X = 2
  12. 2
  13. a deog. r-
  14. de; quare eum x non sit numerus
  15. affirmatiuus, procedo ad alterum casum: hic est, d = a5
  16. 7.
  17. e
  18. 1. f= = b. n = - 1. X = 2. ad eoq Y = 3
  19. a5
  20. 6XY + b= 1
  21. BZ. X
  22. = 2.
  23. 2, Seu = - a 5Z + a 5b
  24. et area =Z in Z
  25. 1ZX 2Z
  26. = O
  27. 32
  28. bX. Z
  29. X 3200 hoc est
  30. 30b6 + 296= = 16=Z Y
  31. 10566=Z
  32. .
  33. - 2
  34. -
  35. a5Z + a6,
  36. 62Z ZZ + bZ
  37. Exempluq. sit denique ordinatim applicata.
  38. o
  39. c-3aCC22 + 3aa cZ3 = a3Z7 haec ad formam Regulae
  40. reducta, fit 673YC aZ3
  41. O= 3. e = c. f- - - a. n -
  42. Z
  43. :5C
  44. 56
  45. 2)=
  46. =2aZC a
  47. 5. Indeq est d = b.
  48. 5. X = - 3. r = 2. 5 = 2.
  49. 5. N = Z: et areu = e
  50. =7a, id est -- 30abZ3 + 756c
  51. 28aa
  52. 152 =
  53. XC- a25
  54. X
  55. 7.
  56. Quod si res non successisset in hoc casu, existente r vel frauione vel
  57. numero negatiuo, tunc tentassem alterum casum purgando terminum
  58. =aZ3 in ordinatim applicata a coessiciente 2, hoc est reducendo
  59. ordinalim applicatam ad hanc furmam bZ = i X - a + CZ 3) 7: et seg
  60. in neutro casu fuisset numerus integer et affirmatiuus, conclusitlem
  61. curuum ex earum numers etse quae non possunt geometrice quadrari
  62. nam, quantum animaduerto, haec Regula exhibet infinitit aequa onibus
  63. areas omnium, Geometricam quadraturam admitlentium curvarum,
  64. quarum ordinatim applicatae conseant ex pocestatibus, radicibus, vel
  65. quibus libet dignitatibus binomii cujus cungue.
  66. At quando hujusmodi curua aliqua non potest Geometrice cun
  67. sune ad manaes altia Aeore matae pro compaeratione. suro carmu conscero
  68. a 1ZZ
  69. LC - 2CC22

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 2, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068204:0009?run=74