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Leibniz-Handschriften zur Mathematik LH 35, 3 A 27, fol. 7v

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: 0.69.

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. 8r); this page is its left half.

The machine reads it as

  1. Ut ex his vel aliquam saltem novam
  2. consideremus ab A + 2od eaco
  3. u
  4. co +a
  5. determinationem traham
  6. a
  7. . 4
  8. et 2a l. p B debetesse ponendo d 1.
  9. 1d2+ aY
  10. aqua debet esse L - 1. aequalis quadrato, ponendoque
  11. deber esse fier:
  12. 1
  13. NpEAd
  14. non quadratus et
  15. Ata
  16. C
  17. H m
  18. e uedu
  19. UD ergo numerus datus nuos quadratos dividi possit, non esst necesse ut
  20. jum habeantur duo numeri quadrati in quos dividi possit; ad alios inveniendo,
  21. sed sufficit eum dividi posse nis atres quantitates quarum numeros ex
  22. quibus duo suit quadrati, vertius vero sit one u numerus rectanguli
  23. Tub duobus quadratorum lateribus multiplem peranierum quotiens per numerum
  24. cnus quadratum unitate diminutum relinquit quadracum
  25. Hideamus anseliceat facere
  26. fiet
  27. e2 + rest +ucf 1p7 ab.
  28. et + re R + A2
  29. +2e f
  30. +24f0
  31. +
  32. 2
  33. 1I abat A2 +2Af ef
  34. ma um.
  35. et e + A + f Y) V ab + A
  36. a + 2Af + fr
  37. + 21f
  38. t
  39. V
  40. e
  41. HI H. . A + n
  42. 12An + n2 et A A
  43. 11
  44. v 1
  45. n-
  46. e
  47. 2
  48. f :
  49. sed quoniam haec ipserenda un aequ 3. hiniccusu non sunt
  50. + V 1
  51. c - Z2 b 0.ponendo e
  52. X. y aZ. v. b. c esse integros
  53. 2
  54. 2
  55. Ergo X vC divisibile per 2 seu et H Z ad ergo B1G. ergo C ∞to
  56. et yrgec H v a e. ergo quadrato est autem c. datus
  57. t
  58. porro ponatur Cr b + f frecti
  59. .
  60. v
  61. 2
  62. +27coV b + 27cov
  63. corv b + corvt
  64. e X1Z+ co, fiei
  65. e
  66. b
  67. quod si jam vf + SC +yf posset fieri pro. seu exd
  68. seu 8 v
  69. mus quaesitum
  70. s
  71. vesi 1
  72. ∞+ I
  73. solvi posse generaliter si f4 F posset sumi pro aibitrio
  74. sit X
  75. 2
  76. e
  77. integro si c non sit quadratis poterit nec d esse quadratus Resolvatur 3.
  78. a
  79. in suosi pro e none SZ pro v, pone multiplo poters
  80. mempe Z1 Ysf. ert X F (~S ) m vH (Y5+) n.
  81. a, i ouins anter un triperes e, st nti, ves et
  82. si c ponatur esse numerus primus, reliaquemus:
  83. aneoque
  84. um

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 27, fol. 7v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068240:0014?run=74