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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 132v

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 133r); this page is its left half.

The machine reads it as

  1. Sroblema:
  2. Invenire tres numeros, quorum differentiae quadrati;
  3. et differentia quaoratorum etiam quadrat;
  4. 100
  5. 100
  6. Calculus hic est, sit primus numerus a, erit secundus al = X, ita ut differentia eorum
  7. X sit quadratus; et tertius erit al - x - Z, ita ut differentia secundi et tertii t
  8. sit etiam quadratus. Jam etiam differentia primi, et tertii, nempe X + Z1, debet esse
  9. quadratus. Quod ut fiat ponemus + Z et y + 2CZ + C f 1Z Xt 2CX+ C
  10. et erit Z X +Z~ Z + 2C7+ C2
  11. seu XX-C p Z. smatis coet xpro utia
  12. Jam videamus an differentiae quadratorum quoque, sit quadrati possint reddis,
  13. ergo Zal X A 7dl X dC
  14. d vq2al + vV
  15. 21
  16. 1ergo X
  17. ral7 v
  18. 2V
  19. Differentia inter quadratum termini secundi et tertii
  20. (N
  21. neanempe
  22. u
  23. Salt d
  24. 4
  25. --aju
  26. ∞ - 6:
  27. -b4 + 9b =36
  28. 2go n4
  29. a l - 24lX+ X - a l + 2al X + 2alZ = X - 2X L
  30. =2 f
  31. sive 2alZ = = X v7 b- Z4 equalis ciundam quadratoAZ W divisisque omnibus
  32. perfZ habelins positoque W Z + 2fX +f si scilicet differentia inter Z. et f. minor
  33. est, minore ex ipsis; habebimus. 2al -2XV = Z ⊓ - Z +2fZ- fa
  34. Z e 2al + f2
  35. 1 +
  36. -
  37. v
  38. C unde ralc +fC 1 Xf = fc
  39. c
  40. sive
  41. ponendoque, C. B X + g. fet nalX + f + 2alg + f X + fg F, XY - fX = 2Xgf. g7
  42. sive XY = fX, se destuentibus, fiet X = 2 al g = gr f ponendo 29f p 2al + f
  43. 2 al + f - 29f
  44. Restat ultima conditio implenda, ut scilicet differentia inter quadratum primi et
  45. edi tertii, sit quadratus. Ea differentia est.
  46. at- a t +2a lX + 2a(Z - X 4 - 2Xiy v 94.
  47. aequalis quadrato cuidam - Ita rlh
  48. vel 2+42
  49. cuus quadrati, radix lh - X - q, ponendo di eam esse minorem quam X +
  50. afa
  51. im etg
  52. destructis ergo destruendis, fiet +nal X + 2al Z - h + El hX + 2lh Z cumque
  53. Ih sit pure arbitraria, ponatur r la + Im, reformataque aequatione, habebimus
  54. vV
  55. la + l’am + lm r. 2lm X + 2lm
  56. et pro in sumendo D2=
  57. poterit utrobique radix extradi, ac fiet la + LN py X n SX +Z Nam
  58. y
  59. L +X quadratum esse effecimus jam tum supra,
  60. Unde habemus problema
  61. solutum indefinite, ita it trium numerorum quae sive la
  62. fierque la +An
  63. et Z e 2al Ff
  64. 25
  65. C
  66. 2al + f2 2gf
  67. Jam g. et f possut sumi pro artitiio ergo sunt indeterminatae
  68. ergo quem admodum et a, et n
  69. Utergo a, assumi possit pre arbitrio, tantum efficiendum est, ut quadratum ex
  70. Unde
  71. alicuu ex literis, a n. g. f. evanescat: mimirum aequatio haec est
  72. la +an rien al + nfr seralgn - ngf +ng:)
  73. zal + f 29f
  74. - 29fn
  75. 2al + f- 29f
  76. 2al + f 2- 29f.
  77. Epofta 4 e, HX al 4 XsE, in Ergo. ifla + 2fnp e 2n ab e f a. diris
  78. aX
  79. PH s, er f ni ex posteriore egntione D, eor prn D dabit F p 245 tatu
  80. cem
  81. il +2
  82. al 2f 2gse 1g 5., ten ras at 5 4 188, 14 X ral r 87 teo 49 ft
  83. eaque reducta a lf +faltu 3 la + pn - 495 al - 29f n p ad l’nrrabif t entr
  84. + nfa analgf nf9, - 4g fn
  85. Sumtis d, g. f. pro arbitrio, et NX e
  86. Sed brevus satis faciemus,
  87. = 29f
  88. + nC

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 132v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0266?run=74