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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 129v

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.

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The machine reads it as

  1. sb
  2. 2ab
  3. ne ioventa junu
  4. anferatur tum factu ex duobus numeras non quadritisategris.
  5. C= X+
  6. et X4 d7 fiet e
  7. X F DX, + cd ex
  8. +c
  9. V
  10. ergo 7 cd, et d, a, ilem D naC SI ergo a= a +C
  11. s
  12. unde sequitur CH Hac nc a pi et vel a A e. ergo dejoc pya.
  13. Sed si aurmeri essent in aqualas. i A+ C, et X. +cF d. 1. fie multi
  14. plicando:
  15. ~
  16. + ee X +c
  17. tnc
  18. et habebimus a + cd
  19. Ead
  20. 1
  21. a
  22. 74. Cum Domini a Osannam i_ et d = ME. item id 1 a ∞ E ergos iac - c 54-
  23. Paulo aute communicationem suarum
  24. artium mihi negasset
  25. fiet ergo a H c. Ergo d 0 equare alia ad rem istam consequen
  26. y + c + d, sive y + 2c Y + c
  27. + d
  28. Ergo 2c + d 2b + 2a. sive d 1 2b + 2 a = 2C. Item d B
  29. + cd
  30. 62 29b + a - c
  31. Ergo 2bc+ 2 ac fc YI eb +2ab + a - sumendoque a F1 1, fiet:
  32. 2bc + 2C 2bc - c - b X +a + 2ba = _ 2 ca ergo + b +C FI a + 2b - 2c4
  33. Quae summa ita formanda est, ut inde extrahi queat Radix debetero a, esse quadratus sive fiet
  34. + bl+ ce, 2b a e s et
  35. et
  36. 0
  37. dam methodo opus est, nimorum tentenus pontre y b F, X. Junque
  38. y + c
  39. Quarendus ergo tantum
  40. duorum
  41. est numerus quadratus, compositus ex alio quadrato, et duplicata differentia quorum libet aliorum
  42. numerorum. Ideo loco et, ponamue X + n 2fX + f
  43. conferenda cum X + cgX
  44. fiet
  45. Ergo conferendum cum X + 2h X + h
  46. Ergo h H +f + fl sive
  47. Ergo h
  48. V
  49. ergo
  50. v
  51. s
  52. 2l + b
  53. f~ + 2fl + d.. Ergo f +2fl+
  54. 2
  55. vel
  56. + 2
  57. +2gl -
  58. 2
  59. il
  60. et pro b, ponemus X + g.
  61. Unumque ex numeris ponemus X + g,
  62. aeterum R, fiet 2bXl + 2gC
  63. es - 2cl
  64. I f + 2gl, - 2cl
  65. 2fl + l 5 29l - 2cl sive 2f + l ( 29 - 2c. sue fr 29 - 2c - l
  66. ergo e 1 4g X
  67. et +2bl = 2cl, dabunt
  68. 2xt +2gl- 2cl
  69. 4 2
  70. + 29 - 2c - l X + 497 + 8gc - 4gl + 4c + 4cl + 12 2
  71. ex qua quantitate extrahi radix potest, et quia h B f + l, eris et
  72. h radix quantitatis propositae, et habebimus: +bl+ et
  73. +qx) fagl +4cl
  74. YX + 29 - 2C - l
  75. s
  76. +. 29l
  77. c
  78. 7
  79. 2
  80. X
  81. 9- 2c = l erit radix X +79 + 2c . l +
  82. 2X F29 - 3c- sl 2.g .c. t sive xl Agl + Ac lsi agX 4eX Elx+
  83. et e erit X seu X + f, erit X + 29 - 26 -l resumendoque aequationem
  84. C, fiet +4Xl + agl facl ( et sive 4X
  85. 12 10
  86. ++X + AgX. AcX 3X jamque ponendo 4X +49 -69l+ +C (7 0. sive fX (+) g(+ s)C
  87. batebimus: + (4) gl f (+) 4 cl + 4cl
  88. pro X ponatur Z + m. et ZN (+(9) (+)c sublatis
  89. qu fiet 4Z2 +49- 89c + 4c5 p7 0, omittentur ergo sed ex locis ubi g, vel ex in xdrcuntur orientur quodrata nova, fiet
  90. et loco CX nmp 1t termim examinandi loco 4X + 12gX + 4g = BgC + 4c, habebimus 4m (4) +mg (+) +C (+ )12 gH (+) 12Cg, ubi
  91. et rusus quoedam comescanti purenus es n + _. fet Fncg er Zugn F ang. cstietrem 4)amnspin celi. Sed ita incidumu
  92. t 2
  93. e
  94. pro X substituatur Y + h, fiel

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 129v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0260?run=74