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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 131r

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: 0.77.

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. 130v); this page is its right half.

The machine reads it as

  1. duorum quorumlibet
  2. Tres numeros invenore, ata ut eorum summae differentiaeque sint quadrati.
  3. tertius
  4. al. secudus al- X sus al -X = Z tertie Cyss. differentia primi 3 secundi erit perua
  5. et tertii Z2. Ut vero et differentia primi et quandi sit quadrata
  6. seu aequalis C + 2cZ + Z et X C = 2CZ. (srvC Z +x+
  7. lam summa primi et secundi ral - X. 5 _. Ed
  8. N +X secund, d- X fertius d x ergo ap d + x. Fiet ergo primus denmus
  9. summa et primi et tertis eut (d - Z BC d co + co
  10. summa secundi et tertus est d = Xt - 72. side e
  11. sive de vel cot + 2c038, y+
  12. 4∞2
  13. vel Ponamus cd HZ. fiet:
  14. sive 47 eFf2 +c2.
  15. fiet primus terminus:
  16. Secundus:
  17. Tertius:
  18. pone 5r1. er c+A
  19. secundus s
  20. f2, 2fV +
  21. a c +2c4
  22. Co + 2C0 + V
  23. 5)+
  24. f= + 2fC2 4c4 + f
  25. fiet:
  26. vim tennirus
  27. L4
  28. 209 + 4) 353
  29. 1 18-
  30. 128
  31. Tertius sad inde sequeretur nihilo minor.
  32. igtur lemendus f talis ut f sit major quam s
  33. sed dem debet esse major per teminum primum. Ergo
  34. quod est impossibile ideo mutanda suppositio
  35. co + 2co G~ + Z
  36. 2c
  37. sed resurmta aequatione
  38. cor
  39. y4 + L
  40. porum ad A e 2. feo t
  41. = = - 2.
  42. 2 C
  43. sive: 8 9u 4 F Z + la TK
  44. 4(2
  45. 12C
  46. , sive Z,
  47. qu
  48. ciec licet ponere conL
  49. F
  50. Mc
  51. L AS
  52. +Z+ 1
  53. 44
  54. e D- c Z 2 225 2
  55. q + nequ ( ) Eit e et s d
  56. pro tf ct Z sume Z. pro A + c + +Z sume co +Z a g, sive
  57. + + E4 1
  58. (4) 200
  59. 4l2 4l
  60. Fe + g.
  61. explicando per E Z fiet = Z + 2 + d sive erit +fc + +Z H E
  62. e. - 9 1 f2. Et cut DEZ e F + 4. Ponanus ess-
  63. fiet ergo: CqZ + ldZ.
  64. e+
  65. F2CZ
  66. e 2 et (+) ese . fiet Z e S + g.
  67. et C C Z 1I L,g. ponendo + f ese t er t F esse, ergo C p g
  68. pn 1 + EZ Z
  69. Explicatis jam terminis fiet prumus: ex + He
  70. Explicemus terminos, ponendoque f H1. et 95 1. fiet Z et 2 Est autem et l71. ++
  71. CH = + F Z CF) ++ GZ+ EZ 4fg siue cy f + + 2( 14 1f fil + x13. 2t +9
  72. Et fier Danius prings. o e 1c + + Z d E 4 +C f a F C 2 G 1 a1 4
  73. Pone Cr 10. fit et + p et crc +. fiet.
  74. Ergo c
  75. substitui ejus valorem
  76. Z potius eliminanda erat
  77. 2 5 2. etc r +2 4 2 +
  78. 10g04e 144 eo 10) 10o =1 sive 37 - 102. et X H 484 8-
  79. . Ergo d e
  80. Jam ergo Terminus priaus:
  81. al primiatsccndio al - X
  82. 10000
  83. ogeoH invod
  84. et Video in eo a ne erralum quod pro X
  85. qui tanen non centenebat characterem formamque quadraticum grtiu
  86. rebus de integro sic assumtis:
  87. al - X - 22
  88. urgo X (2) ∞, C 4 2Z Z. Ego Z
  89. Jam summa (2 al = X H d. Ergo _ a r d +X. Fient ergo: prinus terminus d’+X Secundus d
  90. tertus. d - - Z seu 4 X -X2+ 2XC - e pum et terti smmma: (NC - Ct a reod (
  91. Ergo d pu co2 X+ +2X C- c+
  92. tra
  93. nc
  94. secndi et terti summa; d X ZV siui ;. cot - 2c X 3, 2XC - C+ X 1X8. XC
  95. 1aEC. Ex C+ C. X. L 6 HI H
  96. c 6c2
  97. 7c0.
  98. Ponatur primus
  99. fir sal - ad x + Z. quadata
  100. co +Z s(4) Z
  101. (+ 2C0
  102. sive W 2cZ
  103. eritue des
  104. +03
  105. 10404
  106. non
  107. 256
  108. 289
  109. rona
  110. 1 + 16 Hgit
  111. sive

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 131r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0263?run=74