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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 10r

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.

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The machine reads it as

  1. X
  2. Tabula Binomialis
  3. sit X = a + b. Erit
  4. X - a- b = 0
  5. XX - aa - bb = 2ab
  6. X - a - b3 = 3 ab7
  7. N - at - b = 4 ab XX - 2aa bb
  8. X - a = b = 5abX = SaabbX
  9. X = a - b =6 ab X - 9 aabb. XX + 2a13
  10. X = a - b = 7ab X - 14 aabbX + 7 a b X
  11. 28 - a - b = 8abx - 20 aabex + 16a b xx - 2 a
  12. X = a) - b7 = gab X - 27 aabbX +30ab x - 9ab
  13. Xo - a - bo = 10 abX - 35 aabbx + 50ab x - 25 a6 x + 2 ab
  14. X = a = b = 1abX -Aa abbX +77abX - 55abX +mabx
  15. - a - b2 = 12 abX - 54aabbX +I2abX -105 ab X +36abXX = 2ab
  16. Et ita
  17. porto
  18. quaecungue
  19. Esto jam proposita atequatio quae Tritermina gradus imparis
  20. Tritermina, carens termino secundo
  21. exempli gratia X + hqur
  22. sit sequatio X
  23. sit aqualio X a r XX t sumanti
  24. Ponatur X = arbre et sit ab+ ac + bc = 0 fiet c = -ab:, atb
  25. fiet a+ be XS + sabc XX = a - V+ C = 0 fiat abc= r
  26. et a + b + C L +5, sit at
  27. Z et ab =hv, per
  28. d 1et 6 fiet Hlivo = (13Z
  29. Curjus per 3 et 2 est a + b + r (. k N) = 1
  30. a a + 65 = Z - 5 Z hV + 5Ztlivo = - Y (. k v) + +5
  31. (. -(o: pes) p1o + 5(K: 19) V h 5 (hk: B3) vellivB = - r (:R v ) + F
  32. seu X. k y
  33. HB) V 5h
  34. a v5 p2 V7
  35. = v + V
  36. ab + ac + bE quaerantur et his, quia ab 20 + atbr cx
  37. fiet = (sabC aabbec set ab + a c + b = - 5a b’ c X
  38. ab cct
  39. sit jam a+ b+c = t, fiit a a
  40. si esset abc = r, fieret ab ac + b = r X
  41. et C5 = r X - a b:, a + b = r: ab
  42. +V XX = + t5 Xx = l - a u b5)
  43. tu
  44. = 5 abc
  45. =abrC
  46. r- sabe
  47. arsabe
  48. Hanc aequationem ita divellamus: sit
  49. sit aequalio data X + Y XX = f. faciamus
  50. X = a +b+C sd ab tact be =0 fiet X + Sabc XX = a +b +C
  51. et proinde sollendo es fiet 4hXX + - pex = a = sabeXX
  52. seu XX = t - N, :, r - sabe Aursus est x = ab: 10 abc
  53. ergo xx = qu’ a = t a haec aquatio divellenda in
  54. 100 a b r - 5abc
  55. tres, ita ut s habeantur a ab, et abc et ita
  56. solutio propositae q aequationis est in potestate. idem
  57. eris in cquatione tritermina quacunque
  58. ab + ac + b = ab + E (a rb)
  59. 3b (V, ab) abs = ab
  60. ssarb Pessanb)
  61. atbu v
  62. ab + ac + bc = 0 c = - ab:, a +b,
  63. abc = ab a b: (5) (a +b) - Alb datue, 95
  64. a + b = dato S B et ab: qu () (a + b) -9
  65. qu 1d a +b) = ars Av ab - gabo = v
  66. a 4 a b
  67. a: (rb)
  68. ab = v = 9
  69. Si + sab 2 4idos
  70. de B
  71. 3
  72. 118 a vi9s ib- absiem
  73. ser (1 - 99) ab = ab f + 59
  74. abtactbe = 0 - V
  75. abeZ. ab
  76. Erpo ab = D - 5 a a saitut sitp
  77. Ey. si P =0. fit
  78. Gab. de aabe - 5. ab
  79. BE. al t abe
  80. a b = - 10 ab8X seu p - à b, : 10 ibc
  81. qusà b) r = Sabe qu (a 6) = 10a bE 1 - 1ooabé a
  82. Squ (a. 13 = 19 abet qu (aebJ: abc =- 2 +5
  83. qu. (a b) : abc = = 100 abc. a: r3
  84. igitur 100 abc a = 2 l
  85. a c = - ab :, a +b
  86. qu (ae b + (a + b5) al
  87. () Cat 6)
  88. (r= 3 ab ) 100a V ab, t3
  89. Q sarb))
  90. a1b
  91. F larb)
  92. (at b)
  93. ab ap
  94. atb = V atb - Z ab = W01o
  95. 1+ 3, r - 5u= 100 Wu, 1 - v - v
  96. si arbre. e 10 X +V, YZ. si B 109 10, l5- Y 10
  97. erit arb = t’4
  98. sd
  99. e Fiaib
  100. ~ B t B
  101. beo v = 2- 5101Z +5
  102. 12 rZC mq
  103. pee
  104. d
  105. int
  106. eee
  107. tou

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0019?run=74