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Leibniz-Handschriften zur Philosophie LH 4, 2, 11, fol. 5v

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. per rationalibus
  2. Aequationum numeralium resolutionem eo reduxi, ut
  3. quaeratur saltem modus inveniendi divibres numeri dati. Hoc
  4. t
  5. ergo jam attentabimus. Sit numerus
  6. E ut 2X +3HF
  7. 238656. Concipiatur
  8. Quod si posset fingi aequatio omnes habens terminos signo + plus
  9. affectos, quae esset divisibilis, si numerus datus esset dosvisibilis,
  10. postemne videtur mihi quaesitum ex jam tunc invensei haberi posse
  11. sed huc non est in potestate
  12. ex pressus dyadice
  13. videtur vera methodus esse, ut tentimus omnes combinationes
  14. X produri potest ex X et X, item x et X; utrumque tentemus
  15. X +bX + cx + dXtC
  16. x+m
  17. CTonXIt CmxxtdmX + em
  18. 4 + Ex bs
  19. x +SX
  20. +2XX +ZX.
  21. gn
  22. e
  23. ponamus nmeros omnes notas esse dixadicas
  24. nempe dvel l
  25. X significat 2
  26. quia B est em, itaque pro e et in sumendi
  27. divisores psiqus D, eritque utrumus = ipsi D
  28. B =1, sed si 6 -0 erit vel e vel m,
  29. vel utrumque 20
  30. quadsi B20 fit f = Z
  31. et eltom =3 quod si
  32. praestat sem si B =0 sumere pro numero
  33. ato ejus dimidium, ut habeatur impar, seu D = 1
  34. jam l= 1 ergo
  35. itaque e=1 = m
  36. fit el = et dia Ergo si Z =.
  37. dm = 0 ergo d-0. Ergo CM = E
  38. ergo C =E et fit b = d E, quod si BB minor E, fit absucdum nec opus progredi
  39. pet non procedit, nec opus progudi. si Z
  40. Ergo vet H si
  41. q= 0 fit d =1; sin Z =1 sit d =d
  42. Sad 8 = 1- f. ergo G = 8
  43. d
  44. itaque 3 d = _ 1. 3 = f-h
  45. 1FC = 23 +9
  46. 1-3 + c= Z+g.
  47. etd = qu a 1b = a tb + 2ab
  48. = et d - 2ed = Z. sed C = 1 ergo d = E
  49. addantur in unum d+ c + ed sit Lrct od red seu 1 - 3 + c + e - ez, sed e = 1
  50. sid e= 1 fit 1+ d - 2d = Z seu d = 1 - 3
  51. b (arb- ab)
  52. fit 2 +C= 28 = LZ + lZ +C considero ut tres quantitates, quarum quaelibet nota
  53. (a +b =
  54. a+ b = ata ( ab addatur C sit a+b- rab - rac- 2bc + habe ssak + be u gc - 2abe abc + abc
  55. dyadica sed a +b +C = a - 2ab + 4 abc
  56. atbrc = ea 1. ab
  57. -2ab - 2abc
  58. tgabe
  59. Hoc calculo non funsset oru
  60. D+ C+ ed = d+ 198 2 2d +C
  61. Ergo 1.3+ 1. 3tC
  62. dabit
  63. fit C = E, trans fertur ad A ( in seqsit d.
  64. prodit C + b + d = E+ b + 1 - 3
  65. seu E+b +1-Z. 2 (E) +E- E( + b - b3)
  66. hn E+b+1-2
  67. i
  68. = 2. 1-3
  69. 4 (1 Z
  70. + 4abc
  71. +4 (1.3)
  72. 1- 23
  73. +2 (1-3)
  74. -2c(17
  75. 158
  76. Ergo
  77. =
  78. bci -2abC
  79. b
  80. 2abc
  81. +ab habe tabe
  82. et fit tandem E = C
  83. et jam in unum addenda
  84. c+ b + 1g+
  85. sit _E+ b + 1-g =
  86. = 2abc
  87. +1-Z+ e+ b
  88. = S_
  89. +2EE, 3+S
  90. 52 +5 + 2E7+2E3
  91. e -2, C. 62. + b -bz + Eb
  92. E+ b - 2E + 2EZ -2b + 2b3 - 2Eb + 4Eb - 4E8 25Z, 31E- 3 +E + 2E3t259
  93. -2Eb - 2E+2536, 2b + 268 +4bE- 46EZ =d
  94. +4(bE - bEZ) F
  95. 1
  96. +4 Eb (1-8
  97. +2bE+ 262 + 2Z -4 b13 - 5 = = fu. 1. 31 E18)
  98. Et b = 18 + Z + - 2EZ , = 1i 8E, F3E+ 75) L 13- 8 -2. big G
  99. seu 1 - E - E - b + 223 + 2b3 + 2Eb - 4 Eb2 = d
  100. =+ 1 -Z- E- b (E+ 3- 2E8
  101. l = 8- 143+E - 2C3
  102. b- 541136E + 2h7
  103. fit
  104. =(4 2(2
  105. s transferendum
  106. continuato ita calculo, oportet ut ubi finitur ultimae aequationes determinent
  107. 4(3 +E- 2E8)
  108. seu b = 1 - 5 + 72.013 - 1 - 6f8E F 230, - 225 8 - 2E38
  109. =B
  110. (2tEY)
  111. in sequeatem
  112. 13+E. 2EG quid possibile. Et itqe pro quolibet gradu fere Calculo instituto semper
  113. +28E+ 8Z- 28E2
  114. P. 2 (2tZ - 228)
  115. 6= (3 +C 23) (g1)
  116. i
  117. Fillet degnire stitum quando numerus produci possit ex dxte et lxam deinde quando
  118. i ob hneri quaesitum Tabulaeque edo possent
  119. ex CXX+ dx +e in lx+m, deinde quando ex bxtcxatdxte, in lx+ m, et ita porro
  120. 2.E+2
  121. Hinc corsitligi pl quando numerus pruducipt in ex (XX+ mXtn in et dxtCxX, vel in e+ DXFCKC+ X vel
  122. nost
  123. in C+ + Cx + a dignotiend
  124. .. sic pervemetur ad regulas generales pro
  125. X+ ClZ +dLXt elX
  126. X)
  127. ct a
  128. a
  129. a
  130. n +
  131. alX3+b
  132. +ar
  133. EAXCZ
  134. ∞BX+)

Cite

Leibniz-Handschriften zur Philosophie LH 4, 2, 11, fol. 5v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068571:0010?run=74