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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 251v

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: 0.83.

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. 250r); this page is its left half.

The machine reads it as

  1. (D sit = D = 1 ab 4 12 abc + 13 abed 14 abede + is abedet
  2. fiet () - D = L, na + 12 ab + 1abe + 12t abed = l, 0, , - 2. 11 ab - 2 12 ab c = 2. 13 abcd - 2. 14 abcde
  3. itaque 0, in 1 - 2- 1 ab - 2. 12 abc - 2. 13 abcd et c debet faciere V a + 12 ab + 13 abc + Ct;
  4. jam C = a - 2 ab + 4 abc - 8 abcd + etc
  5. ( in + 2) = a -r ab + 4 abc - Y abid +1b abide - 32 abcdef + 6+ abedef
  6. in - + D. = = a +, ab 62abe + 4 abcd - gubede + ibabudet
  7. C = a - 2 ab + 4 abc - 8 abcd + 16 abide + 32 abcdef - etc
  8. si sit D = 1 ab + C 12 abc + 13 abed + 14 abcde + 15 abcdeF
  9. 2006 -08 3 -1: 1 24
  10. oportet ut na + 13 ab = 13 abc + 14 abcd + 15 abede + etc. prodeat matiplicando C per 1- 2D, et cum
  11. que
  12. aequatu pademens debent dentica invenientur eo ipso incognitae 11, 12, 13, 14, et.
  13. terminabuntur
  14. Et quia habemus = 1 ab. = 2abe + 2abe +0 abid = 4 abed + 8 abcdes - 8 abidefg +0 abidefyhi + 6 aui-nrantt
  15. o
  16. osd
  17. huno similiter si jam fiat 6 = 2rabe + 23 abed + 2t abide + 25 abidet, etc
  18. habe oportet ut 42 ab +23 abc + 24 abed +25 abide etc prodeat maltiplicando
  19. C = 1a = 2 ab + 4 abc - 8 abed + 16 abc de - 32 abedef + et 6) - 7: l- 50 = 0 - 20D, et 0D = 0 -8; 2
  20. = () 3 = l. 0, L2d (5) 6 = t, O, D, - 20
  21. ael 9 = 82 ab + 23 abe 124 abed + 25 abite + 26 abede f. + 27 abedefy + et (1. 8, l2d t 610 = b gt+
  22. 5 = 33 abc + 34 abid + 35 abide 1 36 abedef + 37 abcdefy +38 abidesgh + eu
  23. = 44 abed + 45 abide + 4bubudeft 47 alidefg+ 48 obuasgh +49 al defghit ea
  24. Prodit 22a +23 ab + 24 abc + 25 abed + 26 abud et etc. multiplicando O per 1- 23, quod at fucerdat invenientur 22, 23, 24. et C
  25. 33 ab +34 abc + 35 abed + 36 abede +37 abidef tet
  26. 3 4 abc + 4g abidta babide t47abedet + 4Y abedesu ea
  27. exc
  28. ex
  29. CD per 1-26 seu 0 - 5V, 4 - 5 invemtntur 33, 39, 35, etc
  30. DS 1 sen L0 - - - 7, per
  31. utea
  32. s
  33. (5) - D,: l (6) - 8, :l (4)- Z.:l (4)- 2, :l
  34. 5u = O per 1 -23 2 = 0D par 1 - 26 8 = 0D6 per 1 - 28 7 =0984 per 1f22
  35. 5V
  36. si 2 =0 fit
  37. O=151 + 23 + 4787
  38. si 4 =1 fit
  39. O = 15 + 22 + 43-8I
  40. et ( + 97 = 15 + 22 +4
  41. si. 2
  42. dD = LO - =5V 4 = C3 - 20D8. fit 6D6 = = CD, 3)8 = 2C - 8- 7
  43. B = 4 - V - =A - 20808 fit 0D64 = 6 - L 5V - + 3 - L B
  44. et eodem modo fiet c2360D68 = 160- 16s - 4 7 = 3 = 7. Et ita porro
  45. 1+. X Ethug
  46. Unde prodibunt theoremata aequationes, quae ut fc succedant incognitae assumtitiae invenientur
  47. quidem talia, ut nunquam nisi duae series in seinbicem ducantur. O= sa
  48. est
  49. S = que 2O, per -8 2 = +cd- de, per C 6
  50. Scribi poterit utique
  51. 8(1- 2) I = 5P+ 2 7r 93
  52. Se = O, per 1 - 2D 3 = +0 - = 5e, per 1- 26 3= =0- + - + 4, per 1 2 8 7 - 20 - 1 5 - 4 7 - 2 3, per 1 - 28 f
  53. S+ = LC per L-D + - 40 + N, per - 8 3 =
  54. Seu 51 = O per 1 - 2D 27 = O - 52, per 1 - 28 43 = 0 - 8 - 22, (er 1 - 28 81 = C - 51 - 2 + - 4 3, per 1 - 2 2 f5t ita pon
  55. g
  56. Quaram aequationum ope, ut fiant identica, lite qcoefficientes assumtitii determinabuntur, qui simul reperiuatur in N et 2,
  57. item in 6 et , in Q et 3, in 2 et T; nemper per pimam harum determinatia aequationum determinabuntur
  58. coefficientes 22, 23, 24 etc pro Columna 2da; per secundam 33,3435, etct pro columna 3tia; et ita porro
  59. sed et aliter rem tautemus hoc modo: + - 6D, 26 (2 - 4,:l seu 7 = 0d84, 1- 2+, C+
  60. A(4) - Z, :l sen 5 = 038, 1 - 8, et fiet 036 = 3 3:, 1 - = 2: 7(.- 21) seu
  61. 9, 104, :, 1=24 = 7: 3. sed quia quadratum ab 1- 24, itemue ab 1 - 28 est 1, ideo
  62. quadrando utrobiu fit = 77: B3. ubi notandum est 77 non esse = 2,, nec 33 esse = B
  63. fiet
  64. nec habent, semper
  65. netae dus adjue Fer alia
  66. hotamum diut eyadicarum, possunt
  67. genotae dyadicae
  68. quia et quia C S, , X, 7, etc. non suit
  69. latus aequale quadrato, cum enim sint differentiae duatum
  70. Eodem mobo dehebit esse C = quia (∞) - 6,. l = 1. fiet
  71. ses sest: 1 = O seu ses = (1) - C vocemus 2 fiet O = 505: 2d.
  72. esse 0 vel L vel - 1
  73. investigemus jam quid sit 2. quia C = a - 2 ab + 4 abe - 8abed, ete fiet (6) - C = l, 1 - 24. + 4 ab - 8abe + CH
  74. Et 0) = l, 1 -2 Ergo (6) - O, :l seu 2 = 1 - 26, et firt C = S2S :, qu (1 - 20)
  75. sed qu. (1 - 213) = 1, et constat ergo fiet tandem Se se = C
  76. Tentemus experimento: L D = 1ab =- 2abc +habe +3 abeo = 4 abede + 8 abcd ef - abedesg +0 abcdefyh
  77. tonteo experianum in fit X = 1a - 2 ab + 2 abe +0 abc - 4. abid + 8 abede - 8 abidef +o abcdesu
  78. Ex Experianum in simplicissimo, ubi solum a, fit sus = C nam 1.1. aa = 1a. pugpedianum ad b, et fiet
  79. As = 1a + 2ab + 4 ab = 1 a = 2ab sit X 22 a +27 ab + 24 abc distamuus in his tri sistamus in D, et
  80. V 1a - 2ab+ Tali dat. 8
  81. +R. 22. 23 ab +6. 22. 23 abc _
  82. 16. 3. 4 abc et 22. 24 abea
  83. oasit. - d aib et qui,
  84. et quadremus prodibit 22. 22a +,
  85. L 16 cy abc + 9. 22. 25 abco
  86. fit 22 = 1. Hic ob ab sit 2 + 4. 274 23. 23 = -2
  87. seu 23. 23+ 4. 23 +4 = -2+2 Et 23 + 2 =0 sen 23 = -2
  88. ob abe fit - 12 + 6. 34 + 24 - 12. 24 +24. 24 = 4. seu fiet
  89. 24. 24 - 6. 24 + 9 = 1 seu 24 - 3 = - 1 sin 24 = _ 2
  90. + 1. 23. 23 ab + 6. 23. 13abe + 6. 23. 23 abid
  91. +6. 33. 24 abc + 24. 23. 14 abe
  92. + 12. 23. 35 abca
  93. F1. 24. 24 abC + 12. 24. 24 abc
  94. + g. 24. 25 abcd
  95. +G. isusabio

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 251v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0502?run=74