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Leibniz-Handschriften zur Mathematik LH 35, 3 A 31, fol. 5r

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: 0.81.

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The machine reads it as

  1. si
  2. N 1+V = 1+ C y + C. C-1 y + e. C- 1. e 2 y dtc et quolibis termino vocato si erit sepers B = A
  3. 1. 2. 3
  4. Quolobet jam termino appellato A, et l , 0 vel 1 vel 2 vel 3 appellato V, est
  5. es
  6. -36. C. d. . 14 = 997. oppeals. B, B Ed, erit B = yA. C. B, : v+ 1 et C - B. C- v- 1: v+2
  7. Ex priore aequatione est: vB+ B= eA vA. fit v- eA B. A+B ex posteriore vC+ C = BC BV-B
  8. seu v= BC - 2C - B∞. B +C. Ergo A+B: Bt C:: est- B: CB. BriC Hinc si relationem
  9. inter quatuor terminos velimus adhibere possumus tollere ev, et e, et y
  10. rursus si sit 1+ Z = 1 + hZ + h. ha 1 97 + R. h - 1. h- 2 G3 esc et terminos hos appellemus L, M. dtc
  11. 1. 2. 3
  12. 1.2
  13. fiet: M = Z L. e - V,: V + 1
  14. Ergo 1+G in 1+Z = AL + BM etc + AM + B N. et C + GN+ BP dec seu EL +A Mi
  15. B2
  16. in
  17. c
  18. 126
  19. complehendendo sub A_ omnes ubi rescondentes in se se invicem ducuntur, sub AM, omnes ubi i
  20. qui ieono quorum loca unitate differunt sea primus in secundum, secundus in certium, in
  21. Et ita porro. Oi AL t sron aliter hic exprimitur At BM= XyALCBFV
  22. Unde etiam haberi posset relatio inter AL, BM, etc ex quatuor terminis asspintis.
  23. se ducuntur
  24. loco AL smbea possumus AL + AL. Ey 2. E. v. h V
  25. rec beni
  26. AM = 2. AL. 6- B, v11 Z- AL. y. E vAZ . V
  27. LB = y. AL. C- B: vtI.
  28. v+1
  29. AN= ZZ AL. h= hati. v. 11YC BB2,. AL Y9. P. V. E. V. L A
  30. LC = yy AL. E. B. C. v- 1. BH Vst va. h v. h. B 1
  31. AP + LD
  32. (IVAI
  33. = A Jus. e. B. (v. 1. E. v.r +
  34. VE1. 2. B13S Z3. h v. h. B1. h. v
  35. + esc
  36. + dc
  37. + dsc
  38. vt1. V+1
  39. itaque
  40. sine B. + AC + LD + LE dt C 14 e. V eav. ea va1 2, e. v. . P- 1. e. vot dsc: H. sed eo casu si incissimus
  41. AL 3. C- v
  42. v+I
  43. v+ 2. v+ 3.
  44. a primo seu si A et L = 1, et v = 0. redit res 14y = 1+ ey + e. C.) y
  45. 3+2.
  46. Ut 1y et 1+Z per ompendum in se invicem
  47. multiplicemus, considerem, 1B + y + D2 y + 13y + 14 y dtc per 20 + 21 Z + 22 f +238 ec
  48. 1+Y in 14 Z =
  49. fiet: tron y 2 + 1y dtc
  50. 12. 20
  51. 12. 21
  52. 11. 20
  53. Gtacta hor lao 1s 20 - 1.) . e - _ h. t 11. 0 - 1 ) 1x 22 hbot b. 2 11 - h h. B C. 1
  54. 2.2
  55. 13. 20
  56. M100 e 2
  57. Est autem hoc loco 10. 20-1) 10. 21 - er 1t 20 = _)10. gl = h. h. 1. 11. 21 = h. e 12. 20 - C. e-1
  58. 1 21 = h. 1g0= C
  59. 10. 23 = h. h - 1. h- 2.. 14. 22 = C. h. h- 1 12. 21 = 8. 8- 1. 1 19. 20 = 8. C- 1. C- 2.)
  60. 10 22 = h. R=1
  61. 1. 23
  62. 1. 1. 2
  63. 10. 24 = h. hat. h- 2. h. 3 11. 23 = P. h. h - 1. fur 12.22 = c. C- 1. h. h - 1 13. 21 = C. (-1. P- 2. h 14, 20 = 8. (-1. C-2. (-3
  64. . 2. 3.
  65. 1. 1. 2.
  66. P.1.2,3
  67. l. 1. 2. 3
  68. 1. 1. 2. 2
  69. fit ergo: 1 + h y X br. h a1 Y + h. h - 1. her 1,3 h. h - 1. h. 2. b. 3 1
  70. 45 _E.F.
  71. ee
  72. 1. 2. 3.4
  73. ubi videndum an possit relatio inter
  74. e et h, reperiri talis, ut relatio
  75. inter p. Q. A detur
  76. 10. 20 + 10. 21 7 + 14. 2Y
  77. 10- 2279 11. 1y
  78. 2. 3
  79. C. h. h -1
  80. 1. 1. 2
  81. c. 1. H
  82. 1. 1. 2
  83. C. P-1. C-2
  84. 20. 10 y
  85. 1. 2.3
  86. 20. 11 yy
  87. 10. 23. 23 11. 21792 20. 12 y3
  88. el
  89. et
  90. etc
  91. 1. 2. 3. 4
  92. e. h. h- 1. h- 2
  93. 1. 1. 2. 3
  94. C. e 1. h. h- 1
  95. 1. D 2. 2
  96. C. C- 1. C- h
  97. 1. 1. 2.3
  98. (-1. C-2. C-3.
  99. 1. 2. 3.4
  100. 1. 2. 3.4
  101. .
  102. 149. 11X

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 31, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068244:0009?run=74