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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 182r

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.

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The machine reads it as

  1. quaeritur
  2. si in data serie infinita datur finita relatio, inte perpetuo vera intem
  3. e
  4. terminos vicinos numero finitis videndum an hinc problema reduci possit ad
  5. aequationem finitam x. Idquidem facile si non nisi differentiae
  6. et summae aequationis datae per x potentiam ab X multiplicatae componantu
  7. sed si duae affectiones ab- x, ut si y + dus + xddy faciant 0. saed
  8. si difficilius est negotium si una affectio insius y in aliam multiplicetur. Sic
  9. v.g. si y = - a + 10 A ux + 12 x + 13∞ 414 x, et.
  10. dy =
  11. xddy
  12. 1.H +2. 12X +3.13X +4, 14X3 +5. 15 X ere
  13. 6) 12. 12X+2.3. B3X +3, +.14X3 +4515XY etc
  14. ) E 3
  15. 0
  16. 0
  17. Hinc si ex aequ. 2 et
  18. 3 quaerumus 13 et 14
  19. habebimu eas ex 11
  20. et aequatio illa differet
  21. ab ea qua 14 invenitur ex 12 et 13
  22. quod numeri Nithmetice proportionales crescunt, itaque peraed
  23. tantum pro +ic H 2B scribemus +a B) +XX B
  24. a2. 12 BF3. 13
  25. 11. 2n. 2.3
  26. +nb al20
  27. Tn. n1)b
  28. e-0
  29. .
  30. quod si velimus etiam n tolli ad hibendo sequentem praeterea aequabionem b + (nH) C + (nnrik-0
  31. tollendae n, habebitur aequatio vere generalis inter a, b, c sed contra si detur
  32. relatio inter a, b, c, an licebit vicissum invenire aequationem differentialem. Hoc esset
  33. quod vellem. Sunc si den Nemee si relatio inter a, b, c; plures aut panciore
  34. sit talis, ut a, b, c assurgant ad potentias, videndum an intermiscendo n, liceat
  35. Eivellere aequationem in duas fac simpliciores, in quibus onta, b, c non
  36. it erdunt ad potentiam, ipso n ad eam oscendente sed oportet eas duas esse
  37. similes inter se, ut quemadmodum in uno se habet n, ita in altero se habeatn
  38. hoc modo proprietas differentio differentialis, ex. 9. reducitur ad differentialem, vel
  39. d differentio differentio. differentialis ad differentiotam differentialem.
  40. aeterum si p perprexcora sint omnia si affectiones ipsius y ducantur
  41. invicem,
  42. y = 10 + iX + 12 X + 13 X3 + 14X 1tC
  43. yy = 10.10 + 2.10. 11 X + 2. 10. 12X 2. 10. 13X + 2. 10.14X et Hic perdifficile est, ut efficere
  44. Sane si tullamus
  45. + P. 11. I1. . + 2. 11. 12. 4 2. 11. 13.
  46. = dio + 2IX + 22X + 29X
  47. 0: 15
  48. q
  49. ut relatio sit constans pro
  50. numero terminorum finito
  51. F 1. 12. 12. (in qdidalo pesi relatro sit constans
  52. + 24 XY erc in y
  53. et pro sequente termin
  54. 21 ( 22 = 8. 18. 12 + 1. 2(2: 4. 10 etonegue
  55. sit = 2EF. E
  56. et 23 = 2. 10. 13 = (8. 10, 21. 22 - 1. 213]]:, 510t
  57. seu 23 = 16. 10. 1 + 8. 16. 21. 22 = 1. 213,: 16
  58. et prosequente 13 = B. 102 23-B - 8. 10. 21. 2 + 21: 1b. 10
  59. 24 = 2. 10. 14 + (8. 15t. 21. 23 - 8. 10. 21, 22. + F 213: 1610):
  60. 24 = 32. 10514 + 8. 10, 11023 -9. 15. 21. 21 + 214, : 16. 10
  61. e
  62. Cs 12 et pro sequente termino 14 = 1610524-816+ 21.23+8. 102 21, 22 -21 3
  63. itaquef pro 1d scribam 20. pro 20 scubamus 20. et 10 =20.
  64. gy. = 2010 + 2. 20. 11X + A. 28.12 X + 1646. 13 X 32. 16.14
  65. 1. 20.
  66. + 2421
  67. 4.207
  68. + 9.20. 2. 22
  69. = 2(3
  70. 310
  71. +8.+ 2.23
  72. - 8.2027. 22
  73. 21
  74. 16.20
  75. Ita semper terminus quivis habetur omnibus praecedentibus
  76. sit X=
  77. 10 + 1X + Ve2 X + 13 X
  78. Sit y =. 20 + 2 Y + 22 X + 23 X + 24 (X + 25 X + 25 X
  79. stu
  80. erit
  81. t
  82. peri=
  83. e.. 1.
  84. 10.20 + 18. 21X + 10. 22 X + 10. 25X + 10. 24X + 1.25 X +. 10.26 X
  85. + et ZBX + 11. 21 1. 22 H. 23
  86. 1720
  87. 12.2
  88. ete C
  89. 1. 24
  90. 13. 22
  91. C2
  92. H. 25.
  93. 12 3
  94. e
  95. cu
  96. etc
  97. 30a +. 31 ax + 32aX + 33 ax + 34 a
  98. 1+ap axE + 36aX eC
  99. ponamus dari relationem constantem inter 10, 11, 12 generalem, et similiter inter 20, 21, 2C
  100. et intis similis inter et assumo autem unum ampli
  101. terminum, ut scilicet communem 10; tollam; eodem modo datur ratio constans inter 1. 21, 1122, v. 28, 1.24
  102. dabitur et, inter 10.22 10.23, 10. 24, 10.25
  103. et eodem modo inter 10. , 12. 20 12. 21, IL. 24, 12. 23
  104. Ergo jam comparenti rorp +H. n.2C eum
  105. + 1 1. 22 + 42. 1 =,7 1920 et 1.241 n23 +12= 34 - 1 _ 4. 20. in quibus aegus. consiteremus
  106. considero ob telationes inter i0, 1, 1 possa tolli 12, et inter 22. 21, 20, posse tolli 2
  107. retacta tum
  108. i puc 23, et 24et pan sure
  109. i v 20 21. vdanus deinde ex his postis itaque in valoritu valore)
  110. et hin valore 35 adeade
  111. etc
  112. in
  113. en
  114. Ergo
  115. verte

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 182r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0363?run=74