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Leibniz-Handschriften zur Mathematik LH 35, 6, 26, fol. 8r

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: 0.75.

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. 9v); this page is its right half.

The machine reads it as

  1. Quaeritur SEaxYD. Hoc ut tentemus consideretur differentia ipsius OY.
  2. 1 e2
  3. _ jam d (0Y1 =, d0 H + Od (VB) jam d(83) = d yli e = C 91-e,. 8. d D = e
  4. Ergo d3 4
  5. d 83 = d8D. itaque d (OYD) = d0 1 + 88 des
  6. Itaque opor ut evitetur fractio fiat C = efD. Eritque ed (7) YD) - (ebdD + DdY + 43D) e
  7. ((e+ 1) 4 d + eDd8) VD. Hoc debet aequari ipsi QdxV D + 2 dx VD posito esse
  8. F et d esse data, sed _ et 4, esse quaesita, et quidem E esse simpl 2 esse simplicius.
  9. ipso quando id fieri potest. Ita saltem propoQt padritura proposita reducebur
  10. ad simpliciorem. sit e gradus a, et D gradus B et E gradus Y, et 2 gradus S.
  11. As est gradus dD est gradus proxime infra gradum ippius D. itaque dD est gradus β-1
  12. 8d) est gredus 1+ β=1 et D dB est gradus β+) -
  13. porro aequationibus compora
  14. titsis opus est I, adeoque et solidem arbitrariis literis. dut Hinc aequationibus
  15. comparatitiis oposest +β. Quod si ponanus β3+V -1 = a Eri Y = a - 3+ 1
  16. et aequationious comparatitiis opos est 2+1, sed arbitrarias habm literas ob 8
  17. habemus )+1 seu a- β+ 2, re supersunt ergo adhuc quaerendae tol
  18. quol prodeunt et ob 2 habemus d + 1 ergo habemas arbitrarias literas
  19. a = (+6+ 3 quae debent esse a + 1 ergo fict CBS = β - 2
  20. saeterum haec vera siil etsi gradum aestimemus non
  21. sit ergo .
  22. tantum ab uner n exponente maxima potestatis, sed etiam si aesti–
  23. memus ab excessu maximae poteslatis uara infimamo, seu a numero ter
  24. us
  25. pincrum demto infimo, computatis intermedius etsi non adessent. Uende sequitur
  26. pro 4 diversas formulas posse assumi modo esuiedem numeri terminorum. Et haec
  27. locum habere etiamsi exponentes graduum sint negativi, sec si inter terminos artlie
  28. geomeliice desen decrescentes computentur X, X, etc
  29. sit D = 10X Q = reX 10 + 11X + 12 XX L. 13, X r 14X + 15X et = 20 + 2XFyN V
  30. et fist 8 = 3 +31X + 32XX + 33X et 4 = 40 + 41X, et fiet:
  31. et 1, 1, 21.30 + 21. 3X + 21. 32XI + 21. 33X
  32. 2230 22. 31
  33. 23.30
  34. 21.3 2. 31
  35. 2. 32
  36. 21. 32
  37. 20.33
  38. 22.32
  39. F22. 33X
  40. 2331 23. 32
  41. 23.311
  42. 22132
  43. 21. 33
  44. reruo
  45. 23.32
  46. 22. 35. 21
  47. 25.33X
  48. 3.1
  49. 33= 15: (e + 33
  50. C (te3C)
  51. 32 =14 - 215, 2(e117) 13C - 5et
  52. 312
  53. inier, se
  54. 3(et 1) +2C, 23 L5et1)2)
  55. (6CH1) 14. 23 - (eF 1) 15. 22
  56. Set1, 6e+3. 23.23,15.
  57. 15. 21 1ber1) 4. n et
  58. 3(et 1)23. 3 (er1), (eu) 23
  59. 3e
  60. 3 3C 3C
  61. si
  62. 20. 31
  63. H1 X
  64. C.d
  65. 12XX
  66. de
  67. (e+
  68. le
  69. e i
  70. seu 3
  71. 15X
  72. de n 3 =83-
  73. 3x - 14 ler) 14 Lord J1 23 - 2le+1) l1g
  74. 2=
  75. etisensa
  76. 3 en Z 23
  77. en 6) 3set
  78. set
  79. 312
  80. S
  81. = 2(C+1) 15, 22
  82. C
  83. este s cesarus rter
  84. de
  85. i
  86. s
  87. 2C
  88. 31= 45
  89. unde vigula habetur. Nemp 13, 14, 13 sunt in quo.
  90. membro denominatoris et 2s si quaesitientor sit
  91. otee au etee pi
  92. 31= 13
  93. 2 f14. l. 3L en f15. 22.2 8s. 2C
  94. re 23 C8417] 3 (er1) 1 23. 23
  95. 30-
  96. ler 9313.23
  97. 33 (C+ 1)223
  98. 3 (er 1)) 2 (et 1)7 (4. 2. 23 Heniprtes
  99. 3C 52c
  100. 3ler )eti) 23 (et 12
  101. 3e
  102. 2e
  103. Ad. sive notm Nexta n. Erit ipsius in 9 maximi.
  104. dc. 7
  105. = 15
  106. et) 14. 23
  107. 3 (e +1) 3 (C+1) 23. 23
  108. 3(ess
  109. 353
  110. 31 3(eriM3ter1)) 3(enR 233
  111. B. 22
  112. 2e s es

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 26, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068071:0015?run=73