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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 72r

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: 0.76.

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The machine reads it as

  1. dic + dio + 1odu
  2. II + 10y
  3. +
  4. d21 + d20y+ 20 dy
  5. 21 + 20y
  6. Si in data absit Y du fiet n = -m.
  7. 10, 11, 20, 21, M, n pendent ex X
  8. dividatur au
  9. t
  10. 2 per
  11. s sed pongmus nunc quidem potius in aeq. data esse 11I =0 = 110.
  12. fiet m, ae - 420 =
  13. 20
  14. 120. a seu log. (0(Z a (120
  15. 00
  16. 20 00 M
  17. entis ipsius dus (divisus prius per 102 10. 20) est
  18. d11. 21 + d10. 21 Y
  19. + dl. 20 Y + d10. 20Gy
  20. 11d21 + 11 d20 y
  21. + 10d21 y + 10 d20 yy
  22. +10. 21 dy
  23. + 11. 20 dy
  24. +10. 20y dy
  25. S
  26. + 10. 20ydy S
  27. n
  28. e)
  29. Data
  30. =06 100 +by + 1209y150) dy +Ilydy, oua
  31. ubi 100, 11V, 120, 101, I1, dantur ex X
  32. quaeritur y ex X
  33. 10.20, it aq 2 par III vel ponater At =1 d ac coincidet oefficientus ipsius idu coefficiantes
  34. a et firt n =-m. dividatur aeque 2 per
  35. 1 10.20, et 4 coefficiens ipsius yy,
  36. posita igitur m cognita, suo arbitrio assumta Habetur 20)
  37. 20
  38. 10 a
  39. a
  40. Porro loefficiens ipso coeffi
  41. M, 218 - 11. = 101a Et fiet 21 = IIY + 101. 20a vel 21(18) 11Z 4 1 0110c Y
  42. 20
  43. 10
  44. 00
  45. 00M
  46. 6
  47. a
  48. et multiplicatio per m: 00 flam
  49. Ob coefficientem
  50. ipsius es divisum per 1B2o sit in 44. 2, Cg in aeg. 2, aequalem nihilo I10 = 0, evon superflua est divisio per 1d. 20, C explicemus autem in eo 20 = 10l:a
  51. L
  52. 20 et 2l jam inventos
  53. fint (d10. HIY + (d10. 10 (101. Y
  54. ut divisis omnibus per 10, fiet
  55. erminus ulismus
  56. a
  57. I1 = a
  58. 10
  59. od
  60. k
  61. (=11 Y d 1o) - 11, 10 dt )
  62. 00 m.
  63. I (+ dI1. IOY L
  64. a
  65. 200d
  66. a
  67. a
  68. sate
  69. c
  70. -11. 10dr - 10. 11 dr (-10X d11) 910r7
  71. a
  72. a
  73. a
  74. de01Y). quod si faciamus M= 10) nam inarbitrio est, erit ratio I1 10 constans
  75. mq postedivisionem per 10. 20
  76. at qui utrinque comparatus
  77. repertos fit 00 du. H. X M 4 00 dH. t
  78. otn
  79. d
  80. 2
  81. i
  82. d10) 10 d(
  83. 00m
  84. 01. Y
  85. 12
  86. 00m.
  87. est autem 20 = 10Y
  88. merest
  89. 14)
  90. et 10 = II. 200ar:, a d (iolr: M) compendr 10= - 11 t:a
  91. a
  92. u
  93. Ergo 10.20 = 10. 1Orea =, 11. I1 EF: aa. Et tandem d1. 21 - 1 421, V 00 m = 100. 11. 1Et: aa et vel 21 d - 1d2x a
  94. l 11 d21 = 21 d11 - : 11. 11 = = 100H: aa, id est 21H7
  95. evanescet aequandu duoqvalores ipsius 21
  96. ∞
  97. m dI. 21m = 00 11 d21 m = 100, 10. 20a et substituendi valore
  98. 00H
  99. a
  100. 21: 11
  101. fiet ex aequ. 14
  102. e e et-
  103. e1 = H,
  104. a
  105. e
  106. et
  107. (100tF.
  108. 00. aa
  109. andem prodit oome= m 110ott= quarm - 101der, eet porro ex eg7 est
  110. Sed ita postremo quaesita
  111. (ex 11g. 10, 14) 11Y
  112. voaa (100.
  113. C
  114. 120
  115. 1D. 1= bcn
  116. a
  117. 101. pL
  118. a
  119. -
  120. Er: m = 2. vordr: aoirim) m. sed ila apparet ut quaeratur M, prodire aequationem ipsa data dificiliorem.
  121. ooma
  122. Eryd
  123. assumta

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 72r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0143?run=74