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Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 42r

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: 0.80.

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The machine reads it as

  1. sit
  2. e
  3. (1)
  4. 26 Augusti 1b8gR adix aequationis extracta
  5. Xaequy aequ bX + Cx + x + fX et
  6. per seriem infini
  7. dy aequ b dx + 2CXdx + 3Cx4 +q erc per 1.
  8. tam
  9. Methodus salis
  10. r sine calculor pro Besta
  11. sit aequ l + nV = ny + p+ q etc. Hc mojus cubendicpotepli at serienm
  12. dx aeqo mdy+ 2nydys +3Py474447 dus etc
  13. =I
  14. infinilarum, aut aequalio nesque ex ipsis per
  15. arbitraria, multiplicatis compositam
  16. X aequ l’+ um y _lny + Elpy +9y. Oc +2lry +215y
  17. s+my +Emnus +mpy
  18. +n yt
  19. +2mqu’+ 2mry
  20. +2n p7 + 2n9
  21. +3l my +3lny +3Ipy + 3l9y + 312
  22. +lnus +stn
  23. + p 70
  24. V +3l
  25. +3
  26. +3lm 5 oblmnus tblmpy + Clmqus +otmrys
  27. +3In y +6Inpy +olngus
  28. m’y
  29. etc
  30. +31 p y
  31. Aliter sine interventuo differentiatum
  32. Y aego a + bx + Cx + _x + f + F
  33. X aequ B+ 1y + 2y+3y + 4 y + Sy +6y etc
  34. e ccd
  35. X aequ O + (2)0ly+ (2)0.2y X2) 03. G3 +()04 y + (30 5y 4s0by ek B. quomodo
  36. + 1.1 +(2) 1.2 1() 1. 3 +6)1.4 +()1. 5. Cognoscemus an radix s se
  37. +22 +)23 4(32.4.
  38. 43.3.
  39. X aequ 0 + (3)0 y+ 38. 2V 63y4y 1605y b6 y6
  40. +(3) O. 1 1)0. 12 +(6)a.13
  41. (30. 22
  42. +1. 1. 1 (3) 1. 1. 2
  43. aqu. Hoy +202H 0oy A obs
  44. 46)072 +(26O 12 + (3. 6) 613.
  45. +6)322 + (6)023
  46. icuoie
  47. valor ipsius X sit impossibilus
  48. et quomodo diversas a–
  49. debet etiam ea esse termino.
  50. s
  51. um natura deficientrum
  52. tes.
  53. utitur Tangente curoe, forte
  54. +6)035 + (.6)034
  55. facilius ostendie
  56. eo redit, ut primum tem. Fuotere
  57. et quol modis aequatio duta
  58. quantitates (4)O13+ (34)912 + (234)0123 poss revocati
  59. Din infinitum decres cat
  60. Facila aurem apparet termini cujusque ipsius y polentiae oefficientes, auipe ita inX
  61. psius X
  62. ut exponentium summa aequalis sit exponenti gradisexgrat. Oi Ent
  63. lie
  64. seu 0112. sue exponentum summa est 4 im et at nuo semper eadem
  65. u
  66. pem summa ipsam literarum sit etiam aequalis sidem, ita 2 seu ottfa
  67. militer gradui il exponenti gradus ipsius Y. ita 0112 seu 0+ 1+1 +2 facit 4
  68. s s0 it et
  69. et oet 3 seu 040+1+3 facit 4. et. Numeri autem praefixi habentur
  70. ex omnibus modis possibilibus producendi, ita O11Z. varie produci potest, ex
  71. primo ex orin 2 ium es. rursus produci potest ex orcu + vel ex omi vel ex nmo sebr tera
  72. seuoexge
  73. in 0, ursys3 Tertio (012mF p et sumi possunt ex Tabula
  74. alibi condita
  75. X
  76. aequ
  77. C
  78. a+ b+c + d
  79. 10
  80. so
  81. a WX
  82. anattbaetia
  83. dices a se invicem distin
  84. quemus Nota y debet
  85. esse minor Unitate, et
  86. O, 1, 2 ete. ut termini
  87. sim in infinitum decrescen
  88. caccedens Metho
  89. dus per difcentiales,
  90. amus an
  91. jam
  92. impossibilita

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 28, fol. 42r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068241:0083?run=74