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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 54r

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: 0.84.

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. 53v); this page is its right half.

The machine reads it as

  1. Fortasse servaretur Analysis si primum poneaemus esse datas
  2. ady
  3. aequationes 100 aa = Mav + 2 ay + 112∞ F mrgy = + = 0. et 20oaa + uav + 22VV = 9 = 0
  4. multiplicetur illa per l et haec per m, et conjungento fiet:
  5. 100 laa + iu lav + 1rlaq + 1. Lvo Y 122l gy C5= = 0 l:m = - 212: 12 = - 1: 1 seu H = 2
  6. Si 1o at + (m1) _g + (129 + (112) a dv + (122) alilus) 1) et 200 at. 7 B + 212 adv )
  7. +200 maa +, 2um a + 212m qv
  8. 16(121) uilx
  9. fial (9) = yr t v. At ex 14. 1. fial 100 cdex H(1) D (112) adV + (122) adu fiatid ant (11) 2) s
  10. H hv + (22) h do
  11. Git
  12. e
  13. (112) + (n9)h (22)
  14. ADh A, at atque adeo effici potest quaesitum
  15. Unde habetur aequatio per quam datur
  16. sint jam duae dalae ambae continentes y et dus et v’et do, Ras con-
  17. jungendo formetur una in qua absit 3 et dy. Quod fiet
  18. simili fimi Ie thodo.
  19. deinde ex data, una et producta formetur
  20. nova ruisus explicatione in qua absit v et av mydx
  21. Sit aequatio data 100aa nav I nray 100ca x + i adx + ex + UEadve 122 as
  22. et 200a ux + 2U Ddx +212 adv0 sit ay+ E et aduadue
  23. sit ay = aco + hv et ex aequ. 1 L+Et ady. adu + hdo + vds
  24. Et exaeg. vfin +100adX + 1 Ddx + urand t + 121 aco dx + 1aadv + maado ∞
  25. + 12IhVdX
  26. + 12a dh
  27. 6200alx Z Eulvdx
  28. e
  29. +122ahdv
  30. 4212aldo
  31. l= 12aF 122h,: 21k
  32. Ergo ut destruatur vax fiet
  33. 111. 212a1, + 121. 212 hext 122. 212 adh = 2 112. 2ua dx + 122. 211hdx, cujus aequa
  34. ut destruatur du, fiet
  35. adeoque et et podibit aequatio
  36. + 121 a cd dx + 122a4do = 0 ita 5g. l et 2, reducta est ad 2a
  37. tionis ope habetur h
  38. habitis ergo V per aeq. 2 et co peraey. 4
  39. 100.212a DH. 200a fL122
  40. + 100. 212 a fdx
  41. - H12. 200aQ dx
  42. et h per aeg. 3 habefur 7
  43. 100a dX + 11I vdX + 121y dx + 112 adv + 122 a dy 0
  44. = 122. 200 Ahdx
  45. 1. Et 200 a dx + 211 v dx + 221 y dx + 212 adv + 222 a dy = 0
  46. quaeritur aequatio
  47. in qua solum sit dx, v, do fiat aV = a e + F gy et siet: etay = e
  48. sit
  49. + 109a dex + 1I E dx + magZ dx + 112 au d8 + 1120qd
  50. + 121 a dx
  51. +142a yeg
  52. 127 ala
  53. Eoodasdx P2n af dx 21fgqx 212 aaf d8 ( 212 afgdis
  54. x
  55. ree
  56. 212 af sdg
  57. =222
  58. 1
  59. t su pererit aequatio sed
  60. Et supererit destructis aequali
  61. + 100. 2 aadX) - + 11I. 212aG dx) (1, 2212 aa d8) =0
  62. - 200. 112 = 112 211
  63. = 12. 212
  64. et faet aequatio ipsius Et ex aequ. 1. fiet
  65. +f.
  66. et 100aa dx = Igydx + 112 a gdy = 0
  67. in + p a es dx +121 a ydx ( + 122 dadus
  68. + 112aad8 + p3 aydq
  69. in aequ. 7 abesset 22 et 222. ipsa potius
  70. lteremur et fierec
  71. fiet f- 12a: 212 lor inum
  72. end male
  73. et ravo lort 9
  74. et 111. 212 gAx + 121 212 a dx + 12 213ad9
  75. aequ. 112. 21gdX + 112. ∞21 ad X + 112. 222ad
  76. fra ito habertur fet g
  77. + 200a adx + 211gydx + 112 agdy =
  78. +MI a SIX
  79. 2et agex
  80. 212 aydque
  81. +212 a4 d8
  82. et ita habatur 8 = 10. 212 - 112. 200
  83. dabussemus e
  84. 1∞ 211 = 111, 212
  85. seuodatur 8 per X, habetur et 9
  86. Haec via ergo mihi praeferendu
  87. videtur priori s licet
  88. essent 221 et 2228 essent 0
  89. in 5q. 2. Ia enim opsa
  90. ipsa aeq. 2. non amplius est opus
  91. in aeq. 8 vel 9 tolli potest dus
  92. ope aequationis
  93. nemm-
  94. sipraepararia aliis datis tale
  95. i paequationibus et 2 debe habeetiam q haberetur absolute nec risi una foret opus
  96. (1 prius fuissetae ratio secundum V et secundum ∞ et pro 121, 122, 221, 222, affuesserit
  97. 112 222 = 122
  98. tu
  99. (121) (24) (221) (222) ita pro D ponendo ey, pro 121 fieret (121)C pro 22t fieret (21) e
  100. praeparationem, ut si
  101. sed quia F imoltoit g. esde a non pilet ad habere hanc multiplicatimetu s praectat
  102. exilicare, et qsed forum per Cr
  103. cedi
  104. et V per a8 92 ita res oplime
  105. Hac optma latio
  106. antils
  107. reper

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 54r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0107?run=74