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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 114r

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. 115v); this page is its right half.

The machine reads it as

  1. d
  2. - 100 + 111H + 112 des + 121V + 122du + 131 8 + 132d2
  3. 0 = 2 = 200 + 211y + 312 dy +231 y + 222 du + 23+Z + 232 dZ
  4. unse incognita varians
  5. percnamluaria
  6. B 100. 311 F 11I. 311y + 112. 3Iidy + 121. 3uV + 122,31 dv + 131.311Z + 132. 31 dz
  7. 0 = 200. 311 +31. 31yt 21. 31 dy +721. 3HV +222.31idy Y231. 3117 + 232. 311d2
  8. 112 d 32V F 112. d35) + 112. 32Idv + 112. 331de Et, 200. 311 4211. 221 V ∞ 211. 3312
  9. inde explicando (b 100. 311 + 111. 321V + 111. 3717 + H2. 32
  10. slieret
  11. 07
  12. +212d32V + 212d3317+ 21232) dv + 2n. 331 dz
  13. 121. 3I1V. + 131. 3u1Z + 123. 311d∞ + 132. 311d2) +221. 31V 4231.3112 222311d vi 232. 31d
  14. F EIII. 331 F 112. d331 F 131 311 = 211. 331 F212 d 331 + 231. 31 res non procederet, quid 1 et 4u ssantes
  15. iatC
  16. 212. 331 + 232.311
  17. fact he bit, B - 31y + 31 W et Z = +11y + 4412 G et prodibit
  18. 112. 331 4 132.311
  19. rober
  20. pedeundo ad aeqqe
  21. ado
  22. 0= 100 + 19 4 112 dy + 12l. 3 411o 122. 34 du
  23. 4 121. 311y 122. H dy
  24. 131. 41Y 132. 4u dy
  25. 122 deq. W
  26. 131. 441W + 132. 441 oW
  27. 132 d441W
  28. et rususo = ut ante tantem primam
  29. notami mulando in 2
  30. et fiat 121. 341 + 52t 122 d341 + 131. 241 + 12d441 ( 221. 341 + 222 4341 + 271. 491+ 23 =d441
  31. 222. 341+ 232 441
  32. qud sed hic diviesio institui uva potest, ut numeritor numeralori, et denomi
  33. 122. 341 + 132. 441
  34. nator denominatori aequetur
  35. An ergo sic.
  36. 126341 221421 seu 3IF 132. 441, 13 222 341 + 232
  37. 122. 341 + 132. 14F
  38. 228. 34 123044 B
  39. 231 44
  40. 121. GA 121
  41. L et d441 = de. 341 + ed341, et ex aequ. 11 fiet
  42. 231
  43. 121. 391 + 122 d341 F 131 C. 341 + 132 de 341 + 132C d341 221. 341 + 22 d341 + 231 C 34112) 2de 341127
  44. 12. 2. 4 132e
  45. 222 + 232C
  46. 121. 222 + 13 2x I 1tC. = B31. in + 132. 822 Ae1391 1122 122d + 12432C 1 d 3a1
  47. 127. 232l + 131. 23288 + (132. 232ede
  48. aequ.
  49. +22. 22 + 122. 234 + 122. 232de 1 391
  50. 132. 221e 4 132 231ee + (13223 2 ede)
  51. +122X328 + (132. 232C8)
  52. 122. 22d F 122. 272e d3a1
  53. XBC + (1m2. 232 e0)
  54. Ita tanden res reducta erit ad (d341: 341 per meas cognitas vel arbitrarias
  55. sit aequalio dy .dp = Xx =+ gy: aa
  56. vy
  57. sit y = (E s dy = v I B dilus = dex B + vP s. erc
  58. Ergo omnis aquatio differentialis simplex unius literae sicareat
  59. termino absolute deni potest attolii ad altictem
  60. s ntumus sit 1044G+ (2 dy + 13ddy = 0 sume 20+21 y = 0 fit 420 f 21d) + 21
  61. et dd 20 + dd21 y +2421 dY + 2) ddy =0 componantur in unum, etf
  62. uic adunur
  63. Pdd2o+ padrius Crpdidus Dp 2ddys Vtio +tu yAt2 du + +13 day
  64. 9420 +9d21y + 421 dy
  65. Y 20 + Y21 G
  66. fit + = 1 21p: 13
  67. unde 2p d2j + 921 1. 21 p: 13 et 9- P, F- 2 det
  68. et Y. = dd21 + d21 - 2 det d21 1 Et p dd2c L. p d21 - 2p d21d21 + r21 = 11, 21 p; 13
  69. 21
  70. 1321
  71. 21 13 = 10. 21 - d20 + 2. 201d2 = dd28, sed hoi perplexiys
  72. 13.20
  73. 21
  74. 1.1
  75. 21. 20
  76. 20
  77. 10+ 112) + 12 dy + 13ddy = sit aequalio data. Asjumatur alia arbitraria
  78. 20431 9 + 22 dy +. 23ddy =0 et fiet +13. 20 + 1321y + 13. 22 dy =0. Et differentiando fet
  79. peedir 30 +3 2t 33 di
  80. = 10. 23 = H. 239 12. 23 dy Hinc
  81. a(t d8B + d31y + 31 dys +32 ddy 0 quam aequationem conimmendi print t
  82. +dyEdy
  83. conferando equationes a et 6
  84. fit
  85. fit 13, 31. 31 , t 13, 31d3 2 1731. 32
  86. aqu 13. 32d31 = 11. 38. 32
  87. pur
  88. fiet B dao + 13d3, y (4 13. 31dy (+ 13. 32 d1y
  89. 1
  90. + (3432dy
  91. = 10. 32 - 11. 32y - 12. 34 dy = 13. 32 ddyes
  92. fiat 32 = X 31Y et d32 = 31dr + rd31 Ergo ex ag. 7. fiet
  93. 13. 31. 31 + 13. 31. 31 dr ( 13. 31Y 431 = 12. 31.31Y =31Y d 31)- 11. = 31. 31YY, et divisis ommbus
  94. per 31 prodit 17 si 13(1+ dr) 31 sublatoque utrodius d3t, sit aequario ordinaria
  95. quod mirum nempe (13 (1+ dr) - 12Y) _ 11. 3C 7Y = 0 sed ita evanescit 31, et dificitter abetuit
  96. 134 13132 = 12 32 = 13 34431 = 11 32. 32
  97. Sed si 32:31 = 1 fiet aequatio quam dui
  98. Numatur 20. + 217+ 22 dy F23actu + et d d7
  99. 510qy+ su L 13daq 3 diberenti et D sut dio _ud L dy F1 2ddy + 13dddque tonantur simal daus et obu quod talile
  100. c1o. a uus in p. E dy Cot titrenem Ad E qbd2
  101. A 2, 33, 24 = 13d17
  102. Sit 311y = 321B + 3812
  103. assumaturque 3U ut constans
  104. et muttiplilentur 499. 1 et 2 per 311
  105. exde fiat explicatio
  106. filatur

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 114r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0227?run=74