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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 199v

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: 0.81.

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. 200r); this page is its left half.

The machine reads it as

  1. Ergo ady 7 20 adq + ax pox. a
  2. Hinc duplicu modo debert
  3. eriri idem nen nempe summando ha fiet a(1) ay+H
  4. 20x:a sed idem et obtinebitur et quaesitum hanc
  5. aequationem altimam differentialem cjungendo cum prima
  6. houx ter S Ex
  7. sib dy: dx = Xx tayaa fiet y = aadu xxdx,: a x
  8. drllun dydex 2X ddx dada
  9. dadx
  10. et ay- a d d = 2Xd 4
  11. seu avddx + adydx = act day - XX adx - Xdx dx
  12. sit a dydx cde xdx di adu = a dq - nta - ta - d xdx
  13. eu a exodus - adu dex = dxdx dy t Z Xddx dx3. Sanc aqua
  14. tionem divellamus in duas quarum una sit actydax =dxdxus
  15. Ex priore
  16. ut paulo aute, altera sit aa ddque = 2X dx dx=
  17. fit X =-logdx. Ergo in proxime praecedente pro Xponendo. log. dx
  18. et praq dx ponendo = a ddx fiet aaddus = - logdx. - a ddx.
  19. seu a ddy = - log dx dux = esx logdx. log seu day = ex logax - dx+ hde
  20. adeoque fiet
  21. .
  22. Hic
  23. 11
  24. X: a C
  25. ubi per praecedentia est de = + dx b
  26. ady = dx logdx = dx + = dx bX: a
  27. novam inciditur difficultulem, neque ervim oeccunt alias summanda
  28. sane
  29. Xlogax-
  30. sed video reme
  31. quantitas dx logdx.
  32. adeoque ax logx + Sxdax: de
  33. d, X logdx = de logdx, + X dx. Xddx: ax
  34. loco: Ergua Esce remedsum logax loy (ade)= logax +x: a
  35. avc
  36. praeterca videamus an non liceat modnire logx tollere logax
  37. luy de= log la de) = logdx +x: a
  38. iit prodest
  39. Ergo tandem
  40. ay = Sdx logdx = X + fdx (2: a
  41. fac l
  42. A ergo Sdx logx = X. l0g (adc) = = xx: a
  43. logdx - 1 + hbX. a = xx + ay: aa = log (ad e) - x: a
  44. +
  45. ay = X log (a de) = xx - X + h sax b=ea
  46. EbX: a
  47. eruo habebus duas aequatiopes quarum ope tolli potest loglade) et habebitur
  48. sed nursus aq dy: dx =
  49. ame non videtur spernenda
  50. liber
  51. Haec melhioque non procedit, si divellendo non possit tolli dy
  52. difere
  53. six
  54. tandem qua me thodus
  55. lab
  56. A Re sumamus Methodum Raginae praecedentis nomihulii ma
  57. Et posita aequata pe data dy: de = sext yy,: au
  58. fiat ut ante do y: a= de: devaqe et Yia = d. x: a = dZ: deo. Uende
  59. tatam, et fiat:
  60. quod faciapnns L) logdz: logav et fiet
  61. ddo log du (5) adz logi Unde, dv logdv. du = dZ logdz - dZ + hdeo. sed compendii
  62. ddv: ddque 3 dodo = d Z. 1Z,: deo dco
  63. causa opmittamus haco seu ponamus h= 0 et erit de: dZ = (7) = A logdz - 1,: logdo - 1
  64. per 4 est dco deo +3) dvdv + dZdZ, logdv: log d Z per 1
  65. = (10) dn dv aa egu Et eodem modo, = (11) dZ dZ ag: XX ope aequationum 7, 10, 11
  66. L ( (per 1,2,) d. X
  67. velutodius Siltollendae do, dZ. Et quidem dvi= dZy: Xinde log dv, L logdZ Flogus - logX. Ergo ex aeq.
  68. +d7 ggdZtloms loyx, ilogaze L y. X
  69. logdz - 1: logelZ + logy = logX= y. X Rursus ex valoribus ipsius acodeo, 9 et aequatis
  70. tollamus d et loyde, et fiet Adq
  71. dz daa: Xx, seu
  72. fiet gy+ XX, log dZ + logy - logX, = log dz. 44. seu log (Z (10g X = log y) (9y + XX) :, gy t Xxdaa
  73. fiet (d2 aq gus: XX) Li_(Z.2, lo9 eZ floy y- logX 3: logdz
  74. et famlibu habe a Hinc habetur et, deuZ, adeoque et logdo et du, ergo et
  75. ecum hasebita2 GClatio inter X e, a intervemenlibus tamen ipso.
  76. p1 4 logAZ XoydZ- X = y legdze log y.
  77. Clogx. Ergo logilz (16 ys logus - ylogx +X,:, x=y. Ergo ex sequatis
  78. logacurmis itrum logt
  79. jam prius erat
  80. xaloribus aequationum 15 et 16 habetur atro idter X et y
  81. Gereraliter sit dy: da = suisions aas ihi a =. C2) luo: deg, et iio riur e alitua
  82. ddc 0. fiet dus: dx ddv: adz; C
  83. loydz: logdo adeoque hoc
  84. Exgu clav: ddz gieo faciamus a lag az:
  85. dav: ddque sint seu
  86. o aq. legazue = adv logdo,
  87. () de logdo = de nde Cav: dque = (10) logdz. 1, : logar - 1
  88. tam id agitur ut sublatis ded, de, dZe redeamus ad y et X Fait autem 1XZ.I.
  89. et summando utrobique, fiet dque lvgdz dz
  90. nun jeur ex 2 et Z est
  91. Erprs t
  92. s
  93. l
  94. gjius gles pro
  95. per 10, en
  96. 1Z-1, l0g dv- 1 = (12) Y
  97. qiiglorem ipsius lu
  98. sab
  99. A
  100. quidia gix
  101. atilia isto
  102. dut
  103. jam ex n est ax
  104. 10gdZ Flogus- lga
  105. P.X et
  106. o s. ,eba 3i Ba . 1) itr 7
  107. et

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 199v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0394?run=74