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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 369v

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: 0.83.

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. 370r); this page is its left half.

The machine reads it as

  1. Exemplo uutamur sit
  2. ac XIX+ odus ad fd = ady. sit e
  3. siet du = Xdx tyAX,: a sit ddx = 0 fiet ddus = dxt F du lx,: a seu ddus = ad x + x dx +yx: aa seu
  4. ddy = dx. atxry: aa et dddy = dx. dx tdu: aa = cx, a + X ry 3: a. et de d4y = dx axtya
  5. jam (y) = y + dy fiet (y) = ay + Xty dx, : a et (y) = y + 2dy rddy, et fiet
  6. (Y)) = y, + 2dx Xty: a, + dx. atxty: a = dy + 2 dx. xiga + ax utxtys,: a
  7. Alia esse potest calculi ratio, ut A y, quaeramus per x ax, et una
  8. diffeaentian ab y. quam longussime remotam fiet
  9. V = adu - g xax,: dx aa ddus = atxde,: dx = aldus - atx dx,: d. etc.
  10. Et hoc calculo utcunque continuato, cujm novissima dado dy, sit aequalis nihilo, seu possit
  11. negligi fiet s ax et dy= dx et fiet ty Hoc posito videamus an sit
  12. dy = Xdx + gdx,: a. seu ady = xax + ydx. nempe pro du, et y substituendo rolores,
  13. fiet: = a dx = xdx =adx = x dx Et ita res sucedit
  14. Ldy B 9 - x x r tadus 1 27 35 + ade + Bady :
  15. Generalius: ulamur 100 a dx +200a dy + 100 Xdx + 210 X dy + 101 ydx + 201 ydy 0
  16. toncns dd x o difecrtiando fies A 4200 a ddy + 110 dx + 210 xldytuo se di urd + 201 yadys + 201 dus =o
  17. intor, ordinanium; cum res redire debeat
  18. simpliciter; patel sec erus
  19. fet. Ita sic ingenitur verum, sed plecumque non invenietu 101
  20. pleruuus ad seriem inficulam, ut quando y datur non nisi
  21. salorem hic haberi rationaliter, ergo velat per seriet appropinquandu non exact
  22. =adus aedes aipldus = x ex tad a sit ddx =0 fint adius x NX + rydy dX, a et pro _ y substutmer de valorem
  23. fiet: deys = 2xdV a +7. y x +2d, dx a a y= a y - 2Y a dx,:, p te r 2lx
  24. cursus cddus = 2 dx ae + 4yxde + EK dya + 2a dy dx3: a3. seu = rdx a + ~G d + 2K dx Y e daytra t traiay, ea
  25. Ergo 9 = a tddus b dx 2a 14a +2aex: aux trar t aaHXta
  26. aectus- X dx 3: adx sit LdX = 0. fiet dy = a ddy = 2Xdx,: adx quo valore substituto in aeq. 1.
  27. fiet : = a day - 2a x - Ax x,: a d seu ddy = a ydr + 2a xdx + a X dx : a
  28. inagnastat Naa
  29. Erpo addy = a dxdy +2a x + 2aXdx: a et tollendo dus fit: dldus - adxaydx ra da x dx + 1a a 2a xost; a
  30. Ergo y - adu - x (X- 24 dx - 2aXdx,: adx. underursus dy = a d: y - 2X dx- 2a dx: adx - ydxo pdx: a
  31. et sit y = ad. G LaXAxt- XK AX: adx et dy = a d’y - 2a dx = 2X dx: 4t X = ay x +X Ax, : a0.
  32. et fit y = aL. y - 2a - 2aX du - x x3: adxs et 2 a dy- 2a dx - 2X tx: a d = aydx + X dx, ia a
  33. et sit y = adey - 2a dx - 2aX dx X dx3: a dx Cumque sic prodedatur in infinituu ergo ft
  34. tenis y= 3a 2aX + XX, : a unde dy= 2adX + 2Xax; a. quos valores substituendo in aeq. B1. fit
  35. alo i a a7a rahidx Exel + X ex: aa qua
  36. adio ves pucrectit

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 369v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0734?run=74