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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 404v

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: 0.82.

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. 403r); this page is its left half.

The machine reads it as

  1. (2
  2. aa XAx + 2ydus + a’ydx = 2aa xdy cX = 2)ly + a ydx: 2 du -dx uende
  3. aaAx = 2 dy- dx, 2y ddy + 2.3y y + ayaax F a dydx = 2y dy + a ydx. 2ddy - dax 8: 44y. a dylxt de
  4. t
  5. seu a dxdd-aadr Bdydx + acax dx =(2y ddy adu + Syus 2dys + a ydax edys a dydx 2did
  6. 2y ady dx-6 is di ax ( ayd dxax (C, ae dy dx ax (= 21y dy 2day - a ydx rally + 21y ayaex ta y 2x lex
  7. (5)
  8. Hil
  9. Jam omnes termini quos ingreditur a ponantur aequales nihlo, fiet: 2 dxdi - 3 cx dus 3 dx - Bydus dilx
  10. 2ydx ddus
  11. seu y EC AX B = 3 dx dy + 2dX dty,: 2 dydax dedau. Unde ex reliquo aequationis 4 denta
  12. eq 5. fit 12 4y3 = 2y dxddu = 6 dx dus 42y dys ddx 20 seu y= Cy. 3dxay:, dis dix- dx dius
  13. sed hos duos valors y aequanto tollerentur differentio differentiales et res ad solus
  14. Aliter ergo ex aeg. ) est aa = 2y dyse:, 2xdy - xdx- ydx. Unde differentiando
  15. differentiates rediret. et linea fieret recta
  16. fiet : 2X dy = xdx - y dx 29 day + 23y dydy.= 2y dy 2Xdayt rdy - xaty- ex dx -yaax C apax = 0
  17. adeoque (2Xdus Lp dldy t exdus L yay -xdx 2y ddy -xaxby dys - yex 2y ddus yax biy dyt idus el au u his dus splrdus
  18. ydyxdax- 2y dy ax- 2ydys yddx
  19. jam omnes terminos quibus in est x ponamus
  20. aequales nihilo, fiet (y d ydais + 12ay - 2) x day - 6 dx dis = dydau 2y dy ddx
  21. et reliqui in aeq. T termini eruntu 1y ax dius Bydx d- 2ydx ay - 27 dy dax. Unde ex
  22. aeg. fiet y- 6ds. dyadu x 6dis - 3 exdu, : dx days - dyadx. sed ita ex aeque.
  23. sit alius rursus habetur valor ipsius y, cujusidem denominatnam
  24. Resummus aequationem 1. et differitum aa xdp +27dy taydx=raaxdus hanc differen
  25. iacidimus in d absurdum, mauto ante occurrens
  26. tiemus, fit ea pdda iect tollamus y differentiando quod si tunc, vel a vel X movasan-
  27. derent, nisi ad unum guodumveme non darentur nisi pure seu uno gradu; posset
  28. simuliter es gradus poni aequalis nihilo, sed puto altius ascensuros.
  29. in aeq. 1. ponatur dy: a quantilus ostans seu y ady + 3y dy = 0 seu, yddys + 3itus = 0
  30. et fiot rddx + cx + y dax (t dxdus = 2X ddus +3 Axdus. sed nilil hnc

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 404v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0804?run=74