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Leibniz-Handschriften zur Mathematik LH 35, 7, 7, fol. 2v

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: 0.88.

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. 1r); this page is its left half.

The machine reads it as

  1. Videamus an et alid ratione possimus Theoremata comminisciim seriebus
  2. Numericis ut d X terminus seniei sit X
  3. dcdx= et differentia seriei Ax
  4. dx = X + AXAx + dx = X ergo
  5. a= X = 2 X dx + dx Ergo X = 2 SXdx + sdx. similiter
  6. X3 = 3 (X dx + 3 (X x + sax et X = 4 (Xx + 6)X + 4 (xdx + sax 2
  7. et ita porro. dxZe = x dZu + ZdXtt Errga XZ = f XdZue + sZ ax
  8. dXZ = X Z1dq +Z L X +d in Ztaq = X Z seu _ XdZ + Zd x + dxdzue
  9. Ergo XZ = (XdZ + sZaX + saxdzue
  10. = - 1
  11. = X + dx - x = x ex
  12. X X+do
  13. Xx dX
  14. x tadx
  15. LtAX = a. 1 - a. Ergo
  16. vel eliam P d. a dc +a t = co
  17. a
  18. ac an. B. sa ex
  19. Sed nunc tandem incipit ratoo primam ratiorem, qua potentias de ((n) X
  20. explicuimus, applicandi etiam applicando ad ((n) nimia scilicet facilitas rem reddidit
  21. obscuram quia scilicet infinitis modis res fieri potest. Exempli gratia sit
  22. Y = 1+ 2 + 3+ 4 +5 ec. scribamus y = 1 Y + 2X + 37 + 4 gc. hcaet subintet si ponatur y = (0) X + (1) X + (2) X + B) X + (4) X + (5) X + (6) X modo
  23. ligere possimus X = 1. unde eo casu X ubique evanescit. Interim secundum hanc expressione
  24. possumus investigare y ex Theoremate supra dicto. sed possimus etiam alias adhibere
  25. potectias v.g. y = 1 X + 2 X + 3 X + X 8 c. posito enim X = 1 res
  26. eodem redit. Atque ita ps eligere possum modum cujus ope commodius habentur
  27. summae particulares, seu colliguntur in unum termini, qui finguli sint ad fummandum aptiores
  28. sit n Hinc cum arculus sit _ - 3 + L - L Nc potest intllgi 1H. 1X + 1 X - =X
  29. quonm diffecita est = y fiet du = C - 2 X + 2 Z = 4 X
  30. dy A- L X + 2 n - 2X = 1 -X + x - k e et y + ix - 2 x 3 x etc. de
  31. = dy 1 L X X en
  32. quomodo autem eligi possit oplima
  33. ratio supionendi, ex calculo. superiore poterit duci. Hinc etim
  34. multa nova Theoremata duci possunt, oriuntur enim multi diversi modi
  35. ac praeclarisima
  36. summandiu qui omnes redeunt ad unum.
  37. sunt magni momenti, utileque crittam ad circuti s expressionem
  38. a me inventam applicari tam pro a = +- f + fesc
  39. quam pro a circ - - + 1-=NC
  40. comlat quod si supra ostensum est

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 7, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068079:0004?run=73