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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 283r

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. 282v); this page is its right half.

The machine reads it as

  1. sive -ft ad X - fl fy X
  2. + ad.
  3. +ad...
  4. +f.Y .. . + fy...
  5. + actg X
  6. treytg
  7. 2acyg
  8. eyg.
  9. -++ ab
  10. fy
  11. et pro X substituendo: act + 2ey+ - 2ac y - reg fiet:
  12. ft + ad +fy
  13. ac t + rey+ -2acy-rey r st + actus i = f+ - ft aeb 1.
  14. +ad + ad
  15. + 2eyt9s
  16. + ad +ad tacy
  17. +fy +fy) - 2acy9 +fy +fy
  18. rey
  19. Sed quoniam reductio hujus calculi nimis prolixa est satius est, opnor ire
  20. per casus sumpliciores, et paulatim assurgere ad altiores, ut appareat, an
  21. an progressionem pervenore liceat:
  22. 1) ab + acy + 9X p 0. unde -29X +at b Ac , 2 ab + 2cy
  23. sive Z
  24. atc3
  25. LFIV
  26. gc
  27. y.
  28. 2
  29. M
  30. ac
  31. Et hac colligendo + ex y. sed si colligatur ex X, fier:
  32. ygesy
  33. 19X+ - b - ac Y sive tp ac V et pro X porendo Y porendo - gX - ab
  34. 29X
  35. fiet: + p gX + ab, adeoque sa p) eis erit 2+
  36. aeb
  37. aet a 1
  38. = 29X
  39. 2) aeb + ac Y + ad X + gX. p v. fiet - F Ex y fixt + - egX - ad X, et
  40. quia uit vero eliminetur X, pro - 29X, ponatur 2a b + 2acy + rad X. fiet
  41. +⊓ 2a b tac Y + 2ad X - ada 24)b + 2kcy + fdX, unde X B et - 2ab - 2cy
  42. et X 5+ qcab F - +C +Y + + a b +8 abcY + +C, unde ex aequaluom
  43. mitio proptosita eliminundo X, fier:
  44. D) a b de (D acyd + ad t a= ad 2abd ad 2Cy) + gc+ - 4c ab9s l- 4629 2)
  45. + 49ab + 8 abc gY + 4cg Y) et pro + subistituendo ya
  46. habebitur aequatio in qua solae ex incognitis restabunt Z et y
  47. L
  48. Sed calculus hic prolipus longe facilius expediri poterat, considerando locum esse ad parabolam,
  49. atque ita ipsam , ac proinde et ipsam Z aequationis ab + acy + ad +90 facite
  50. denivari ex habita vel Z aequationis acy + gX 70 adhibita met hodo genent
  51. ad exemplum ds, ui quemadmodum d atscissae ordnataeque unius directricis ex
  52. alis alterius derivantur.
  53. 1a3 tacy

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 283r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00067993:0567?run=73