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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 19v

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: 0.80.

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. 18r); this page is its left half.

The machine reads it as

  1. Investiganda est ellipsi descersus mobilis in Ellipfica
  2. e- B
  3. obitu lati circa ambilicum Ellipseos p, descensus
  4. sit
  5. 1cD. ex datoradio PC, et circulatione D2C.
  6. in moli
  7. quae temporibus existentibus aequalibus est radio
  8. reciproce proportionatis.
  9. i
  10. sit AD axis parabolae
  11. cujus verlex A, umbilicus p. suma atur in axe puncta B
  12. et Q. sic ut BC BC perpendiculanis ad axer, et QC adcurma
  13. AB = X
  14. BC = y
  15. pa Ellipseos 2aX-
  16. a
  17. PC = V cons ex natura
  18. GXX = yy. ubi a latu rectum q transversa
  19. seu seini axis rajor. Ergo er differentialem ipsius
  20. aeg. 1. fit a dx - a x dx ydy. jam seu ax du erit
  21. et
  22. 8: a - a x:: ap: dy: BC seu y: 8g. Ergo BQ = a - X
  23. A entque jam CD. DZ( 1CD. DrC t B. C: BQ. Ergo
  24. pet jam pB = PA - AB, sit PA = h. fint P B = h - X et PCF
  25. e
  26. et PCseu 0 = h - 2hX + X + 2 aX - a xx. sit a-hs
  27. et 1- = n. fet v h + mx + nxX Et sie vdv max tnxdx
  28. et V:n=h. n + m: n C, = X+
  29. i
  30. Ergo fiet d vdr: dx =(n _- nm) + Gu v. n - ht m.
  31. 2
  32. X
  33. no ntets. m-hu = ete. fiet vdv: dx= Vvn + et
  34. seu ax
  35. vav: vnter
  36. Est autem. DC = dv. C, Et quia
  37. dus dx a ax:g ba et dy + dx
  38. siet dt. a 2a
  39. ap
  40. u Ergo
  41. X +4 X. 2ax -ax. porro dite. porio
  42. 2
  43. C2C = CZ 1x: y Ergo 3C2C = CZ dx :gy jam yy = v - h. X.
  44. seu s jam h - x = h + m: 1 = v: n +et jum m a h et m: 2
  45. = ab XC a-A: 1 sit h + m:n = r, fiet Y 2Y (V. nt C vnte
  46. fiet y = v2 - Y + 2Y v: n + Cr +v: n + 37
  47. X
  48. fot y = a v + 2r Nvon +er + O2 et CQ = y + BE..
  49. cg.-
  50. y= VaX = a xx
  51. denique dx + dusr
  52. aequationum tolli debent
  53. ope tolli debent
  54. per 6 et 4. fit
  55. X
  56. .
  57. ax. a - = x - 7 dy
  58. av + 12
  59. ex vav. sente
  60. et 1-n = a
  61. ergo fiet
  62. on +e +B + a- 22X + a. et Bq
  63. vdv = m dx C nX dx. v2 C
  64. 4
  65. e
  66. ope raum
  67. + eiquatione
  68. rarum
  69. Y, dx, dy. ex in 3 ex 3 tollendo ax et
  70. vdv: Lente

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 19v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0038?run=74