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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 39r

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

The machine reads it as

  1. Eandem curvam referre ad diversos d Axes
  2. Axes duo
  3. et AZX
  4. Sit Curva 8 8 Clecices duae AXX
  5. ordinata una 8X nermalis ad Axem AX
  6. Ex puncto curvae 8 ducantur duae narmales una d Ax AX B X ad axem
  7. Apen
  8. AX, serans alerm AZ in in K; altera 8Z normalis ad
  9. Axem AZ secans Axem AX in C. Quia rectrum Axium angulus
  10. similibu
  11. inter se est datus dabitur ratio laterum in triangulis AZ
  12. C
  13. A XC
  14. hact cnt
  15. 8ZR, 8X C. sit AR M: R: p = AZ: ZC : C , AX: XH5 C
  16. KA
  17. ZC = ZH: M C8 = yp: m fit +Z +ypB: M = b AXIX
  18. et ita por
  19. +ZC+ C8 = 28)
  20. AC = Zp: m CX = yn: m fit +Zp + yn, : m = X = AC + CX = AX
  21. X BK = Xn: M KB = vp: m fit XB + B,: m = y = GXKIKB = X8
  22. (4
  23. AR = xp: M KZ- vn: m fit +Xp - BR,: m = Z = + AK -K Z = AL
  24. desideratur V sine Z ex solis y et X, unde 1 divisa per n et ex2 divrsa per p, fiet
  25. _V = (2 + yP +X (2C - yM seu v = B ∞ _ y(pp- nn -) mm + X mn seu V - x v = my + uX
  26. seuq
  27. mp
  28. mp 1
  29. simuliter ex 4 divisa per n et 3 divisa per p fit Z = XP (-v (Y DnX +D = X(p. nA.) n.- 7
  30. n m) nn P
  31. m
  32. mn m LP =mp. lm
  33. Eodem modo inveniamus x et y ex Z et v. Et quidem invlim
  34. t
  35. PM
  36. seu 7 = aX - ny
  37. mnimus X ope aqu. 2 divisae per n, et opeaequ. qe divesae per p, et erit X = (D et ZP +B(Z)-
  38. X = 2(p B - nn )um + mnv,: mp seu X = mZ + tiv
  39. en
  40. seu
  41. m, nn n pm 1
  42. Similitem inveniamus y ope aeque. 3 divisae pern et Pope aequ. 4 divisae per p et ita fiet
  43. ut (= X) + vP
  44. n
  45. m mia ce
  46. L, seu
  47. -Z(+ X) vn seu Y- vph - nn =) nm C - mnZ
  48. Pm mp
  49. B
  50. 2
  51. nv - nZ
  52. verum etiam est ob triangula rectanus AXD et A28 basis, hypotenusae communis A 8
  53. esse XXLyy = _ 93+ v.. sed hoc ex dictis per sase sequitua
  54. potatu dignum etia reciprocari X v, at Z est enim Z ad X et y
  55. eodem modo velatum ut y ad V et Z. Cumque praeterca sit v ad X a et y, ut X ad V et Z
  56. Hinc patet 7 et v esse ad relatas ad X et y, ut y et X ad v et Z. quae
  57. est peresdegans et observatu institia leges
  58. quidem inversio pereet an eptdignum quaesitu
  59. Exemplum ad hibermus sit AX, Y et X8, y et y = XXt aX, i2a jam
  60. X = Z+ rv: B et y AnB Z fint ere et y = mo. nZ: p- mm ZZ +nn DV +Emh ZVt amp Z
  61. +arp, capp seu mmZZ + nn oV + 2m ZV tampZ + anpv = Lap mB - 2 apN Z
  62. lese
  63. Pp = nm +un

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 39r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0077?run=74