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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 117r

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: 0.78.

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. 118v); this page is its right half.

The machine reads it as

  1. sit curva ANB, angulusque rectus ACB es
  2. dueatur
  3. sit cma tilineum ACB NA rursus sit cuva
  4. sit circuli sentrum C, quadrans ANB, curvaque
  5. alia AYBtalis naturae ut recta perpendiculati ad CB
  6. secansocira curvam in Y, et circulum in N quadrante. in N
  7. sit CX, X, Se XY, y
  8. sit XY = X NE: CB
  9. et XN, V, fiet et radius circuli a, fiet
  10. y -51) v: a=1. Ergo dy: dv = (2d0) C. vel: ae =1
  11. (3ti0)
  12. gto
  13. N et Y tangentes occurrant ipsi AC in R et Y, et
  14. in X N producta sumantur ipsae X P, XS, aequales ipsis CR, CT.. Ex
  15. ob triangula ob natura contactas sit CX, vocetur X. Erit
  16. FZ: ZY =
  17. Ax dgdx seu TZ dx = xdy sed si ANB sit quudrans
  18. ciculi et , jam CX vocetur X, et sit ANB, quadrans circuli,
  19. erit-dv: dx = X: W, et fat ex 4 et 5 fiet udus = ey de X: V
  20. ex qo t in 4 pro v substituendo valorem ex S, fiet-X (aX: dv) = ey dos
  21. Xxxdvidu A m xdoidx
  22. Z. TM-
  23. (Z= - xdy: dx RM = - X dv: dx. TZ. RM = dy: du = c y: v
  24. at
  25. C in circulo BCD. CN = CN : M fit RC = aa : V RC = RM, eu D = aa- DB : V
  26. nc
  27. Yydx = -Xdy et TZ -eR M. y : V RM = XX. V
  28. =eaas:vo =evy: VV seu 7 y = aa - vD: vv = XX: V
  29. jam y: a = v: a. seu a: V = a: y seu
  30. N
  31. sit RM. Ergo TZ
  32. RC = aa: v =
  33. a -a aa - a a - a
  34. eti
  35. a
  36. vy va
  37. ga sed y - v fit qa -
  38. aa , a3
  39. v
  40. aut-y
  41. a = a d9 a
  42. a
  43. D
  44. e2
  45. e3 pe1- v
  46. seu a: D = a v. ya
  47. sei a: v = ve - ya-3
  48. =R Ct RM = vCC
  49. 9. 45 = v
  50. Rursus TZC. RM. y: v, frat
  51. (Z =C vC2 - ey
  52. ae3
  53. Ergo eo casu quo e = 3 fit = T7 = v = y = MZ
  54. vel YN, jam = TZ dx = -xdy Ergo vdx - L ydx = =xdy
  55. sed seu Vdx = + y dX - 3Xdy
  56. Hinc quadraturm tricurei ACBY dependet a quadratura Cinculi
  57. sed. quando e non est 3 non fit EZ = v -y
  58. contrs
  59. ae
  60. 9 = v
  61. aa-
  62. v
  63. sur
  64. vu =a
  65. =

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 117r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0231?run=74