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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 156v

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: 0.84.

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. 157r); this page is its left half.

The machine reads it as

  1. ex
  2. AB
  3. BC, y
  4. A(R, Z
  5. CA:. AO: VOctR:: (C9d: DD: Oc
  6. CA ∞: AO = cd: DB
  7. C
  8. AD: DC = DB.
  9. CA + _ AD + OC)= CD+ DD + DI
  10. Meco PC -
  11. RM. v.
  12. pono dari dy: dx ex X, y, a; pour et dari seu dy. dx = f.a pour et
  13. dari relationem inter AH Z. et co, unde habetur et relatio inter 7 et
  14. posita dari dunensione curva H M. Investigetur relatio inter
  15. CA et A(C), seu quae haberi potest ope fra, adeoque et
  16. ope fa, - f: a, X: a et y: a et ope Z et v, eo
  17. quod si jam fiat PZ ad cA ut Mp ad AMC pate
  18. fiet M P per: MC = Ou. quod si jam reperiatur
  19. C. Itaque
  20. A(C
  21. est autem A(C) differentialis ipsius
  22. V
  23. si tabis assumatur curva . M, ut in curva da
  24. data initio aequatione dynax habeatur dusdx se f: a
  25. habeatur C:) per solam DC, habebitur quaesita
  26. quadraturatio disse tangenbialium
  27. AB, X
  28. l BC, y
  29. dy: dxL f: a
  30. et f. a 2) X: a; y: a
  31. _ jam Me tangit HM. Egofit AB - AN seu MN, ad
  32. BC = NM seu ad NC, ut AZ ad do seu fiet dZ: do (3tio) = X - Z3 :, y- v
  33. MP seu p est aequale curvae evolutae K M. Hinc
  34. AR = Z
  35. Rn = v
  36. PC Ar sit c0.
  37. A(C) est solum incrementum ipsiup AC smestdo Nempe si inter evolvendum
  38. punctum C moveretur in fito MC summa omnium A(C) com–
  39. to)
  40. poneret PC. jam per paiora patet et dp = Ldq d3 + dodo
  41. Jam per praecedentis paginae finem et aass) cod:
  42. aa + su (2) Vrco edioi calculus oriltur talis, pro X, y;Z f seu atque, de
  43. substituatur X- Z, 9. v, 4+co, adu -ddo deo et fiet
  44. da -d2
  45. 1t dtdo = aaaa H ds aa, e ai rdy- dx+, PF C, 1 (2)
  46. de de to
  47. C(5) Ldxd + dys-dv 1p+co La. Alx. 2) + Ay v) ay. do
  48. de
  49. de
  50. tolli potest dy per dx, X, y a. Et tolli pb de per dque, tam ope 6e9. 3. gener aliter
  51. dx -d
  52. jam est
  53. de de + deo deo =
  54. ergo, in aeq. praeter de et deo, ha restat solum dq: dx
  55. adhuc XX = 2XZ + 2) + gy - 290 + vr = Y 2Y + 21c0 + coco, fietque
  56. tX LXdZ - ZLX + AZdZ + ydus - ydv- vay + var d ipdeo + codco
  57. X (H. dZ) - Z(l X. 2Z) + y (dy- de) - v (dy du) = u (+ c0) deo
  58. seu (x.Z) (draz) + y - n (dy d0) = (1 + cd) deo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 156v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0312?run=74