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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 40r

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: 0.79.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. . sit X= yy fiat Ca Cydy Sb hobysus
  2. (A+ bx
  3. dx
  4. AolX
  5. sihtabyus
  6. rgo ipsius s figurae ad u
  7. pholyu
  8. t hoc ergo habetu
  9. halyi
  10. ratur momentum in verticet audem
  11. satur momentum ex uxe seus 5zzdy. itaque datur reca in quam cadit
  12. centum gravitatis nonspens sepper per cocursum condrrectricium
  13. Z eliam = Y h Ab gy - ab s 9: bh-llyy
  14. 1
  15. hat, Z = 15 54 + 9b G yy -ablly : h - ly
  16. tha
  17. a - ly, Z = . . . . . . . . . .. y : h+ ly
  18. halusque + h - ly Z = EhZ
  19. quia datur Jyzdus. Ergo
  20. si daretur S(+ Caus vel sih. du
  21. daretur SZ dy
  22. sit ds ti abhitix - abl- itq d, h +.. vy B-.. . datur
  23. U
  24. ry.g +nG dus + 4 = X teq irtqus +hq
  25. y
  26. datur si. yZ y3
  27. h+ly
  28. h+ly, y
  29. y etc. Namdatur Curetu sit
  30. Datur generaliter (ZXC dx Modo e sit integer. Ergo ponendo X = yu
  31. et ex =ryds fret SzX ax = (Z y et
  32. dy
  33. Datur fax Z et f quaeramus seriem talem
  34. XZdx, SX Zx, sx
  35. haberi posset daretur et
  36. X
  37. dx
  38. 2t y dx
  39. SX Z dx cuius lex
  40. quia nihil refert sit Z = Saa- Xx haec pendet ex quadratura circuli
  41. sed XZ seu X saa- x redigamus ad rationalitatem. Scribamus potius Z = Trax-XX
  42. = er ca xvia fit 2ax = XXa = XXVV seu X = 2a0) aa + vD
  43. et ax = =4a bdv, pilaator 2 2av: aatve ergo fiet
  44. Qex = 4a vD do, (2) aarvo, sit aarvo-
  45. si tangests, t erit a = = - +3 + f etc. Ergo da = 1 8- t + F etc.
  46. erua
  47. HH Ergo dar Ergo an = a(dt. sed + seu A T ad BC seu traxXx
  48. =
  49. 1+ +F
  50. ut a ad auxseu
  51. + = a Y2AX XX :j a = X arcisse arr. A. perK per La = sect A e
  52. et sect = segm ABC + = Frax -XX a =X. Ergo E segm. ABC = arc. A per a = rax = XX (X)
  53. ergo Lt seu 25 Srax-XX dx =aa5 dl = at (a. X)
  54. ad est cum v crescit, X decrescit
  55. ax = XX _ sit Z = VX: a si et ZaX - XX = fOVXX: aa seu 24 = aax + vVX
  56. seu 2 Co X Ed,: Rat vi et dx = - 4 dv;: 12) aatvo Ergo Zdx = BaVdv: 13) aa +vV
  57. d = 2aa0: aatd. Ergo (3dx jam si v = est Et et 720
  58. 4=20
  59. si 220 tunc vel x 20 vel X= 2a, et
  60. a qpitio cum 20o sit fyex=
  61. quia igitur oportet esse infinitam, cum X 20 dinc inverso
  62. nit
  63. vonasi 200, pt bd fit xC2a. Hin fit
  64. plane modo est procedemem nempe meipitur ab X = 2a, quia
  65. tunc v20, et tanc inde cum v =1 fit
  66. Redeaum ad
  67. 6

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 40r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0079?run=73