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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 3v

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 4r); this page is its left half.

The machine reads it as

  1. Datur Sra = Sx co a
  2. ergo aco sit = Ex + bb Sart exis: X+g datur sei dx per
  3. quadraturam rationalem. Ergo datur et Saedco. Quae ratur valor
  4. ipsius X per co, fit aa coco hh XX + 2 hbbX + b, JXX + CX Af = X 129X rgg. Coco
  5. expere mvsi
  6. si sit g = 0. et ehh + 2hbb_ = 0. et 2 hbbff + bt e = 0, fiet eh = - 2bb
  7. unde ex praecedenti fit B Chh = etnff et e = +2f
  8. et aa coed = hAXXF ebsipt echh, XX + ex + _ ec: 4, fil
  9. q
  10. hh X (Cchh XX + 1 ehih = XX con X coco aa
  11. +Petih
  12. + eetti
  13. unde utrobiis extrahi potest redio rihilque
  14. lucramur.
  15. sed si pro X+9 scubamus X + gX, fid in aeg. 1. loco X+ g. fiet
  16. h_ RXX - = eeh = X + grCo, sed nihil hinc
  17. sit X + thXX + g =bx +C co, et fiet
  18. X = GhX AB- 2hlibCoq q +h- at hb C + bb co co
  19. gt +eC3 +
  20. bcX Hocobb
  21. 2tht c + bb coco
  22. 14c3cd
  23. Huius ergo formulae
  24. datur summa
  25. Sit data formula gentralis X= suv pV. fiat
  26. D = bco: p. e. fiet in 5, X V= F L abco + L psup nacb co + bblito
  27. fit - htia et p = a
  28. naat
  29. Nct ibee + Ebpe C0
  30. et mmaa B nahh(t H) = (hF) seu n mma: sis
  31. et immaa hh EbAH) = (= 2btb) + 4C3 seu vel tih = mma: n
  32. nab
  33. cu fiet c c3- nab et fit
  34. X = Omma
  35. 2H
  36. +Lb Co +: na +rigmaatim ed + bb coa
  37. + nab.
  38. Haec autem fomuta comparari potest generalidatae s aus
  39. Sit scilicet px = D+ Saamm taari +ppoV isis mn, si modo
  40. se e id unum observetur, ut sit in data r= p
  41. Itaque jam formulum Assumamus jam formutam
  42. e p ab Z= bx + 12+ siam altrm v
  43. = Y bx + 12 + SbbxX + 23x + 24 = Sbxtnt sit, debet
  44. debet 14= bb pX + 23X +24 aequari quadrato, bb XX P 2bX y + ccyy
  45. et fit, X= cc yy - 24,:, 23 + 2bc9. et fe 14
  46. et fit 14 bb c y - 2bb cc 24 yy + bb. 24. 24 8
  47. + 23. 23CC y9 8- 23. 23. 24) 83 2
  48. F4. bbcC 24yy 24 23. 23
  49. (7, 2bCyF23
  50. 23. 23Ccyy - 2323.29
  51. 23. 2bCC9= 23. 2bc 14)
  52. +26C. 23yC- 2bcB2y 24. 23. 23 +24. g. 23. ky
  53. sentia q de Abcc yy + 23cy + 24b,:, abcy + 13
  54. debet esse + altorvio evantsceret indeterminatas
  55. 64)
  56. +4b023. 24)
  57. +b ec y + 23Cy + 24b
  58. +
  59. Y 2bC12Y
  60. =24 u+ bbccqy
  61. :9 2bcy+23
  62. 2baC S, 4317y + 34yt 3,:, a + H fiet Posito 20 =1
  63. Sbc 43 - 13bC et 32 c et 39 = 23. b fit c = 3t et 23: 2b + 12 = 39. seu 12 = 37- 25. 30
  64. et eb 24: C + 12. 23: 2bc = 34. sel apt 2 et. +bb + 12 23 2b = 34. 4bbc
  65. (9 seu 24: c + 32. 23:2bC, = 23, 23: 4bbc = 33 seu 424bb + 2b.3223 = 23, 23 = 4603) in
  66. seu _ C = 4. 24 blet 2b. 32. 23 -23. 23, :96633 = 21 41. 2. Ergo
  67. 23: 412b
  68. u ulum sueanium et, vie ntren cilica
  69. ita videtur haberi Eddsirum aequaturus 14 summandam reduximus dimensionem cuvarum colicaram

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 3v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0006?run=73