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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 29v

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: 0.80.

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. 30r); this page is its left half.

The machine reads it as

  1. rit
  2. +BDn ut 3r 30.3obbrB + 2. ZobbrrC BZ Hbbcc ZZ
  3. 4110 -. - - - . - + cebbr rr aa + Z. cc bbr ra a Z + Ccbb ( H. ZZ
  4. _bb
  5. OdD5
  6. sit r= c+f
  7. Videamus, tamen an non liceat facere e) constantem magno utique alculi compendio
  8. Ergi Si esset C= obix, ex aequatione fundumeritati fielet
  9. do
  10. =aat1, 40
  11. sit C = m et D = fiet mDD - bb D + cem = 0
  12. sit jam D) = 30 aV + 40 aZ:, 60Z+ 56a, Et fiet
  13. FM)D.. . . . . 30. 30 aavV + 2. 387aa v Z + 40. 40 m aa Z3
  14. = mm 5)
  15. abb13...- 3160 .. .. 30. 60 (b6 a v7- +0. 60 5bb a7Z. = 30. 56, b 7. aaP - 40. foz n n 1442
  16. MM
  17. Enm,
  18. 26b)
  19. +cem
  20. + 5b. 5b cem aa + 60. 60 ccm Z2 +2. basbemaz + 1. bo sbcem az
  21. Et fiat 40 = c + 60 = a. Ergo, oCCaa = a a Cbb) aacC C) =0
  22. fit ox 2uacem - uac hmm
  23. Ergo exito. 4omaa
  24. o. siqbt za profilo-
  25. +6060 cem
  26. tccaa f aacce
  27. 2aacCf
  28. L= ac
  29. F ad, c bb,
  30. caycets
  31. Quia bbenim = 2Cm, hirc tota aequatio diridi potest per m
  32. desructa tma
  33. atb, a b = Ba - b1, c
  34. Tollitur e sublato termino aZZ, reperio toli etiam terminum aazue, num
  35. nam fit. Rc. 56. 2cm aa Z + 2a. 5b. cem aZ=c
  36. itaque tandem ex aequatione nosta fiet imo tllitur etiam VZ
  37. Itaque calculus tam facilis non procedit ad scopum
  38. 30. 3 a ox
  39. Videamus an evitare incommodumliceat, non assumendo 40 et 60,
  40. ut fecimus, sed quaerendo, (compendio sit bb +m = ag, et aequatio ad destruendu
  41. nimum
  42. terminum Z3 est 40. 40 aa m - 40. 60aag + 60. 60 cem = 0. Et si
  43. Hinc 40. 40 40. 609 + 60. 6099 - 60 60gga6060a am n ce
  44. mm
  45. qa nm
  46. seu 40: 60 = (_ aagq- mmcc): am
  47. 40. 40 aa - 40a60a9 + 60. 6aagg- 60 60 aague 60 60cc mm
  48. amm
  49. amm
  50. fiet 40: 60 = ag + sCaagg - 4 cemm), : 2 am
  51. si faceremus ag = 2cm, se Haaggs dumm) =0 recideremus in priora
  52. et fieret 40: 60 = ag: 2am = 2Cm: 2am = c: a. Sed si facerenus
  53. ag = - uem fieret 40: 60 = - 2c m: 2an et posset esse 40 = = c et 60 = a
  54. et fieret bb + mm = - 2em et mm t rem ec bb et nim + 2cm + cc = cc = bb
  55. et m = H(Cc - bb) = C seu M = f-c. Videamus jam an etiam hoc modo
  56. destruantur iqe et a7, Ut vereor ne sit idem. ll e pro aZ f 2Cm Ca +2aCCm =
  57. et pro vZ vZ, fit -2. 3oema +30a rem. Ergo relicta adhuc m, faciamus
  58. Faciamus
  59. 40:65 a ag + (aagg- +cemm) e: et 60= 2am,
  60. vel 40 f0 - bb +mm + YCb + m + abbum - q ce mm)
  61. bb +mm = 2mn, fial 40 = n r. 40 :60 = n + Vbin- cc): a
  62. nn-ec
  63. Et fit aZ, = + Nan -c4)) 2mn F a ccm. = ram_. e _nlun - c)
  64. Haec stare possunt
  65. =a 2mn = 2am, dena - cC)
  66. ut Quia r est arbitraria, modo apta, faciamus nn = bb + cc, fiet m = n + C et 60= a - nt B
  67. aZ, +2 (n + + (un - c))ma
  68. mm - 2mn + nn = nn - bb fit m = n + senn - bb)
  69. Vemamus ad nostram aequationem et his valoribus pro 60 et g0 substitutis videamus an destruatur 22.
  70. o= nn M H2nomixbbmaa au-a (-armub) Laaccm fit bb FcC = nin, ut oportet
  71. no mntbb ponendo 2m, fiat 40. quaa =240. boAN + 60. bocc fit 40 40 : 60 = n + Y(pn - cc),: a
  72. seu m = p + C
  73. seu 240: 60 =. n + b,: a, sen 40 = n + b et 60 =a, ut prius et quia mm +bb = 2MN, A sit m = n + Y Cnumbo
  74. Repotaums quraes
  75. un FEkb +bb 2 nF X
  76. nten
  77. tecai
  78. 0. = 2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 29v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0058?run=74