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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 12r

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: 0.82.

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. 11v); this page is its right half.

The machine reads it as

  1. et licet haec aequatio ex duabus novissimis ducta
  2. suffecisset ad habendiam f considerandhm est d
  3. jam haberi ex praecedente. Et ita aequando
  4. eis ralores haberetur determinatio in datis contra
  5. intentum. Batodempe hhg: p unam constituunt
  6. quantitatem, nec g et p aliqui habentur
  7. Resumamus
  8. calculus nonsconus
  9. se Quaeritur fdx (ex tab, XX +ac)
  10. Xx + ab = aa sus + ab -1 3
  11. est N + ac 13.
  12. ExSN = ffOD+ aa 42 + 2af210Y
  13. = ab, 0D + + 2t il 3D
  14. +55O5 + abOD, 2a52O)
  15. erit ex tab in Xx+ aC, + al 74 ab q q 2ab
  16. f5OD + aCCD, 2a57) ()
  17. aa 2 + act + 2ac ti
  18. Sit ras 2 + 2act, = - 2a52 - 2abt
  19. estaf -a(b+4)q seu act+C
  20. semf = 2f7:, b+c compendia sit
  21. -2afi,btC= 9. fiet at- 4
  22. Sit a1l + a) (O) =9Z = gVOD Et primum
  23. Ergo ex pa ita ita 3+ VD in 1 -1(OD erit
  24. idem quod 3 + SOD in 43 - 2 105=
  25. 433 = Q OD aqu. quadrato s
  26. ob identicitatem nuperam, fit, 2=
  27. seu 2a54 +2acZ = 9 2af2 + 2abt
  28. seu (ab + ac) +HF (a+9) 4. Atque
  29. ita = - f(a +9) 2: a (b+C) = - p7.
  30. Et e ob a TI = g3, fiet:
  31. gff0D +9 aa 44 affOD + a24
  32. gab ODFgab B aac ODa CB
  33. ff ducitur in (aqu (b +au =Q qu(b+C) aatib
  34. (ab anca qu brd) acaab iu (b+C)
  35. Ergo f uanessit sportesua
  36. ab agu (et d) raba- ac aqu (b+C) 2ab
  37. Corficiens ipsus f. et gusbtc) - aqu (b+e
  38. (ab anetua Ac aabtna)
  39. itaque evanescit f, sed non ff, seu
  40. Tollitur egno terminus secundus aequa
  41. superest coefficiens ipsius
  42. (a, qui est. aqusbte) ab = ae u(btC) ac
  43. (abaaC 4a (6+) acaab ta btC)
  44. (qu bC) rab =a quo rerab)
  45. itaque aequatio sordinata
  46. + quexe
  47. Etri (t) p qaequbre I5 - rabi f alijpestas eu
  48. quae aequatio sividi post potest pen. bdc c- b
  49. et fiet (4f = a a qu (+ C), f + 2abff +a abb
  50. A) 2 ft = +a (b+C), B+ ab
  51. _f = acbrc) f + aagusbed
  52. aa qu (b+C) = 8a (b+C) ab
  53. +3. a CbtC) tat (rebct ebbtu
  54. seu= = 2a (b +C) t (qu (b +C) +8 (bt96),: 4
  55. quod vilstm sucedere semper, hatem sucedit in fonicis
  56. cum Xb4 C) minor
  57. im 4 4qu C0FC) sit minr quam
  58. seu gD = 3 3B =b5151
  59. D = 31 (9. a) -51, a.
  60. posset Z sumi constans et posset esss
  61. fiet g=a +aa cpi a + abpp = afs taac,
  62. pbsolutus in pigisi gaxitime
  63. ubi f alcendit ad
  64. nequit, nisi ii casu quo b +c
  65. qu (b+ C) tq aac ueta
  66. est coefficiens termini sum seu
  67. cb. iad nec hoc tolli monesteu
  68. ouihilo aequanicusosse umstuqe
  69. at Bforet f20
  70. ata sit pp= Haat ss ggt 2ssag
  71. issicaque res non semper succedet eaes rsto min
  72. fiet, aou (bc) + aa Cff qu (a +9),: at qu brc) taabfs qu Catu)= sftac; 1ff + ab
  73. porto p= F
  74. qub++ Ebteb
  75. fiat = Zd9. a) + 51, q.a (i
  76. ub destuotur se licete ta Mutetur haec imbyc se
  77. aequatio in identificationem, et fit ob ()
  78. fiet g = afftaac,: f5 + ab Et ob 27
  79. vedendum an possit tolli fb et ff
  80. compendib x B ++ to pro Numeratore
  81. 3+7 OD in 1I - IYOD
  82. X= Pa. F10+ a 4 = as
  83. ubi prorsus pn a+g ponendo valerem 2af5 +aa (b+C):, f + ab
  84. fit a que brC) ( qu (5ftab) taac ff qu (2aff + a a (btC)
  85. aqu ( b+C) qu (1F +ab) F aab ff qu (2aff + acb +)
  86. oportet autem
  87. ita fE vel ac surgit ad aequationem biquadraticam
  88. esse gsf ut mujorem qua fF+ ab, et fs +ac, simul affirmativas vn simt negativas
  89. itaque si ff possibiliter inveniri potest, res est absoluta
  90. e hs clipiis
  91. quod si utrumque evitari non
  92. A+ac cum ft tab, ejusdem signi
  93. aesolbendam prxinam prituam
  94. datoe ut Ss sit affirmativa pollilili ss eatu
  95. Non ausim fidere adhuc blondimento Entus
  96. successus quia hinc duceretur quadratura abso
  97. nte rationalis, cn 10) possit aquau quo
  98. t l
  99. eubbusor1) ab aabb su b)
  100. a)b)
  101. 3be asbis) pb. unis
  102. i
  103. L i BEP
  104. Mputram ipsaum Z et
  105. ponendo equalem
  106. Au liot facere fftabu
  107. nec ff + ac 20

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 12r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0023?run=74