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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 41v

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. 40r); this page is its left half.

The machine reads it as

  1. XX - bb, XX = CC = 0
  2. XXD ab, XxHaC = aagus. sit X - m nun VVt aupV aq:, Yer 1 exat V aat
  3. Xx+ ab = uM V+ 2man B + naa pV +2maqu
  4. taannv + ranaap V Lap aequr
  5. sit X am v nanV + C; ro prratotunt + vo 1 aap aqV + agq
  6. xtab, XX = X1a =
  7. quiar
  8. 4b-
  9. amv taun- p
  10. H
  11. X: a = mo tan: pV tar
  12. =X + b = amvtan + bon + abr =0 et
  13. sunt quatuor radices nova aequationis am V + aat ZBN (,V + aah -bpr, v aat + Cpr L nat
  14. D.
  15. au ex
  16. aptus
  17. a bP
  18. Et afes
  19. si esst aaR +Vp = aa _ - Cp fieret (a R + abp = aat A = bcqr) = ( B - A N + aabk b cpd
  20. a+b
  21. a - c
  22. fietque a(brc) pr = na (b+C)h et prodirent duae cadies.
  23. t abcar = aa (bC)n, quod inutile
  24. itaque non possunt fien duae radices aequales,
  25. quaeritur ut silut ut tollatur terminus ultimus et penuttimus, pro ultimo tollendo fiet aan = acr =0
  26. oralis f sestruatur
  27. temantur termini primus et secundus iptro primo destruendo it sit am-cp =0
  28. seu an = CY. sit tercinus renulli
  29. sut p: n = a: c. si destigatur et pe selundus fiet summa omnium
  30. aequalis nihilo, fiet Nan +b + anbr + an + Cx + an -er =0
  31. amtab
  32. amop
  33. am+cp. am-
  34. an FbZ + an -br = aamn (t ambr - bpan) -bpbr + aman an bu tbpan) bpbr
  35. am tbp am-bp
  36. et an +Cr + an -a =
  37. amcp
  38. am aamm = bbpp
  39. raamn- 26 pr
  40. aam = cepp
  41. et omnes quatuor dabunt + 2amn = ZaabCnmpr - 2aa mublpp + 2bb ccpr 1 =0
  42. amtep
  43. +2mn = 2aa bbmmpY = 2 aamneepp + 2bb ccpY.
  44. i po qponendo a, prossaenc, fut 24a Cn + a 2bbccar aa ctaraa enbbaa
  45. seu divisis omnibus per C sit
  46. Haabbccr Paannccaa
  47. Casiet 2Cen + 2bber - 3Y = abbn = 0 = cetbb,
  48. finqus sen: Y = + bb. = CC, C, :, 2 (ce b q (bb- c1), seu nn: Y = C: a = m:p quod heliet
  49. sit X -
  50. seu M: y = - b: a
  51. v mrotanvtaap,: quotarv +t a
  52. bquotabirt
  53. pabe
  54. a
  55. bber = acen
  56. si terminus imus sit o, potestfieri ap- et =0 seu p. t = c. a
  57. ut tolatur pe secundus fiet Gan. + 4b +.... pl quam quatuor, partium summa
  58. eadem quae ante solum pro ponendo q
  59. am + bq
  60. frit. 2On 2accn 1 ibe C, -4a mase tm- 2a ammor (bb +CC) traamnqq bbtC) + 4bb
  61. et pro M porendo b, proq fint 4 4abn (bb n) + 2aabbar (bb + CC) 4 Elaa bnaa (bbrcC) F abbccaeY = S
  62. ta
  63. et firt -r: n = 2aH H - ( a (bb +CC),: b (bb +CC) - 2bcc
  64. seu _ r: n = a Cbb = cc); b(cc - bb) firt r: n = a : b = - q: M.
  65. pari jure si destruamu etiam penultimum fiet r: A = = t: p = a: C, sed ita fieret a = b contra lyp.
  66. sit tamve tanno+ ap quadratus ob D + aan tabrx + a p, aabt quadratum
  67. superest dispiciendum an liceat habere quadratos
  68. 11, 6,5, 1, 3,2,t
  69. am +bq
  70. cntba
  71. +bquo + bYV + aabt fiet 2 qu aantabis- aep + abbt
  72. am +bq
  73. amtbus
  74. seu aann + 2aabur + bbir= Lamap + ambt +b gap + bqbF= ap+ It, amtbus
  75. aann= 2aab nr + bbrr L) ’amaxt an ab -bt, am -ba
  76. qu (an +br) =iam +b9, ap +bF) fiet 4abir = sab t gabpus
  77. m seu enrntiva
  78. du (an -br) = T, am -bg, ap- bt et Znann Fbbrr =4 aamB + bbat et L Y nanniblrr a
  79. unde fiet, ac r, aap Ipgaax =aannt tborrt bbqet, et sit dg a n Tann +bbrC 2aan
  80. bbIt- aapp
  81. et m = a bb arttZaanrpp) Laanh ebr) Ea: bb t3-napsit
  82. 4
  83. marpor
  84. seu mD (aann +bbir) P = 2bburt; Aaapp - bb H
  85. superest una aequalio acun -Zaaeu 4C qu (ap - er) Aaamp- acmt - ac qu iccqt
  86. ex 1 et s siit an qu (antbr) gul an cr) a nc amtaco. ot (b+C), bc
  87. bbm alran cer reran 2apt (b+C). Et nom q
  88. ubi absuntg et
  89. pro m et substitueno valores, habebitur aequatio in qua ns t afsurgit ad qua t: p assusgit ad
  90. ut rusus Iqu (an +bi) aump, b qus an CY)+ qua
  91. datu et tabatur, ipsi n ir manentitus. sed oporeat rem absolvere

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 41v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0082?run=74