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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 85v

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: 0.78.

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The machine reads it as

  1. Quadratura altior reducta ad sonicam
  2. = a, t a fiet X = a - a y,: y se X = aY a) a y 7
  3. (B = a:, X + a fiet Z7 = a a v,: v bu Z- a a v.v
  4. atbus + slemus = co fit a +bus lxmu +2 satibus, lamus 2) r
  5. Aey, nepus
  6. cteu utpus
  7. et co + ae + 2by + bby4 + (2 Ulmytn - 25 at by 42Cd (+ my 42 an, camus
  8. sitit addenda
  9. utpis
  10. C+2C ey+ eegy n+ inputppy.
  11. arbus, lamus
  12. ntpis
  13. etey
  14. (0 + SD = co fit O + D + 2S0D = W0 et 40D = at + O= 5 = 20D4 - 2. 20D
  15. (4) creys, ntpus
  16. seu fit O + D + c = 205 + 20c + 2D at pro O pribamus 0: 6 pro D scribamus D: E. fier
  17. +(32 ∞ et Oet + D6 +964 20096+ 2086c + 2D86 co sont atbus 6= ct ey D= Lamy. P.nt
  18. fiet an tap tan + bny
  19. P3
  20. cl -
  21. -
  22. 6
  23. 63- 05 =0
  24. Bpgy =0 seu bp = em an = cl seu p = em: b n = cl: a
  25. et bn+ ap= elt em, undetollendo pet n fier
  26. vel: a +aem: b = el + em seu bbel taaem = abel tabem
  27. siet mo m bb ccra abetb
  28. quibus valoribus ipsamur n, B p substitutis in D. 8 fiet = l + abel bbl y,: cl_ + em y
  29. et fiet m = bbl abe l - bbcl, :, aae- abc
  30. ec et +acel sy sed ita moncratire e nominatore divisis
  31. per ael -bel, sit D: E = 0: 5 contra intentum. Ergo sic tollere non licet, ut deprimatur, aeq. 2 ad coct
  32. seu 3: 8- aaet abet rat da et Y 3y: +
  33. videamus an tolli possuit termini in quibus extant s et is sed ad eam rem opus foret aequationibus
  34. ascititiis sex id est consunterentur omnes literae nostrae, et fortasse nec sufficerent
  35. s estet si redemmus ad aeg. O2 + D + cot = 2OD + 2O CS + 2 D C et faceremus atbytcyus
  36. et B = l 4+ my + ngy et cd = V, r+5Y+ non tamen habtiemus literas plures quam ante et
  37. nitilominus ascendemus ad et yt. quid si faciaamus C = a+bus ei D = l+ m y et co = v Tresy hoc
  38. posito habetimus n ita ut detur satbu + VLAmu = v seu tarbus + stamus = v Trtsy
  39. aa + raby + bbyy _+r tersy + Ssyy v = + 2aY + 2a5y + 2b5yy
  40. Ita ex O + D + c0t = 20D + 20c0 + 2D cot fiet
  41. U +2lmys + mm yy
  42. =2b m yy
  43. 2al-2m y
  44. =2bly
  45. ve
  46. + 2 b r 1s
  47. + 2F + 215y +2mSyy)
  48. adraturas Conicas promovendi
  49. mi
  50. o altiores, cum aliqua genealitate. Nam si faceremus 5 =0 non esset
  51. a
  52. quadratura ionica, sed quadra tura absoluta
  53. aequemus hanc formulum generali simili
  54. 4. y neyu + igrv + 29ne royy er
  55. ∞ 16 + 15y + 14yy + 24vD + 23yVP + 22yyVV + 32V F 31 y V + 30yyv = 0
  56. sen Y16. 19- 15,
  57. et coparando fiet: a - l = Yi6 b - m = v14 2ab + 2Im - 2a m - 2 bl = 15 C r - (25, 5 = 130 31 = 2130. 3
  58. et a + 1 = - 24:2 et b+m = - 22: 2 et 2a + 3 + 2b+ m = 23 sive - 24 430 - 22 132 = 23
  59. (a = 2116 -24 l = - : 116 - =24 b = 5 114 - 1 22 m = - 1, 4 - 2 32 r = 132 5 = 130
  60. 15 = 2 +14. 16 31 = 2 (30. 52 23 = - 24132 - 24 10. Itaque tres adsunt cestrictione
  61. perinde figun alquam aquatio est conice Quadrani potest Figura ad quam aquatio est
  62. 16 + 2 s. 4. 16 y+ 14yy + 24 vv _ - 22 So2 yWV + 2yy V + 32 v + 2 130. 32 y v + 30y vt =0
  63. X
  64. poro 4
  65. nam fit pelle
  66. + 2. 16 + = H4Zy
  67. -+ 4 222
  68. 132 + 130y
  69. (.Hib LVy
  70. + Y- 124 - 5 22d
  71. t conditiones, possumus
  72. 32 + So
  73. introdue y, ex pro a substituendo ny +M. ubi _ arbitraria scopo inservit C
  74. intreducere y, pro X substituendo mytn, ita duae nobis occurrunt vibitraria. sit scilicet
  75. se ab + 45Y + 44 gy + 54 vv + 53YVV + 527XVV +62V + 61XV + 60XXV =., et pro x substi
  76. tuendo n, fiett 46 + q5u, 45nY rAnnyy + SAWV tSSRGBB + SEmHyVB F BLV L binyV + Sonnyy v -0
  77. seu
  78. eu
  79. 62
  80. +45m 2 +244may
  81. 44 m
  82. +53nVB L. 52tiy bB
  83. +58B VV
  84. +6.m tabo mug
  85. +60u
  86. + 15 y + 14 yy + 24 vV + 23 y VBF 22G9 VBF 32V 4 31 yb 4 30 yyV = 0
  87. 16 15y + 14 yy + e4
  88. 16
  89. et ob 15 - 21.918 et fiet (2) 45, f 2. 44m nn) = . 46+4 5m + qamm r 44 n) et habetur M
  90. Basteruirgharum
  91. iga potestl.
  92. ob3- . - vel ob 31 =, 10. 32 fieret 1 61 + 2. 60m (2n) = 62 + 61 m + 60mm 4. 60 (i n) unde etiam haberi potest H
  93. ob 23 = - 22132 = 24 130 fieret. 8853 m + 2. 52 mn = = 5Enn 162 + 6, m + 60 mm - 54. +53n L 5 2 nn n 160. Et
  94. ila habetur B, et proinde unica saltem restat determinatio, seu
  95. fit
  96. 53m + Z.52 ma = C = 52 nn, 61+260m - 54 + 53n+ 52nn I 160
  97. ut indagemus n, biet 452 (+ 4. +5. 44 m + +. 44 mm) = 4. 44. 96 + . 44. 45 mt (4. 44 mm. Itaque evanescit n
  98. M, seu res redit ad 45. = 2 144. 46. similiterque ad 61 = 2=
  99. itaque posito m = 1
  100. fiet XL e 51. 6) 1_ +C0 Et ~ + 2. 54. 6d 4 253 6ON, adeoque sit n = - 254 60 52. 61 + 253
  101. sed in aeq. ultima haberi potest m plane, neque enim licet facere n =0. neque etiam licet fatore m
  102. e
  103. estant
  104. di ones datit a i e ecurs a
  105. sicetores oie ane ntus ao erei
  106. relinguere utcungue vel assumerer nere qo ita aegu
  107. aa bb+cC,
  108. 2ab- 2ac. 2be
  109. non est extrahitit
  110. 1
  111. unde res hucrda
  112. e
  113. etey nepys

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 85v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0170?run=74