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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 88r

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: 0.77.

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. 89v); this page is its right half.

The machine reads it as

  1. invenio Quadraturam meam Geeralem Arithmeticam
  2. Sectionis Conicae ex centro ic consignatam. ertor Genem
  3. comprehensus areu sectiones (ontea à vertice
  4. ad ejus extrema ductis aequatur rectangulo subsemi
  5. et rectis ex centro
  6. targentis in verbce, inter verticem e tangentem alterius extremi interceptam
  7. et rectargulum sab dimnidus lateribus recto et trausverso seu quadratum asemi axe
  8. conjunato, esse unitalem. Et + esse + in Hyperbola, sed- in circulo vel Ellipsi
  9. = 444Ht- 49ttX
  10. XX - 4 gtt X
  11. AC semitatus taus versum q
  12. CV = a erit r latus aa = qr. postso
  13. esse Y semitatus rectiuem SR, si ssit focus. AT, erit F,
  14. fiet ACG A = 9t - 59l + 9t 9t
  15. Baa Sat
  16. q0 etc=
  17. differentia foret at - H dt + + - b 1 et c = dt 4a
  18. aa
  19. a
  20. aa(at, quaeratur loguithnice
  21. aa+It
  22. 40
  23. aa - (t1) a+ t. -1, ac LF -1
  24. a- tf-1 a+ fY-1 D
  25. 2a,4-tr 2a, a111
  26. = -2a tog. et (vat = log (a - + f - 1) + log (a + t + -1), : 2a Y - 1
  27. = a log (a - t r- 1) +28 log (a + F Y- 1) :3 - 1
  28. rlog y = log y
  29. Gaaloque (aa + H): 21 -1 = W = au lou aa tE B S
  30. CB OFR+ R5 = 29 A5 = 2q FR = 29 - = F5 + V IY-
  31. Ergo 4g9 - 4qr(+ YV = FS( rr = 4 C5 ergo C5 = 94- qu
  32. Ergo semidistantia focorum est media proportionalis inter semilatus et
  33. differentiam semi lateris rectiX transversi vel pro gr, ponendo aa
  34. fiet C5 = 9q - aa et CS i BG.. Est autem BG - y
  35. cee quam operae pretium erit investigare ex t.
  36. seu yy :, r - EX = BB seu 2YX - ZXX∞:, r- =X = BB. Et fiet
  37. 4 - 2
  38. et AB: X = AY: y fiet 1 : + 2 = AT: y Deu AT - Y:, 1- X = +
  39. 2rX GGXX, : 1- v + XP H fiet CZ = 2X :, 1
  40. AT.F
  41. N, 1:, 1-2
  42. fit 2rgqx - rqxX = 44te - 2gX t+ + XX H sit . Y = = 4qu
  43. 1q:9
  44. en -2 aaqX aa XX = 44 l1 2gX + XA CA arK, GXx- 499 4qx + xi
  45. XX (a+( 29 tt) - 29a) x + 49 = 49 . 9g H 99 aa (t gq. ut 4g H)
  46. aatH
  47. et fit X + q = ga: + aa + tt et X - 1 4
  48. aa + H
  49. Saane
  50. et X = a faa + E et y = t - = + - ta Haartt tsa 1. ta
  51. t Laa +H) ta (tsaa+tF: saa +tt =y
  52. et CSG = L tgq -aa ta: Faa H = _Z
  53. 49912 +99ttaa + a99 Cujus numerus . Ergo
  54. 1
  55. =
  56. 499+ etc -gget 2d fit W + = log (a + HF 3- 1) + log.
  57. a gaau (+ Ergo b
  58. aat t
  59. V, a+ +s. 1 + v, a -t f1 = 2a0 = - + , seu v -
  60. et (ataa
  61. Saa +t+
  62. BD - X = (3YX (ZXX = YX, + Y XY):
  63. (aa + ltV
  64. seat
  65. exsoc
  66. sanoit auistErx areo sectoris
  67. (9+39ag eaq
  68. 49914
  69. a
  70. yy = 2 rX - Z XX fit dus: dx -E_ r - ZX, :y = (BG: BD = y: B
  71. 2AAGX = paXI
  72. +XX Et seu
  73. _ HE
  74. 1 aa +FF
  75. et
  76. verso, et recta
  77. t + (3+ = +E+ f etc posito t esse, urtionem resectam en portionem
  78. 2799X - Y9X =
  79. 499lf- 49Htx
  80. +RX +F seu
  81. a
  82. aa + et
  83. F-I
  84. log. (aa + FF.
  85. 28-1
  86. 2
  87. vaatet
  88. id sit nunus logaritham
  89. 20a) = cd
  90. y - 2t - x)
  91. 4g. aa 2t = rx = 2GAat- 29t- 4a H + a, , sqqu. at
  92. aa +tF
  93. aa +H
  94. dx- pa 1H) 8p + - 9 (Att vaa) 2F, dt - 8eaqt 39t.
  95. 5
  96. 5-
  97. aatt emet
  98. aarr
  99. fit dx = 6aa4t de
  100. laaret
  101. (5 + ga = 49
  102. hoc patet
  103. nam SV = CA = FV
  104. y= 7
  105. = aa.
  106. quia qu ac

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 88r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0175?run=74