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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 130v

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. 129r); this page is its left half.

The machine reads it as

  1. W=
  2. NZ db
  3. ZVdZ =
  4. SSEao a + (svaq der
  5. ipsi
  6. Sit et sint Z et v ratices quadaticae, potentia commensurabitres
  7. erit zax rationalis. Et proinde (ZudZue faciliter quadratio quam szudr
  8. aut
  9. dt = 1Z0 = a F Z0 = coco _ Zdo + vdzue - 2c0d. seu
  10. deo = (2 do + L dque sit v = a + sx et Z = x
  11. fiil co = Vax+ xx = L ssat sx p +: (satX) dx quaeambohiber
  12. ZXX
  13. possunt quadrabura rationali. Ergo haberi potest et dx Fax+xx
  14. quae resolutio notenda
  15. Repetamus. C0 - +Z ergo c0 = sq S Ergo deo =, (2 do + L de
  16. Sit eL (ex sit v = a tZ et do = = dZ: 1Z.
  17. Ergo, ce
  18. aZ +
  19. +Z = (L (10 s + saqe s =) , is 2 posu sato
  20. a Sunma Schi valyta
  21. ee
  22. Hinchabetur sa
  23. Hinc haeetur sdz
  24. sel si quia Y∞ + 2) dque vaz +qs sesd t E + SdZ sdz
  25. 7 = x erit sdz t= as ax Sa + Xx. H Hini patet X d... et s...
  26. pendere ex se invice
  27. (tZ 2stZedque = sa sdu SZ + sa saque s
  28. ( (17 1Z
  29. et fit E( ZB = datirta,
  30. bt sgra, szra
  31. si esset sq + a = v0 + al i fit Z- v + 2ac WV +ac - a
  32. b+qa pendet ex sdq S,Z
  33. s
  34. si = sded
  35. (b+ t2ta
  36. fiet 77 = 2b
  37. U W0o Z
  38. --
  39. 104
  40. +
  41. Si v = b+ 1Z+ a
  42. fit du = 2dZ:, tEta
  43. saque serota
  44. btrzra, rita
  45. + 4b610+ 4b101o + 1 ((bb) 1t (+ 4bb10) +4blold F)
  46. 418
  47. e
  48. 4106
  49. Ergo pendet ex curvae conicae dimensione
  50. sit Z+a = cp 1 sit Z - Y4 - a. Ergo feod - 21 sb + . Ergo et hoc pertes
  51. ipapa
  52. ex Corica
  53. Vra, Xb, XtC = 2(d x xb, XC: nta esx Xra. es, nrb + x L XTB, Xtb, :, XrC
  54. 2
  55. Ergo Vixta, X+b, XtC = x Inta, xib) + (X+ a, X+C) + (XFb, XtC). sxta, Xtb, xtC
  56. xta, x+ b, x+c.
  57. seu lxna Bxib, nic = (dir Cna, nib) Aera, nrC) + (ur b, 21C)
  58. . VyX+a, X+ b, X+ c
  59. 3XX + 2a X + ab
  60. seu tyXra, neb xac = (dx
  61. 2 V, X+a, Xtb, XtC
  62. V. X X + tabe = 3 Sax XY
  63. (X+ abC
  64. ergo Cgxrrca, hxnato = (dx
  65. 6C
  66. sit jam atbic =0 et ab tac+ b =0
  67. et in vtx x + qu aberunt
  68. termini intermedii fietzue
  69. Quod est magni momenti theorema
  70. Corin+
  71. peraa = Suidr, Ex ib omia hubi rnimbi a
  72. ua agx sure
  73. tB
  74. hx (hrri ) + gX (grx la
  75. gnxtar, hxx + b
  76. Sax
  77. hXxta, gXX + b
  78. hhx3 + hbx
  79. dd
  80. ga.
  81. FgXXta, tXXHb
  82. x9 = fxdus + X syx = S (Ax sydx + sxydx ita habemns regulam de
  83. summa summatum Hinc Mxra, suqua = (hax psperb C sea vacio
  84. Et pari pire Thxxta Sxdx sexxib
  85. ia
  86. Schxta Exta Soxi
  87. exta = hxdX Ndx 1
  88. hxxra
  89. Idx (hera ptgrrb
  90. ixta)
  91. X+X +. X +X

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 130v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0260?run=74