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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 93v

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: 0.81.

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. 94r); this page is its left half.

The machine reads it as

  1. Idem plone
  2. in circulo alibi
  3. In oini figna constat ex alibi a ut demonstratis
  4. productam dare differentiam applicutarum
  5. applantam dvisam, per
  6. Est applicata y. producta p. critse diteletia applicalte Datarra proxine majore
  7. In Htyperbola, cum applicata y sit sax, + X) erit Y= ax+ x. et ut habeatur producta
  8. Sax+X a + 2X, vel
  9. fiet: 27 = ap + 2X p, vel, 2aX ut 2X = , et ep = 2AXA2X
  10. a + 2X. a+ 2X
  11. Tax IX
  12. sarte
  13. a +
  14. Ergo figurae hujus, iiqua aequalio est. a + 2xa = y. quadrtum
  15. haberi potest. Quam ut per partes examinem pate
  16. =Y, dare
  17. TaxIX
  18. ax+x2
  19. inde fit: a+ = axY + X5 vel aX + X,, vel a2 + a = aX +X + a, vel
  20. Sa + a= a + X. sumta jam aequatione hac.
  21. vel posilo at =x
  22. Ya + a = X. Comisso a, quia istante) potest rursus aci.
  23. = Fx a
  24. + unde y =
  25. aX sive
  26. vel vel y --. 1. , vel y = a
  27. o v0
  28. r a
  29. vvel X y - Y a = a. vel X = a + a vel
  30. idea in Ercul facaedu
  31. X = _ S +a. Ego in tanc landem figuram superior aequatio redicitur.
  32. -y. Jam altera: fra
  33. Taxty=
  34. =Y. dabit Xa y Side X. = y.
  35. rar+X
  36. aXEX
  37. est trgua segnituted
  38. ac pronide Xa = ya + Xy. Ergo X = Y) XC = X = ya, ver X = ya d eet
  39. fier potests inde Y= X. vel ay = Xa = Xy, vel1 ob
  40. auyr
  41. a = a v
  42. tam a =X in falle alibi ex ostensum ex Z pudatura Abpribolae pendere.
  43. pu vel Y aex - Yx = a vel aX. a yx vel a - 9 = y. vel 1- 2 = y; vel
  44. y - 1 -= sae-. Ut productam huus figurae habeamus, fiet:
  45. aX =X = 27 X ac pinde a p - y p = 2y x, vel p = 27
  46. sulstituto aequivalente, fiet:
  47. a2 tn
  48. ut P ad y, seu ut prad 2x X ad (a) a, ita p- X ad 7.
  49. fietque a- a
  50. et pro is
  51. a= 1a- ax- 2X -_X. Jam fiat
  52. a - a + a
  53. 2X -+X
  54. 2XLX
  55. F vel 1X = 2X ad Z
  56. sa= a -
  57. 2X - X
  58. vel a a- ata. . Atue hiorum summa
  59. ida a -id q a
  60. 1X - a
  61. aequalis segmento duplicato summae omnium sae. Ergo dimidiata
  62. Bad u
  63. allorum summa aequalis segmento hujus ergo differentia inter summa
  64. differentiarum inter suntmam Ya a, et ra-a- a ta-a
  65. semper ect Triangulo post absectum segiaentum residuo
  66. 2X -a
  67. aequalis
  68. vel
  69. 1a- a - sa- a + aa a quatrabiles, g 1 1x+
  70. Ergosi
  71. Aa
  72. 2X- a
  73. Sa a + aa a=, erit umma
  74. 2X - a
  75. omnium y quadra
  76. Alterntia ergo horum quadrata etiam altra quadrati erit? Inquoramus
  77. fantum in a a - a = y. fiet à a- 8 - y, vel ax - a= aXy + axy- aXay
  78. 4X + a- aXa consiveem pine.
  79. sed haec nimsplis
  80. vaey
  81. aa a
  82. 4 =y
  83. ide intirculo
  84. Ergo in circ, X Maja est
  85. inor, in Hyp. hoc loco
  86. major quam a.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 93v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067993:0186?run=39