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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 179v

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.

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. 178r); this page is its left half.

The machine reads it as

  1. Caxis A Ex Y agatum nomalis in rectam
  2. AB, quae sit YX, et in rectam BC quae sit YZcomplatur rectan
  3. gulum Y ZBY. Habemus trimnenlim sunt secae ntque se YX et BV in W.
  4. sint AX YX, BZ, _ 1Z EBA, AC, CB AF Et
  5. Set 32
  6. pL
  7. Triangula sunt similia ABC, BXW, YVW
  8. BX,
  9. DC BW + WV = V XIV+ WNY = y
  10. BW
  11. L(D)+ Aq = v
  12. nx) + Z - y
  13. fit y = n + unque seu y- vn + Z -
  14. m.
  15. Cecom -Zu - gn hn
  16. un
  17. Em
  18. = vp 4 Z
  19. H= 1M
  20. seu g nB, + MZ et l - X = mV nZ seu X = l + nq- mo
  21. x
  22. m
  23. sit AY curva conica, cujus vertex A talus ricam semctats redum lates
  24. sit AY curva conica cujus vertex A, semilatus rectum Y, semitiams versum 9, fit 22X + xp = yy
  25. B .52
  26. Ex puncto C dato ducenda est perpendicularis CY ad conicam perpendicularis C3
  27. es agatur normalis EF et EY produratur dubidem
  28. eidem occurrat in p.. Diserentiando Erax + 2xxd Lydus seu dy: ex = Y = LX,: y - IX
  29. rit pX Y G: GE firt r + Y X,; X+f, s re t Z = r + ZX, :y = X+f, :, e-y
  30. sit ex Ex E in
  31. fiit re +r ex = ry = Exy = xy+ fy
  32. su (147) Xy Xfriq f Z ex = r e
  33. compendo d +r = h ftr = 9. et fint hxy +gy + xex - re-
  34. +ErX = 2r + 2rnzu- Ermr
  35. 6=q + 2 ex- +EF + UnZ +2rlu fr unez frmmvo
  36. =
  37. n
  38. ADX BX - l - X
  39. L
  40. Im
  41. duner
  42. LMV
  43. - re = - rell
  44. +Gea = + X el 4 eh F etmv
  45. + gy = H
  46. + gluz + glno
  47. t 4nque + h lbib
  48. =HnZZ = mmo +2mn
  49. +h mnZ
  50. mn +ek mn
  51. sexta per arbitrariam
  52. et fia et primum in summa destruatur q sfmnioz seu fiat + + 1 + pl
  53. aequationes 5 et 6 addantur in unum, multiplicata prius
  54. hxy =
  55. 21
  56. a
  57. seu B = + ar = aq: h. seu p= fr a, ( fr-9,:, +rrq. si p posset esse a = R et p- +r. g
  58. 2
  59. debet jam esse
  60. xun =nn +h P mn = ir mm-mm- h P mn,
  61. Pema -0
  62. q0
  63. +X (mm. un) e (mm- nu)
  64. 1+X) (mm - nn) +2 hP mn =0 seu
  65. n
  66. r.mn
  67. (mm-nn)lemn
  68. q4r -0, quod non licet nisi in casu circuli, vel ert m
  69. vel erit mm-unrmn seu nm Fnn -2mn = 2nn
  70. a
  71. et firt a
  72. = n 12. seu m = (1 = Y2) n
  73. et p = + r -9
  74. ergo vel erit
  75. et fieri poterit h=a a = h = 44 fr + q
  76. seu m -n
  77. nm + un = (3 + 212) un = I l = n YC3+ 2t2)
  78. sit jam circulus descriatas radio At, centro R, radio AK
  79. curvam AY scans in puncto Y ax R agatur in ipsam BZ normalis XK R
  80. dato circulo, enunt et AA RK datae
  81. sed video si non datur relatio inter AX et XY, ad conitam et
  82. ad rectam; etiam non posse dari inter
  83. et
  84. L Y
  85. ila trastra
  86. ali pristeur
  87. suns
  88. qud utitte inii
  89. ut si eaut earem
  90. mnota AC sit Y B K sit K
  91. radius
  92. BF sit 1. R sit K BI sit i RI sit K. dfferentia
  93. stitui mp
  94. u stit
  95. di
  96. inter ii +KK et rr vocetur +t, et erit aequatio
  97. aqu
  98. ry +XX -2iX = 2Ky = = H: et + erit + cum Y est major qua B
  99. sed _ + est =, cum RB est minor quam Y, sed si sit neque major
  100. neque minor, sed aequalis, seu cum B cndit in circunfentiam cidculi
  101. 0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 179v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0358?run=74