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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 178r

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: 0.82.

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. 179v); this page is its right half.

The machine reads it as

  1. inter
  2. si problema aliquod Geometricum construi potest persectionem duaru
  3. locate
  4. nearum, potert necesse est ut ad binas aequationes educi possit una sit
  5. ad unam lineam, altera ad alteram, et ambae habeant coordinatas
  6. uter se nonnales.
  7. AVY
  8. sit recta positione data, relata ad aliam rectam positione datam
  9. AX X per
  10. eX normales ad
  11. Tt AXIXY a ratio iata. sumatur
  12. alia recta positione data BZZ secans ipsam AX X in B et
  13. ipsam AYY in C et ex Y. in BZZ agntur rormalis YZ
  14. jum relation inter AX et XY, quaevitur relatio inter BZ AVZ
  15. Habita
  16. voce c A3, b CAC 1B48. AX, x. XFy. ABZ Z t 2Y∞
  17. inci
  18. Profbema est celebre mipimam m
  19. vel maxima
  20. puna
  21. Conicam AY ducere minimam (CY Ex in Axem Conicae AX
  22. gngatur normalis YX, sit vertex A, ta semilatus rectum Y
  23. semitares transversum
  24. AX vocetur X, et XY vocetur y. Erit 2YX +X XX = yy
  25. Ex centro in axem agutur normalis CB, et ABsit b, et BC sit C
  26. minima producta axi occurrat in p. Erit dx: dus G= y: XP
  27. seu xP = ydy: dx Ex natura autem conicae
  28. differata ejus aequatione fit 2rax + F 2xdx = rydus, seu
  29. dy: dx = Y + YX, :y seu y dy: dx = Y + 7x = X s.
  30. jam XP: y = YE: EC = x+b,:, y-c. Habemus
  31. r
  32. Y (X + rX, : y = X +b, :, , seu . b + xy =
  33. seu by + xy = rC f Xx = ry = s y seu a(bersus + (1+ Z Xy - rc + 2 x
  34. si punctum ladat in axem S
  35. quae est aequatio ad Hyperbolam, itaque commode solvitur, problema
  36. fisk
  37. bxr+
  38. inter sectione Conicae data, et Hyperbolae si mocum Ccadat imnaxems sitm tomud
  39. eriorem secans in Y.
  40. Ycujus overtex L. Axis Ln
  41. in eod em plano
  42. sit eadem sectio sanica alita
  43. 1
  44. t et Y ad L M normalis 5B
  45. naspriorem AAs in M. sit
  46. Z Ht Z et ZY sit veis am, En
  47. aigatur in RX pormalis L, quae vocatur n, et N M vocetu
  48. jungatur YL _ Er YCq = Rt ~ X qu + (XY N1) qu. habetur ergo
  49. cgu intoloratio s YL centro Y radio YL describatur arcus circuli secans ipsam LZ inp
  50. quaeritur LB. punctum Z est intersectio rectae per Lm, et circuli
  51. as ex YR qu + ZRau = YL qu. ob
  52. rectam LZ est MT: 79 =mn
  53. Sed 79 = Ns Ee ZA et
  54. MY = pM SY + YR NM = AN A AX + YR AN - AM fit
  55. nH = X + YR AM. Ergo fiet AX+ _R = AM, :, NS - QR = AM+AN. LN
  56. habemus ergo duas aequationes secund YA et AQ fint exs et
  57. seu LN. AK + LNYR- LN AM = NS. AM ZR. AN et fiet utique
  58. YR = (NS. AM + LN. AM L N AX AN. ZR,
  59. Z secet AX in L. triangula MZZ, MNL sunt similim, rursus MNL et sunt
  60. simibia fit ut LZ LM - LM seu sed Z M = LM - LZ
  61. 39 = ZY -Y
  62. MZ: Z2 seu LM- Z,:, ZY - Y Z = MN: LN lon a Y = YX B ML: MN, fiet
  63. LM = L7,:,: Z (M L. XX: M N) YX - v. hs ursus X Q = XV. LN: NM et similitem
  64. YM -F A(Z n =). LMF LZ, C LM: VN
  65. jam AX + X q + qm = A M
  66. et fiat AXF XY(L N: NM) + (M - LZ) (M: NN) = AM. sit ZM, l, MN m. NL, n
  67. LZ, Z et ZY, v. fiet l = Z, :, v - (L: m) y, =, m: H, _ X + y(n: M) +(l: m) l - _: 12
  68. = p seu l. 7 = pen: l) B X (m: 1I = y(n: () = vim: 1 - l al st v r t (pxsm: 1)
  69. et set xp X + Hl.m) Htnd et Z- l +X p: 1) n +. ye: )
  70. vetene te d tete u se e u t. esitet riti
  71. t ny.m
  72. a om
  73. ta
  74. potest punctum
  75. inde quataor
  76. perpendiculares C1 Y, (+Y
  77. (3Y, C4.Y ad Gonicam
  78. duci possint. sit cit
  79. minima, sit erm ea
  80. cressat usque ed CEY. Quodsi
  81. Jam perpendi colaris pips
  82. potest ad
  83. nessetist reviss
  84. nde urus decrepere, upque ad NY
  85. rurtus ex
  86. ou
  87. nns luu 3
  88. teste
  89. Aeit
  90. a
  91. ut
  92. AM, P
  93. AA, qu.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 178r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0355?run=74