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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 181v

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: 0.80.

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. 180r); this page is its left half.

The machine reads it as

  1. Anquatio ad conicame generalis, prosito vertice. I
  2. aloscis
  3. axe XE XhZ, ter V ardinita A5 seu Z
  4. fit 2. Y V + 70 = Z2. et pronatur
  5. dp loco Ve. V1. seu v = b~ + py - 94, : 9
  6. ponatr
  7. et toco L AY seu Z = P5 - by, : 4
  8. Erv - 25bE 127py
  9. vo = - 2 7 b97. 27899) 1 = bEG + Z 1 yy + 27 bpEy +
  10. 27=
  11. ppls =bgy 12b85y
  12. Ex problemate Maximo in minimae pauloante
  13. posito habemus cum ex M diccenda est ad conicam
  14. inima vel maexima MY producatur MY in B, ut
  15. distaclia ipsius M ab axe est MN, vocandaM,
  16. et abserssa maxe, a vertice, YN, vocetur, n,
  17. ibi curre occurrataxi.
  18. = r+ fV. fit r + ∞6,: - Ytr B +V +M: m
  19. fit rM. + Y mv - tr + (1P + 1) v r+n = e rt t -5
  20. fiec -rm - rmv + ey + fvy =0
  21. rniv= - = mb. B- fal4.
  22. tbesz - bx k 1
  23. +eq- + et = eli y
  24. +
  25. +rmq
  26. 12
  27. Aequatio a Addantur in unum aequationes 1. et 2. multiplicata altemtia per consantem
  28. +3, vy = - f pe + fby +
  29. tmultiplicata utraque pe constaltem, et summa eam
  30. conferatur aequationi A ad Nirculu, multiplicataper constantem
  31. + ff =0
  32. Quae aequalio ad circulum erat
  33. = 29X - 2Cy + XX +gy
  34. quando uni md maous determinandi locee ad interseotionem,
  35. cirt figularum g. circuli conice datae non
  36. succedit, necsme.g. per norm ale sud rectas easdem
  37. nec foicedet alis modo, utcunque mavietur modus cosrdina
  38. interia jenus dat faciliorem constructionem quam alter
  39. Oriia atce possunt esse parallela. et si coordi.
  40. natie nen sint parallelae Axibus oppositis
  41. g0. e circuleferent 6 puncto Y possunt dusi Y
  42. emales ad rectas AB, AE, inter se non normales
  43. et noestigari potest relatio inter ipsas YX,
  44. rX H d. Y XX = yy (b+ Y) y + 2Cy are ex
  45. si b+r = p q+r = K sit G = 5 ea erX pqy +KXy = r9C + rex
  46. et y = r rqc + YCX,: p9+ KX _ et yy = rrgqec + EYBCC X + rrCCXX,: Ya U P9 KX +KX
  47. = EraX + YXX, : q et fit q rraha ErrgqCCX D YIGCCXX
  48. +2raepp X + 4rgqpk X + 2rgKKX
  49. rquKX + r(CH.X
  50. sint duae aequationes una ad Conicam, sexundum X et V E cajus latus ransvertura rectum dimidium r,
  51. +rgqppXX
  52. geeralis dutam
  53. sit BV, Li BG, m; GV, n AB, d
  54. Aequatio ad circulum, et kxroo -igc rty= +H
  55. quarum petollendo B, ut reliaquatur e, bebitura quatio quais i 1. p etc. Comotar anda datae
  56. quad si succedit comparatio ut arbitrov habetur constructio. stibitrariae sunt m,n, a; f, g3i,
  57. it duae aequationes una ad conicam px+b HBY bXX + exV+ (Cx d AlCX +s = 0
  58. oinduen identificationibus opus A
  59. lastua ad circulm Xr +BBL. G X t ig gesta iX A k = 0 tollendo 1B sil bexx ex B hd A hoxt haf = 0
  60. fit = (h - b) XX +lhi - he) X CB K - ) il 3. 7 ex + d 9) E X -hg = hi X - Ih K C
  61. V
  62. IX, X. XIy
  63. B
  64. =f
  65. +X
  66. pro e ponatur 4+X
  67. in aequationibus 1 et 2
  68. et buis
  69. crtatien ae3 ditnbitarit mulliplica
  70. erit
  71. n
  72. et a. si s
  73. polamus
  74. omissa a
  75. enbitum
  76. eo
  77. conserendae aegus. 6.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 181v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0362?run=74