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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 284v

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

The machine reads it as

  1. tam una functiones eanus, invey.
  2. quad. circ. et Hyperb. ex se
  3. invicem ex et alias figurus
  4. figura proposita esto parabola, cujus vertex A. absussa
  5. applicata CD - y = SaX. posito X, latere recto
  6. EE infinitesima seu unitate constructionis = 1 vs
  7. rentia inter duas applicatas proximas non nisi irta EE distinte
  8. erit aX + a= Sax. quod si figura aliqua eogilatur
  9. differentius applicalarum pearabolae homou enea, ejus appl citae
  10. crunt: a axta - a ax. = y., vel utroque quad it:
  11. axta + ax 2 a X + aX =
  12. seu 2aX+ a - Z = 2 a x ax, et ulioeque parte quadri ta
  13. +a x + 44X - 4 X) + a - 2 + 7 = 4a X + X
  14. a
  15. vel 4aX + 4 ak - +Xy a + a - 2ya + yt 4a
  16. siet: 4Xya = a+ y
  17. vel 4X = a2+ y = a + y Ecce dt fi ordinitas
  18. ad basium figurae
  19. cujus ordinatae a axem sunt homogenea differtatis paratolae.
  20. vel axya y a vel 4x
  21. vel aX - a2+ yt
  22. a
  23. a
  24. Applicatae Hypertolae sunt: a different ia a L a = a + a - a x - a
  25. X +
  26. X+ 1
  27. Datis difficulis a inverso modo quaeritur figuia cujusint differentiae
  28. GW
  29. Sin -
  30. posito ergo GW = _, et, WdL = erit W0L
  31. ergo
  32. ED
  33. p
  34. erit ergo
  35. dudum
  36. erit: =
  37. in
  38. X
  39. a 2 ED EM
  40. - p = a
  41. EM
  42. Jam alinde constat esse PE- ED = y d yrt yX +1 Posito scilice
  43. WVL
  44. y esse ordinatam figurae quaesitae nam BE
  45. an
  46. a
  47. ED
  48. Guo vel = WL
  49. alibi a me demonstratum ess. EM esse differentiam inter semiquadrata duarum
  50. frgurae quaesitae ordinatarum, seu e inter semiquadcabum de vie semi
  51. quadralum de y_ se inter V + a + 2)a et y = + v
  52. ergo
  53. erit:
  54. EM la
  55. ad +G1)
  56. es
  57. sive a X 2ya = 2 a
  58. Sive
  59. sive rejecstis imutilibus: a y
  60. Na
  61. sive Y ab a- yX ae yb
  62. XX + a
  63. a
  64. +, seu Unde patet aequationem esse Identicanus
  65. ac verissima quidem esse assumta, sed unde nihil
  66. novi detegatur.
  67. Applcata circuli: V2aX = X E, alia 2aX + 2a = X 4 - 1 + 2X, disfe-
  68. rentia inter eas est: = y Engo = = 2aX - x + 2aX + 2 a - x - 1 + 2X -
  69. D - 4a x + 4aX - 2ax - EaX = 4 a X = 2a v A E + + X - 2, dictioque
  70. seu ac = Da et utraque parte in se brctu, tet
  71. ∞
  72. 2
  73. Aax +ax + EX 1X- 4X, +. 46
  74. e X gax
  75. 4+8aX + 4 - 44X - ax + Bax, 4a - + aX - 4a + 8aX + X + 2X _A. X,
  76. 1Ca+ 164~ + 24 87 + 547 1 4X ax 1X 1 44 10 e
  77. Paeterca
  78. ax + dX
  79. ryx rarZ
  80. cax, 2yaX
  81. 2e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 284v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00067993:0570?run=73