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Leibniz-Handschriften zur Mathematik LH 35, 8, 3, fol. 5r

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. 6v); this page is its right half.

The machine reads it as

  1. pars Aertiaa Methodo langentum inversae seu e punctionibus Augu si 1673
  2. si sit figura a = X. pet: a = ax + YX, unde fies ad P habendam assumta
  3. a + Y
  4. primum X absissa: - 2X = a + y P. et p = 2yX
  5. ps
  6. eta d
  7. W
  8. a + quod est memoratile, inde
  9. et vino y = (a = a X, fiet 2X x - a X - p et quia d = L
  10. 2a aax
  11. a sar- aex a ax=
  12. a +as a=aex
  13. et erit Y= cq
  14. 44 at - ax +Ca3 - a X
  15. 2 gX. a7
  16. vel u lata fractione per- X r. ea X X+ ca X
  17. vel Y= a sa- ax + = ax
  18. 2X sa
  19. b, = X. Ergo a = fX.. unde si fiat. 2X = 4yx fiet 2l = X., vel l - = = p
  20. cum Y -20
  21. Unde res sequitur memorabilis in Hyperbolocide Cubica Reductas esse figuae romogeneas.
  22. quod me credere facit, peculiarem aliquem hujus figurae usum esse.
  23. 3ylx
  24. =X Ergo at - _yX, unde si fiat 3YX = y X et P- X
  25. jam 7 = s et Y = 10 40 = e. = 250 , vel E-
  26. parmloloeis ax = Y. Ego ap - 3y3 = 3aX, ego p - 3X.
  27. u
  28. Ce yx-a
  29. inter quadralum termim poserioris, et rectansitum seriuinotum, duplicata, seu est differ, 2a 10 = - v2 L y - , 1 a x. ce = 10 a X = e. Ego 1D a - 2 Cx. et a X = 927C X fietr 69:
  30. locus ax= a y. est momentum sinuum criculi, ex vertice.
  31. 2a xP - 2x P = 3y Ergo P - 2
  32. =
  33. 3ax - 2X
  34. 2ax-3X
  35. a = 7X.
  36. 3aX -2X
  37. hoc di vidatuo y = 1B). aX = X C 2a - 3x - aX - X 8a - 36a X + 54 a X - 2 7 X
  38. 34 3X2
  39. a = y, fet a = sax, et a = y ax, et à = 1X
  40. Tax
  41. Aequatio cinaae quam Cartesius post (onicas simplicessemam putut, lib. 2. pas 37 hic asfetur
  42. y - 2ay - ay + 2a = aXy. vel X = Z - 2y B- a + 2a. sed si hoc et,
  43. tantum nascetur ex comparatione in unum quatuor aliarum linearum,) ordinatae recta nguli
  44. ordinatae Trianguli ordinatae parabola, et ordinatae Eipsus Hyperbolae. Ita conchoeis ex rct
  45. applecata ordinata circuli et H Hypebolae ad Asemiptoton, componitur.
  46. Ait Cartesius lineas altiorum gradumu potius a Mechanica quam Geometria (oc repudiam
  47. das, ob difficilem earum descriptionem. Id nimis verum esst. etsi iuimi excellens sit earum
  48. contemplatio ob pulchutudinem admorandae rerum harmoniae, fatendum est tamen usum mechanicum
  49. non respondere. Quare illud utile futurum est, efficere, utmodum quo investigare qua linea
  50. quaelibet altion, ex ordinatis infeniorum composita intelligi possit. Sed quoniam descriptiones
  51. ejusmodi non frerent nisi per puncta, cogitavi an non vocatam subsidium optica, descuptae va
  52. seraratum inter se jungi possent, tantum min ita ob idque duabus dactis fante fieri potest
  53. si algue spiatssit pse asi iato cis otaatem s asperte otieas
  54. uet y
  55. 2a - 37
  56. 4a + 9X 4 12a x
  57. a+ XarX Ha
  58. 27X+ 36 ax
  59. unde locus
  60. 2a - 3X
  61. a a - ax + a + ax - 2x (+ 2a
  62. ai
  63. BIBLIOTHECA
  64. RrOII
  65. LiA BHODERMB
  66. 4Xy a X - 477
  67. X. Ergo
  68. a + Y22a
  69. r
  70. a ta
  71. 2yX- 2
  72. ay
  73. ase at
  74. ak = yX

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 3, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068098:0009?run=73