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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 47r

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. 48v); this page is its right half.

The machine reads it as

  1. Ad Antonium Arnalium
  2. E
  3. se
  4. Theorema invenigenerale (cujus demonstrationem c
  5. transse cum sit prolixior hac tansferre commode
  6. qvo
  7. hic supponere suffecerit) segmentum figurae
  8. aequatur dimidiae figurae resectarum
  9. verbi gratia segmentum ACA aequatut dimiduae
  10. bigurae AB AE ABEA, quam voco figuram
  11. resectarum, quia curvae Ipsius curvae AE, ordi–
  12. natae BE, aequantur ipsis AT, refectis
  13. am per c4 tangentes curvae pripcipatis AC
  14. AC sit arcus circub
  15. net
  16. radie
  17. et centrum G vocando AB, X et BE, y. calculo reperietur
  18. yy
  19. seu
  20. vel TE
  21. tune E
  22. C et radium 2. calculo reperietur LX aequ
  23. 14yy
  24. aeqal.
  25. yy- y +y -y etc. in infinitum. (Nam
  26. maltiplicando hanc seriem e infinitam yy etc. per 14yy. rod
  27. Est autem _
  28. gis
  29. prodibit y Poetosumma omnium yy-y +y6- y. ommium
  30. yis
  31. seu omnium LX sive omnium , dimidiarum E, hoc
  32. seu Omnium gu
  33. 3
  34. = Y + y - y
  35. Lu
  36. est dimidia area figurae ATE A) est
  37. (ex notaqvadratura parabolocidum, nam summa omnium yy est
  38. 5, et ita porro) jam dimie
  39. u
  40. al
  41. 3
  42. 9
  43. et omnimu y est
  44. subtracta a dimidio rectangulo TB, (EXy seu Y, seu y - y + y - y ex
  45. +yy1
  46. demonstas relinquit 2 y- = y + b y -8 y 8c. pro dimidia area figurae AB
  47. divror
  48. e
  49. p
  50. AB ss seu pro valore segmenti Circularis ACA t centrum circuli C. addatur
  51. redur se
  52. q
  53. ab AGC segmento ACA, triangulum AGC (seu = BC in (BAG. Est autem AG, X et
  54. nam si
  55. unde ZBC est Z seu y - y + y - y + y etc) prodibit pro sectore AGC
  56. rectat
  57. anferem
  58. e
  59. 14yy
  60. = y + y etc. qui est valor semarcus. cuiquecum
  61. tanglus Kauterica seu Triguaometrica sit u
  62. Si jam arcus ANN, sit quadcans circuli, seu C incidat in N et Tin M
  63. A2E valor y - y 4
  64. e
  65. a
  66. tunc E incidetum N, arita y aequ. 1. ergo quadrans circuli erit
  67. lector quadrantalis circuli erit 1- + = + si radius sit 1.
  68. vel circulus integer erit ad quadratum circumscuptum, ut +- +=-= + et
  69. est ad unitatem. q
  70. 8, vol. 1
  71. sequitur radio existente 1. et tangente
  72. artus existente . ipsum arcum
  73. fore 7 ..
  74. 4 y - y ek.
  75. 5
  76. pa
  77. e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 47r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0093?run=74