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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 348v

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: 0.76.

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. 349r); this page is its left half.

The machine reads it as

  1. 8
  2. Inoestigatio chordarum aequalium e curvam datam dividenti
  3. tit curva HAd HAK, in qua sit arcus ABD arcus cujus chorda AB. jam
  4. centro B radio BA, describatur areus circuli, secans curvam in C. fungatur AB AC
  5. jam pro calculo referentur puncta A, BC, ad Rectam indefinitam 1 Ar demuis
  6. rectis cormalibus Axi. Ob data puncta A ob dator puncta A, B dantur LG, LN
  7. abhictae, et ob naturam curae resario inter LG, GA, et inter L1, 1B. ob naturam
  8. sirculo excentro B radio BAde scripti erit B0 qu +Co qu= ABqu. et quia B0 = LN - LI
  9. 2LN. 21 + Negut 1Bqu - Z. NC. 1P4 ABqu.
  10. ek NC = 1B, fiet. L LNqu. Lqu
  11. Alimnendo datu qua exhibet Ex naturi curvae relationem
  12. inter LNoet NC, habebitur utraque halum rectarum. Rursus AC, GNqu + (NC- BA) qu, seu
  13. comper pro
  14. AC qu = (LN - LG) qu + (NC=GA qu).
  15. exprimenda curvae natura scribamus GA = LG et IB - L1
  16. et NC = LN fiet LNqu. ( LI qu) - 2 LN. 11 + L 4 4 ( 21.
  17. et (0-
  18. pea- du. VG a thldect
  19. N- 1G) qu + (LN = GA) qu
  20. Habemus valorem AC, et duos ralores AB, C
  21. et ACeju. =
  22. valores ABqu. cum qua Regu
  23. tres literas LG, C LI, IN et harum trium
  24. aequationum ope tollendo LN, LI, LN
  25. prodibit aequatio inter LG, AB, AC, vel
  26. Itaque hinc vicissim datis punctis A et C datur B
  27. qualem ipsi BC vel AB) habebitur relatio
  28. datur ex LG et AB, et BC est aequ. ipsi AB
  29. et posset tollendo LG relatu
  30. LGe. D tG + LIqu en G. La) C . 2. 15) - (15 - 1A) (2E1 4 7 + C)
  31. C1. FC
  32. (si quis id maltet inter LA, AB, AC
  33. n
  34. illodem
  35. BV
  36. Et quia L1
  37. dabitur relatio inter LG, A
  38. Sed sufficiet paucis assum deseripto r
  39. inter AB, AC, Bd. postremo quarendo Ad, poterit relatio haberi inter LG, AB,
  40. vel et prsse
  41. inter LB, B
  42. vel inter AB
  43. Dqu=
  44. DE qu =
  45. et
  46. ep+ Nequ+
  47. P1
  48. 1. c
  49. 50
  50. 2G
  51. Hsc
  52. determinari D, et hinc duci AD, atque unde sublatis reliquis quaeri
  53. +
  54. circulo centro eira
  55. 1y
  56. 3
  57. 23
  58. en
  59. quaryquti
  60. lationem inter A in Ellipsi or
  61. dio
  62. qudud
  63. AB = LGqu + L1 qu - 2(G. L9 + GA qu + 1B4
  64. BCm = ABju = LIqu + CNqu - 2 L1. LN = 1Bqu + XC qu = 2i B. NC
  65. LPqu -2
  66. tL
  67. u
  68. He quesqu LAqu
  69. Dqu=
  70. ed
  71. Z
  72. in = 2 dB
  73. ZN+ GA u Nc
  74. 2
  75. l. L
  76. In Hyperbola H Aequilatera sit ubi y = aa : X
  77. 1, 2X LN, EX. LP, AX. LQ sX
  78. Aqu
  79. GA Gu 4)
  80. sit RGiX.
  81. quabesa
  82. qu BC qu
  83. 123X
  84. 2X - 1X) + qu aa - a)
  85. 2) ju (Ex - 2X) + qus au- aa
  86. qu. CD= qu AB - qu aX. 3X) + qu a - au
  87. M
  88. In AE = qu ( 5X 1
  89. ess (5X aX) + qu (aa- aa
  90. a
  91. -0a)
  92. porre
  93. 17
  94. a
  95. NC, a
  96. qui d E= qu
  97. IX)+ qua
  98. (AX- IX)
  99. AB qu = L
  100. s
  101. Ju Ad

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 348v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0692?run=74