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Leibniz-Handschriften zur Mathematik LH 35, 10, 1, fol. 13r

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. 12v); this page is its right half.

The machine reads it as

  1. seutn - 99- 5r et 1p = 5r = 2r -9
  2. FO3e OG, Sr FG4n. SYtan = 99. E Trianguli OGF atera
  3. sunt 3e, sr, 4n. Hiuc triangulum ita fiet
  4. + 3C + 5Y + 99-5Y = +3C + 99
  5. +3C - Sr +99 -5Y = + 3C +99 - (2)5Y = 3C- 1p
  6. Ergo arca trianguli Y99 - 3 C in 3C - r p. (4
  7. Ergo depeer Les sit Sy2BB = 55 5. 58
  8. et SBD = S3e- 1 p et Trianguli area S7qB 18D. (1) =672
  9. + 3C + Sr - 99 + 5r = 3C - 99 +2) 5r = 3 e+ pip : m
  10. AV, 99
  11. 3C + 5Y + 99 - 5r = - 3C + 99
  12. jam 24c: (2) 6. T2: 5Y = F_ 12: 5 M porro FN: MN: : FG: GM. Ergo
  13. FN + MN, seu FM: MN:: FG + GM. G Ergo 16. 1s seu NM: GM:: FM: FG+ GM: DL: DG
  14. seu sb: B MN = 16IsGM oportet ergo quaerere FM: FG + GM est autem G_
  15. 1b GM b 1b: 5 GM = L 4 n - 12. 5 FM (45 - 12,: 5 = 400 -144, 25 = 256: 25 - 16.5) 44
  16. Exg. F: GM = SA nS N - () 6EFL: =r e suique et 12: 5 FM: FG+ GM :: M 12. SM: a n. 5 mm
  17. Seu:: 12:5m: a +n + S4 n - 125 nm :: 1C (12: 5 m) An - (4 n - 12: 5 n, : 12 5 m (12: 5 W
  18. 3- 2 = 3166 -2.
  19. 30- 25-
  20. (6: 9- 16. 107 2
  21. 4: 380
  22. G ZR + RH = GH. Et GH quia Triangula G2F, et GH) ob angulos FGE et OGH
  23. aliter.
  24. aequales similia suntofiet GQ: GH(:: FGse. CG: An: 5Y et q R: RH:: 4n = 5Y
  25. 4:
  26. a et FQ: OH:: 4n: 5 Y et F2 + QR FR seu 83en: 99 et GH + OH OG seu 57
  27. Ex aequ. 1 et 2. fit GHAn: SYC + gR + RH = GH Ex aeq. 4 et 5 fil OH An: Sr + QK 3e m: 99
  28. seu Qp) Y5CA: 9u .p ON et RH 5r f. . ut prius. et ZR+ RH = 4n+5r Dus prius
  29. QH set RK + AH eq e Se ADA (GH 1 in. 51 ) GH ip. gr et pro Os
  30. A
  31. substituendo vulorem ex aeg. 6 fiet e - 5F + GH - Gti qqisr
  32. seu QR = 4n Y 3esr - 9gOH: 5r9q et RH a est AQ ut 5 ad 4n, et
  33. R ZH est ad Re ut 5r + 14n seu ut 94 ad 4n. Er Ergo fiet
  34. 25-9 = 16
  35. R+ RH seu ZH = 3CSr = 99OH : 5Y = (ex aeq. 7) GH, - n: 51) p. 5 9 tatys 3. 5: 1 10
  36. dut
  37. in per 5.
  38. iame seu (per aeq. 6) 3C5r - 995r + g9 GH = GH ip. et GH = 5Y 99- 3e: 99- 1 mml per 4. dr. Sdi
  39. Ergo OH Sr 99 - 1p - 99 + 5C
  40. 2r. 4 iP = r- 19)
  41. : 99 - ip et CH: GH: BC - 1p: 194 - 3C: D: GD
  42. jam si
  43. x3- 5C. seu funt
  44. D- Ba: Y fiet = da F.
  45. 13C- 1 p: V9j - 3C, an. :: n - ( 99 - 55 03e = ipr:
  46. ran
  47. cgran
  48. Y (A)r An- ON: OD
  49. eu O = (2r 4n = (4r4n - (
  50. Erro O (4) _SranO ((4) Sran) = (1) FranZ O2
  51. seu (4) Sran -C2 = D
  52. seu (4) Sran = 9 + D = 99(-38 + 3C) -1 p2
  53. quod verissimum est, itaque consentiunt duo calculi
  54. nam ) 3Y =qr et n = nam (2) 5r = 99 + ep
  55. et (2) an = 9q - 1p
  56. 3C- 1p est 3- (99 - 3c est axis transversus
  57. sungatur B ex foco ad terminiaxis linusversi et
  58. in ea sumatur F3I, = FC fiet fiet BH = dimid: bea
  59. si jam ex 51
  60. scribatur circulus
  61. normaliter educatur 51 et centro _B radio Bse 194 ee
  62. arcus circuli secans st G in h, erit trangulum h5tB simile triangulo C
  63. t 351 = D3e-Ip eritque CB: B.: CB ad hFC ut GD ad DL
  64. si jam trausferatur BC in SYI firt et j 51 B et jungatur
  65. leut liranguum, ∞B 175)G simile insi GDL
  66. sit DL = dr. jam dp = 2dY et ddr u =a. +se C - 1B2 cui a addatur vis centrifuga
  67. AG tdp = 7Ba e- p: 2G 9+pjam vis lentrifuga GD: r - aD: r
  68. pt ser
  69. : 9+ p
  70. ddp =- D a e + D a pP - D a p9 a pD: P q seu p sijam a-ddp aufera
  71. circulationibus existentibus
  72. aequalibus sunt ipsa
  73. descensus proportionales
  74. usis
  75. 15I potiylinus secutur
  76. h in C, et fiet jungatur
  77. B. ps
  78. il BCa
  79. Ergo 9+ pdp = Ba sec -pp. e seu pdap + dp = p dpba: sec -pp =
  80. Ergo ddp p = d a c p Da p D’a pqQD’ a
  81. si jam a ddp anferntur aB. +d addatur vis centutuga aD: 1) fiet , BC + 2Y4 - 9GY + 2r - 4
  82. 9Sg. 16- 12
  83. 4. 12: 5.9 = 16: 15
  84. d. 25-9. 25310
  85. =9. 25 10-9: 10
  86. 8: 721.1.9.
  87. cujus latus 1. 3
  88. 2Y- 9 - p
  89. q- p = q. 2Y19
  90. =29 - 2r - 2n
  91. qn
  92. 24 n = 24 7,
  93. Seu r- 24- L
  94. en

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 1, fol. 13r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068154:0025?run=74