Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 437 · Huygens, fol. 41r

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: 0.81.

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. 42v); this page is its right half.

The machine reads it as

  1. 2XXy - a ax: ha - 2XY cl: y:: dx: ay
  2. 2XXy - a aX dy = 3a a - 2xy y dx. Seu 2Xxyy = aa Xy dy = 3a a = 2Xis yy dx
  3. L et propus scribendolr fit X + ydx = ldv seu ydx = bd v Liv: y dy
  4. Ergo denique Lovaq - ap bv ly = 3aq - va ybav - vb dus
  5. faciamus 2aa acb - 3aab + 2 a b dv: dy = 2Wv a = afbv: 3a f - 2V + vb
  6. duo mihi problemata proposuit Hugenius, quae redeunt ad Methodum
  7. Tangentium inversam, in literis datis 24 Aug. 1690.
  8. quaeritur scilicet curva in qua abscissa AX AB existente X, es
  9. ordinata CBv et faugente CD an eju Axi Asdoccurrente in D
  10. ipsa sBd (inter vallum ordinatae et langentis in axo) sit gy. 2X = 2X
  11. ve vel quaeritur curva in qua iisdem posidis Dd sit rary- aur: dua
  12. Quoad primum problema, in quo Bd = jus: 2x = 2X se fit
  13. Labad ex mei calculi legibus: dx: dy: : y: 2X - 2X : y
  14. faciamus 58 y: x = v: a
  15. fiet du = Xde + vdx: a. et dy: dx = xdvrcdx + v. a
  16. Et quia ex, L
  17. ex it est x: dy B= v: 2a = 2a: v fiet _2av: Wv -4aa = (dy idx D feuper 3) = xdv a
  18. seu (2aaV) - v - Daav : pv - 4 44 do = X: pax vel - (Lx : x = vy - 4aa dv: v + 2aa
  19. seu log X = (vav: vrt raa - 4 aa flv: v - 2aav quoramus ergo
  20. has quadraturas Et primum v quaeramus S2 Radv: 2aa + vv
  21. vyzet) est momentum curvae meae quadratricis cujus aequatio Z = 2a. taa + v, seu
  22. vo u y = (3. bb + vV. ejus momentum ex EK est (vb2 bb +VV. nempe momentum figurae
  23. HCFGH. sed idem momentum aeqo (VvaZ2 + BZ. 2 et suq = b (aZ. Z - bbZ
  24. Ergo fitavdo. v0+b Ergossosito b = a st) fit B a rE svar: ve + caa = a 2 sch. 2, Z
  25. Jam veniamus ad (dv: v- bbv estea quae quantitas constat, duabus partibus
  26. nempe (do. V et C sed haec ve est loga de V= bbV sed haec summa etiam
  27. reduci potest ad logarithmos
  28. vib.
  29. vb
  30. fiet p= n et m = - 2B Ergo R -.
  31. jam quaeritur summa de = 2 bb _ v2 - bbp. Ergo - mbb = - 2bb. fit M = 2 et n = - 1 = p
  32. 3= bbv
  33. M + P, + b
  34. v+b
  35. v
  36. ergo bl (dv: p -bbo = 2(dr: v - sav: v+b = Sdv. v- b seu = duplo log. V - log. B + b. - log. v - b
  37. seu def. g. = 2log. V = log. diff. vvo bb. Ergo andem fit logex
  38. log. X = log. Z = Z: a s2 + veZ: 4a 2 - 2log. V + log. vv - bb quam aquationem
  39. trantformando in Transcendentem potentialen fiet:
  40. seu log XVZ: vv- bb = voz- 4442,: 4a s2. seu ssiansformando aequationem
  41. loganituicam in potentialem, fiet: 2XVZ: vv- bbd ) vZ. 4a a2: 4 a 52). posito log a = 1
  42. jam XV = ya et Z= a 2 (2: 2a a + vD fiet vVZ - 44aZ: 4 a s2 = vv- +a4: 2 2ac + vY
  43. et Z: vr - 2aa = 2 a F2 : v - 4a.
  44. Et siet tandem.
  45. 4a y s2: v - 4 a = _) ivv- 2aa : vB + 2 aa) sumb C quocunque
  46. Log Hyperbolitus ipsius C
  47. bg a . log. n tat fI AXI ax. dy - Gy. 2X + 2X: y
  48. dx sit gB a + bx axidus = + yy +4XX,: 2Xy
  49. seu 2Xy dx = +yy dy 4 4Xx du da X Y + by X
  50. log ab= c
  51. L ab = v
  52. Exso tog. ab = c log. m
  53. sid a exy (+ df x9) = rexy ex + ex dy +25 8 xy dy + fy de 99id 7 x- 4 ut aquaretur
  54. A...
  55. = -2xy dx 4 +X dy
  56. ponamus h2 et + = + et + = - et
  57. tiuti
  58. T hyydus
  59. summadem
  60. 2e = 2h. Ergo C = h, restat ergo +3hX dus quod impoddit
  61. sit y = a+ 10 + LX + 12 x + 13, X + 19P + 15N + y = 10 + 2. 1B.11X F2. 10. 2
  62. 11. 2. 13 X 13, 19X 4 f. 14X1515X et
  63. F12. 12
  64. yX+ B sit ( sit X-10+1g19+9y et
  65. Teguy ectu ec = 20+ 2 + 22 y + 23 et fil, 10. 20 X102 y + 10. 22. 7 + 10 37 11024) 1
  66. dy=
  67. eim 24= 1: 10 et 21 = - 11. . 15 et 22 = 11. 11 : 10 - 12: 10 fit . = +4 2 + 11. 2 +11, 2F +11. 27 er
  68. Cxax:d = y - 2Xx : sit 1X = 10 +_ ∞ + 12y + 13 y) ea y e,
  69. +1L. 22 et
  70. F13. 2C
  71. y: 2X =2x: y
  72. X = 10 ∞210. 11]4 2, 10. 12 y = 2. 10. 13) + 2. 10. 19 g et Xdx = BCX n d X = 10. 11+ E. 10. 14+, 1012 y 4. 11 4Y eri
  73. 1
  74. 1t f.t 10 114 2 10. 12 96+ 3. 10. 1315+
  75. aseudinius) reiisi haua curys A gy lg. 10-0 et 1- 10 allii 0
  76. p
  77. 12. IL
  78. 14 y3
  79. S
  80. lit
  81. 3
  82. se esles yy 4a a =0 fieret
  83. alone wey
  84. 1X. 2a
  85. fil a fieret y infinit
  86. . sit yv-aaa: er +2a
  87. constanti seg tant itim

Cite

LBr. 437 · Huygens, fol. 41r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-3595205:0081?run=74