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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 2r

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. 3v); this page is its right half.

The machine reads it as

  1. ponamus lineam in curva ferri motu composito ex descersu versus e
  2. et ex circulatione circa C cujus velocitas sit in ratione reciproea
  3. distantiae 15 eauet roi sit temporis incrementum seu ared
  4. sqo seu tuingulam 162G C expositum per constans ad. fiet utique sicus radius r = cG
  5. 19L = aB: Y. i porro vis centrifuga circulantis est ut oGtet ad D: a, ut a: r
  6. seu ut YCB P seu aD: B. Ergo et fal sit in vis
  7. puvitatis, fiet: dde M = dar + aD: r3 nam vi centrifuga
  8. detracta a vi gravitatis, fit demum ve a novus descendendi conatus prioribus
  9. Superadditus.. Sit jam ut = a. Br: a seu in relatione mtermina, sive
  10. patione simplice aut multiplrcatam directa aut reciproca radiorum. fiet
  11. B an3. = adr + a B: r: seu fict: O r’ dr: a = dr ddr + à r: p3
  12. Ca
  13. prodit
  14. ergo fiet: Or: nt a = dr. 2 + ab: 2r. cujus posteri cujus aequitionis dextrum catus secux idem
  15. Ergo D- ddr : r: a: nN = a. r. sit jam n = -2 seu m - Ba: Y
  16. firt D = drr: -ar: 2 - a seu f tempus vel areaintegra + = aror: S- ar: 2 -a
  17. Huc ergo res redit, ut inveniamus aream seu summam talium: Sdrf. FrFt (drr: ErEI
  18. sit Y + 1 = v2. fiet r = v -1 et dr = 2V dp. ergo fiet inde in rationalibus f2Vdo v=1 : v-dov.
  19. F4 v - 25 do: v quae pendet ex quadrature Hyperbolae non ergo curva GG potest
  20. esse Ellipsis, ubi area ex radiis perquadralum Hyperbolae non determinantur
  21. sit ua gravitas in ratiare ratione distantiorum reciproca seu sit n= triplicata,
  22. s
  23. fiet n + 1 = -2 Et fiet B = dr Y coust eruntque tempora in ratione radioru
  24. fint (B seu t et ut r seu tempora t dlinsumta erunt
  25. De 1GC
  26. in
  27. se
  28. uGC
  29. duplicata ratione radiorum. in restigemus qualis sit figura, in qua areae sint in duplicata
  30. ratione
  31. ratione F ut quadrmta radiorum C1G, C2G
  32. sit BG- y et AB = X
  33. et AB - h. fietit f Sydx + 1 yt , et y + tartix a seu Sydx = ati atruta
  34. e firt (9 4∞) + L h dy ( L y dx) = Xdy, ydus a 2bx +2x dx
  35. Ergo (X du = _ his - 2gy + 4hx = 2 X
  36. += hy
  37. Ergos d syd hec estai (yzati( ih Xt X- 1 yt t L yad ( hy (y 9 tx B3
  38. Ergo ag ix
  39. Er quoe est aquatio ad Hyperbolam o sint nor in calculo
  40. Rrepetimus Sydx + Z y h- X = 15 + h = 2hx + X. seu Sydx = y +ti - 2tx +X- ryh. yx
  41. cujus aequatio differentialisuest (9 dx) = Eydus - 2hdx + 2Xd - L hdy ( L y dx - 1 X dy) seu 4d
  42. yd
  43. Lxdus
  44. seu axdx + aydus = 3yda +exdus + 4h x + hay. seu 4Xdx. 3ydx = 4 hdx = Xdythdlys - 4ydu
  45. Si quaduta semporum scribatur Odx = Ddus C dx F Day
  46. et fiet sit ana ldx +MXax ydx = pdus t qu dy + rydy
  47. et het aX 39 ah in F + query Xth ay in Assum atur
  48. l+ mXrny + pxy +qX + r fiet mdx + ntus t prdus 1 pudx + 19X axt r ydu =
  49. Seu fiet Max + Pydx + 2qXx = n dy pady- erydy
  50. Y= at bx rcy+ exgt sxrgy CFhXy Clr + nXAn ec
  51. dyam
  52. si tempora
  53. Ad Neut. A. 50
  54. ZR nocemus M et CA, 4,
  55. k EX. PV: CA: CP porro GV. PV: QV.: BC: C
  56. QN
  57. LH XXXV, Z+
  58. 24 CDr: CB sit L tatus rectam
  59. 6
  60. E sit lotu ZX: qY :: AC: pF
  61. Ergo L. eR= 2BC: AC, in PV. CA: CP. per 1 et 5.
  62. B1. 2
  63. + 2ligX 89XG
  64. Atum +nX -am
  65. sit primaru = 2 BC: AC.
  66. rursus PrE QV. PC: CD G tfiet L. Gp 2BC. (C) in qV. PE(CB: CD. G, VD
  67. ali +a
  68. at CD = QX. CB: q F ex 3 et 4; Ergo ex aeq. 8 firt LGR = 2BC i PC. QT: Ex (CB7 GV.
  69. seu L. gR = CB 2 2 PC. qV. ZF: GV. QY. Est autem 24.
  70. 2+ = ad. sP sit F eR seu pX vocemus m, et PC, C et PY ∞ et GV = 2C - v
  71. Et QX seu AP = n, et _W XV = n H ZV = ALX h + n et QT = K
  72. porro per Ergo fit e LQR, GV.
  73. LX 2C V L.M. EC- D h l + Ehp + nt
  74. 2C. K. ubi ipsique n infinilies infimte
  75. pdoae quadratum (ut infinites infiniteespirva negligere possumus.
  76. porro sine
  77. bb trangula PVX et rCE similia fit PV seu V : VX seu n,: pX seu m: PC:CE: PEseua
  78. Y = Cm: a et n = em: a. Ergo a L. m. 2f- fm: a h = n + rhem: a 28. K
  79. Ergo 24. Me tr 2 Lmh - Lm h: a = 2t K A HCM 4 2RhK M: a
  80. et fiet
  81. Unde jam collegit N si jam rejiciamus, moti: a itemque retik m: a tanquam
  82. caeterarum respectu infinite parvas fit, utique YLm_= 2K2. seu memit ipsorum
  83. nmvodrais proportionales; ut coclusiset Vertonus. Verum talis argumentatia
  84. ep tellisi isfcadtu
  85. x- du
  86. t h-+y
  87. in+ py
  88. 9 349X
  89. h+ X - 4y
  90. m+29X+ PY
  91. taqu
  92. Ahpus pxy ap
  93. = 3y
  94. 2ry
  95. brs

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0003?run=74