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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 117r

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: 0.79.

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. 116v); this page is its right half.

The machine reads it as

  1. Xy. Xb dp
  2. Xy. yC dp
  3. G. 39 Xyh +G. XpL. yh + X. Xp X yh LX. yqX.yh Xg. dp
  4. Xy. Xedq
  5. Xy. yf de
  6. Xy Nyh dp xy. X. 79 dq
  7. xb din Xe (dEn)
  8. yc den yf (dEn)
  9. Xyh den X.yg (d 2n)
  10. 16)
  11. Unde erit Xb dl + X. xpXe aequ X, et yfdm + y. ygyc aequ. ym
  12. reliqui vero termini aequationis 14 omnes simul sunt aequ. X. yn
  13. Sed ut tanti momenti inquisitionem melius absolvamius; : Sit aequatio data
  14. sae dx ago X20 + y30 y L xy X2I + Xy y3I + Ky X22+ X y y32 + Xy x23+ Xy y33 etc.
  15. u X40 + y50
  16. +xy X4I +Xyy5I +x X42+ Xy y52 +x 3X43+ x yB Sc
  17. a. oaequ X80+y90 + XyX BI + xy y 91 + Xy X82 + X ) y92 F X y X83 a X i3 etC.
  18. Al sumatur aequatio: (2)
  19. Superest aliquid annotantum X. yn poni potest aequ. Xy X p + xy Y 9+ XG2n Cujus differentalisent, D egu a sospitdus hyt ry B1 Exry gi ex) dscx A rus dgudus ex Bstx tudidus
  20. Ergo d X. yn seu dn d x + (da)dus erit aequ. y xp dx F X xpdy + y y gdx + Xypot, tyXy dindr +x. y
  21. et fier ax 64)
  22. dy
  23. txBIXdy +yGIXdy AExBEXydy 12y9 Xydy 1 3YB3Xy 379XydB
  24. txBIydx tyg1yax +EXBExy dX FryG2XG dXBXBIXG axtSy9 Xy
  25. d9o + X N8IY Xydg1 + XY. XOL +Xy dos + 3Xy. X93 + X’y d93 &
  26. +X. y91 +
  27. +3X7 y93
  28. +3XyX83
  29. Aequandae jam sunt inter se nalores ex aequ. 1. iafie:
  30. +Xx 4X81 X)
  31. quod et fiat melius considerandum est quamlibet formulam ex una sola latera
  32. a +bX + CXX etc. constare ex parte, a absolytu
  33. modo y90 continere intelligi potest = + SH+ gHV etc. neque enim opus
  34. nam si assumeretur e posset fieri a + e aequ cuidam literae pro litraque
  35. igtur quantitatem a quia tam in XB0 quam y90 reperitur vocemus. 06, et bxt cxxeke sit 80
  36. et fy +gyy sit 90y Nam cum prior character par ut in 40 patet 20 continere X tantum, at 40 continebit, y
  37. tantum. Hinc cum ex. g. _y91 sit aequ. _ + gjysiet X. 991 aequ. BI X + Xy. 9C. pole di y
  38. ita omnia reducemus ad terminus ubi vel litera) aliqua est sola vel liter formula set literis sobus per rectangulum
  39. ambarum literarum ejusve potentiam multiplicatur ubita ubi tamen nota chauncteremb
  40. oisionem unius per aetemm, sed habere significationem dictam ideo posse esse aequ. 0 licet d neque 61 neque G1. sint aequ. 0-
  41. circa differentias etiam notandum, per eas ulteriorem fieri resolationem. Est enim et equ. aei aequ. daeiu
  42. inergo d dys s d et dus per expliationem supra factam. Ergo d d81 nihil aliud significat quam
  43. omnes terminos ipsius formulae et mustiplicatos per numermmne suum exponentem unitate anctum
  44. loco 8 Scribamus compendii causa 819 ita in omnibus minus turbabimur ita jam aequ. 4. correctam scribemus hoc mod
  45. ate 90+_xBIX, xy gyFKSEXXy
  46. +y50 d90
  47. d
  48. a1dgo
  49. +dgrry
  50. X40y91. X + X20y91. y
  51. X2od80 +y5odg0 +x4odgo +XAOXBI.X Ly5OyGLX + y5OXPL. X +y30y91. y + XWOXBI.y +73OX8I
  52. +y50d80
  53. X 21 d 8Xy Hys1 dgory
  54. suidoorus tysidgopus ipiaque
  55. d2n r 22)
  56. aequabimus inter se duos
  57. prius tamen
  58. vateres ex aequ. 1. et ex aequ. 4. ut jacent
  59. Eet:
  60. e xro dBo sy SOdgB LXHOdgO AXAOXBIK + yoygry + YygIX + XHO xSIy H SSo XSL X + yzox BI y
  61. ea
  62. foret aequ. I X. 923)
  63. +2X) Xg2
  64. et ex parte reliqua solam xhabeale bX + CXX erC. ill
  65. 3
  66. LX40XXO
  67. s
  68. aequatio 6ta, et erit d X. yn es seu dn ax + (du) dus erit aequ: xio dBiry +ysodgiry + xaodgrry
  69. +2X g. y92
  70. d8oty. 991 + xy L 81 F.X ~ yg2+ Xs d 82. + 3Xx y y95 + Xy d83 B
  71. Fy. X81
  72. dy8iaeque d8 18 ubi evanescit 80 quippe constans, abit etiam y quia d semp disserentia semper deprimit ad inferiorea ano queda,
  73. 2
  74. Axrorgs
  75. +y50d91. Xy
  76. +y51 dq0. P)
  77. + X40y90. X
  78. 1. XX
  79. e
  80. Xpap
  81. y. sPyF
  82. ftn. xpxes +Xyqxe ypsi
  83. lX. Xpyf +2945
  84. tXC
  85. aequaym
  86. axyt
  87. eodem
  88. t aliam a assumts
  89. dae. Hans
  90. non significare di-
  91. pota
  92. ex habelnius.
  93. X D al +
  94. Gc d xedm
  95. g ad pygam

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 117r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0235?run=74