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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 2v

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. 1r); this page is its left half.

The machine reads it as

  1. ym sit
  2. yy - nn
  3. yyc 80r0X + 12
  4. et fiet
  5. a(dx
  6. et valor 4 videtur pvalore 1. simplreior
  7. f1x + 1
  8. 2 SIXFI AXL 12
  9. 1
  10. ueruum
  11. Aliam rationem trans formandi ex cogito. In omni irationali sumplice y
  12. Cuique quadatum est rationale, (etiam ydu est cu seu cujus quadratum
  13. eham ydy est rationale et yddus
  14. jis est rationale, (it G = Sex nm
  15. vel et dy sau etc. et au, et daque, et generaliter ubi numerus dimensior
  16. est par secus si impar. sit ∞ Y vy m,: 1099+22, fiet
  17. d+C = O: D sit ded = DaB - OdD, : DD fit da Broriu
  18. 12. 1o s 3+ C2OGy+ 2102y + A2
  19. d0 = 1 317 + 11 dy dD = 220y dy et fit ded d
  20. et fit da = 20y in v sit C0 = 1 3+ nyE+ 1 y + 13
  21. 10gy+ 22
  22. fit _ d0 = dy3. 109y + 2. 11y + 12 et dD = 1, 2. 20yB.
  23. ergo ded = d
  24. F3.10. 29+ 2. 11. 20y + 12. 20 yy
  25. F3.1022.. + 2. 11. 22y + 12. 227: 12 (20y9+ 22
  26. -2. 10. 20 = 2, 11. 20 2. 12. 20.. =2. 120y
  27. od video qui ubi tollendi sunt termini pares.
  28. Sed video quemcunque assumam
  29. alorem ipsius ce rationalem, si y simplex sit in nominatore, non posse tolli ibi;
  30. quandando; sed in numeratore video non posse tolli s.
  31. Cd = ir y + 12: 20y+ 21. fit deo =dfl. 201 + 1. 21 -
  32. 11. 20. = 12, 20)
  33. n
  34. seu deo =H. 10
  35. deo= pa run de: vv
  36. Sit C = 119+12: 20y fit, dco 11201
  37. sit jam y= s un fit dy d sa mm
  38. an
  39. orgo datur Cdx C2 tum
  40. sit deo - dyy8: 99+ ab
  41. (2(20y+21
  42. jam ax-nun +2x 2an X Et
  43. x-naxd +cum. ( (Xx. n
  44. Et ita innumerae alia habentur
  45. quatraturae
  46. datur relatio inter co et y ex suppositis quadraturis
  47. erit du yu rationalis et dy y etiam rationalis
  48. sit deo = ydgs. a ofiet a= quaeritur sydx vel sxdue datur sydx
  49. vel (y’ix vel gy dy Cydy
  50. sit C0 = sex + 2y + 309:, 40X+ 517 460 d. fit deo-
  51. sit C0 = 18X + M 9 X + 0Xyt 11 X y L 12XG ratie Ca o ay. 1Gax LXay Hgy
  52. Est auteum ex aeg. data yu = xx mn:, x nn seu Xxyy - nngus = xx- nim
  53. seu X bet AxXydy +aB Xyydx. = 2X AxtnnyA Cg. 2. multiplicebur pere
  54. per 20 X + 30y +, 31
  55. Cd = + 11X + 21 y + 10X + 20y + g0_Xy sit dco = 1et 2idy + 210XdX + 2. 20 y dy + 30 Xdytseydu
  56. ducatur dec in X aY fit W. VX _. deo in 40X + 50y +41, fiet
  57. Ugu Xdx +21. 40 xdy + 210ff0 Xx dx + 2. 20. +0 pydy + 30. 4oxx dy + 2040 xydy.
  58. 4.p0 21 xdu
  59. collamus neque et rylus etga et xtx et
  60. deberent tolli Xdy xyax Xdy ydys
  61. sit 50 = 0 evanescent Xyax et y d
  62. Xay potust tolli,
  63. ergo; restat Aodun Tollend Xxdr ; vel si colli non pt
  64. datur simul (XX dy et syax seu mo dato datur alterum ex casu praecedent
  65. a in casu y exi lentis simpliciter irrrtionalis per X sed generalitr. ex
  66. Ergo ex se linvidem eantur)Vdx et sxydo
  67. e invicem cintur XXdus et Xydx.
  68. . Sed (X y ex datur in casu prosenti. ec itaque haberetur quaesilum remm
  69. I potest oontti et 10.
  70. reassumamus 30 et g1 debent manehe, item 21 et 40
  71. itaque fiat Co = 21y + 20)+ 30 Xy fit deo = =1 dy 1,20ydy + 30x dy + 30y dx
  72. et LCo = 21) + 2 u 10y + 2. 21 1oryy- Et Zlo= 2t u sh ntys
  73. 282. y7 + 2. 20. 30 X y2 + 30. 30 XXyy
  74. additus Agtu ydyt quistu igato
  75. fit XX X y dy +Z Xyydy = fnn y dy = fx dx
  76. Fhop. 3o xydus X31. 30gyax.) 4eo y y
  77. 320. 30 92 X 620. 30. y X ax (36. ∞2y dy. 2(30 X x
  78. gX y dx gxyd y
  79. =2unxy dx
  80. nhut ni discormus qua
  81. ocris aota namloter
  82. Hicis demanteatur dari sxytusa essum
  83. mndlliplicetur per y, et XX yy dy + Xy dx = nagy dy +∞y dx. Ergo Xdu et xydx pendent aje
  84. luvicem, E seid X sxy ex pendet ex Exxyydus quaedatur ergo et sxydx datur
  85. imulliplices per
  86. xytit xx xytdus + Xy dx = naxudu = X ydx. sed sx yd dx pendete aya
  87. sta set pis ayt, fq. e iest sumatitis absiure nm sum r pe h est et pogcus psetts a siam set
  88. Xy ax pendet et
  89. 16. Su 4

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0004?run=73