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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 63r

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: 0.86.

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. 64v); this page is its right half.

The machine reads it as

  1. Alaqe
  2. Magnum Compendium intesi infinitesimalis salculi habebitur
  3. si sit adhibeantur variantes Hombeoptotae. Nam omnes aequationes
  4. X+ d Reg=, fit Cdx fidy . locales seu ad variantes, reduci possunt
  5. ad Homoeoplotas, ut si sit q = xty et av = xy
  6. sit jam d =X + y t b fit dx + dy = 0
  7. O = N b + Clxry) + C xy + f(exryy) fiet o: csilas ty) + C yA t X AGB) A2s (x Ax a y dy)
  8. C B 8 0 = r et 160 + 16 in py + 120 (ex tyy) = 121 (XXy Fyy) + 130 (X yt )+ 131Xy trurgy 1i4ot
  9. Cujus differenbratio erit
  10. Et ita p.
  11. sit data aequateoa
  12. poldxttus) + 11Hdu
  13. assare vr yyax tare
  14. ex + 3. 131 xxy dx 4 4. 140 F + dy
  15. sis exprineturd
  16. R(dx ) + 2 210x dx + 201mdx + 271 Xy dx + 220Xx dx + 202Y9 dx t
  17. ly
  18. dy
  19. puu
  20. yg du exx dy
  21. differetialis forunta
  22. +22IXXydx +212Xyy dx + 230∞ x + 203y x
  23. ryay
  24. xdy
  25. dysit 200 + 210X +201y + 2IIXy + 220 XX + 202 yy + 221 Xxy + 212Xyy +230 X + 203 Y
  26. Aequntio
  27. XXay,
  28. fyy dy
  29. seu = ax 200 + 210y + 2817 + 211Xy +230Y7 + 20d yy + 28IXHy + 2H XXy + 296y + 2637
  30. ffrreulata 3) 110 +, idq + DMy +2. HIXy +3BDXX. F 121 yy. + 3, 13+ Exy t 2. 122Xry 4 4. 190 X. + 131 y
  31. 10 +2. 120y + 1IIX + 2. 121Xy + 3, 150y9 + 121, XX + 3. 131 xyy +2. 122XXy +4. 1470.7 + 13CX
  32. quodsi duo valores sint ideubici suffecerit tantum Nunquatiorem Numdratori
  33. ix quaesita
  34. vel oenominatorem devominatori coincidentiare, et fit 10 200
  35. 110 = 200 120 = 2 210. 111 = 201 121 = = 211 = 202 130 = ,. 20 131 - 5221 = 203
  36. unde jam facile intelligimus, eos numeros qui vacios d plares diversos dant per subbractionem
  37. unitatis, diversis ae quandos, v. 9. 21, dabil 220, et L 211. Nam dissimulato
  38. 1initiali pro (21, scribamus 2 et tollendo 21. et tolled H ita possumus tollere
  39. Fit 20; cui praefigimus semper
  40. sid quia id et ex ita possimus tollere unitalem vel, ab 1, vel a 2.
  41. unitatem tum ab 1, tum a 2. si tollamus ab 1
  42. si tollamus ab 1, fiat 20, sed quia gitur sub traxiums a minore transpositi fit,
  43. 202. totum unctiplicames per unitatem
  44. 21
  45. seu 02. Huic praeffigimus 2 initiclem fit. unit et
  46. tollanus a 2 fit 11. Cui praeficamus A. sit EI1, multiplicemas per
  47. 2
  48. nemper per numerum a quo subtraximus. nitiem
  49. numerum a quem diminuimu, fit 2 ∞. 2Y itaque 121 aequatur tum ipsi 1
  50. Eodem modo ptrocedamas
  51. tum ipsi 20d tum ipsi ZF Z211.
  52. a minore fit 03 mutabitur in oz, p divideur per numerum unde sustu
  53. in 131, fit 30 31; unde ab 1 H ef sei
  54. limus, fit.
  55. 90
  56. praefigitur
  57. 3 Tollendo unitatem durae figatur
  58. q dividatur per numerum a quo sustulimus 3, fit 3221, nec
  59. Ie
  60. sinsequia sustulimas
  61. 202 et 2. E1 203 et 211. Et
  62. neq fit hic, tra
  63. peveraliter quivis numerus qui cui praefigitur nitialis 2. ex quoc alius
  64. initialis 2, fit
  65. Hon Hiuc sem per aequantur
  66. in quo (rejecta initiali nota) differunt duae sequentes, potest trans formetur in
  67. in alium auciendo unitate uta unam noram, et diminuendo alteram;
  68. et notas transponendo; aequatur huic et producto provenienti maefi–
  69. sendo 2 initialem, tum uteus numems divide. ita Ei duo b ac lege
  70. Et hac lege servat proveniens A eadem lege mutatus reddit priorem dividatur
  71. ateoque per notam quae unitate multatur ad tansformationem; et fief
  72. et duo provenientia aequentur inter se. Ha e ein eis Nota ubi
  73. tunc etiam vil prodit
  74. nolae non potest sublrari unitat cum scilicet est o
  75. Hac leqe servata quotces interdum numerus trans formatus reddae se ipsum
  76. Hnc 202, non detalium, Z s
  77. o at quaesita conjurguntur vollendo dy: ex pudibu
  78. 24
  79. lequ
  80. cratem
  81. ex, 222 fit 31, adeoque 22F. 2
  82. heMrinu lio
  83. cum quaesita, id est per eam di
  84. in aal u sunt

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 63r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0125?run=74