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Leibniz-Handschriften zur Mathematik LH 35, 3 A 18, fol. 8r

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: 0.83.

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. 9v); this page is its right half.

The machine reads it as

  1. contineatur
  2. in potentiius radicum aequationis datae, ita investigabimus
  3. quadrato
  4. sinde solidae surdesolido
  5. Quid rationale anveriatur in Badinis datae aequationis, nihil rationale
  6. quadaticae, qu ita investigabimus vel cubo datae aequatimis cubicae, dc ita investigabimus
  7. continantis quadrata aubo, suodesolido, itca ita inveniri potest. Sit.
  8. XX aequi pX - 9 sitque pars radicis rationalis 1. irrationalis H hoc valore substituti in
  9. aequatione sirte XX aequi p 1 e p. 9 Ergo pars ipsius X rationalis erit p1. 4.
  10. datis partibus rationatibus
  11. ag inveniri potest ex eo quod est potentiaum inferiorum
  12. ejusdem radicis ut si scsit aeauntro X pXL GX’ErX + x + D aep o.
  13. posito rationatem partem radicis esse1 (nempe P. S) ipsius X esse 2 (nempe pere p 96)
  14. in radice aequationis simplicis quadraticae, cubicae, continur etc.continetur pars
  15. seu summam omnium radicum per coderum earum divisam) portem
  16. rationalis est terminus secundus aequationis mutato signo per numerum gradus divisus.
  17. seu Aro aequationis N X+p aequ. 0 X+ pX etc aeq. 0. X + pX et C aq0. X pX CH 6g. 0.
  18. erit pars rationalis - p. 1 = p: 2 - p: 3 - p. 4 etc.
  19. Sit jam aequatio X + pX4q eq. 0. ergo id quod rationale in pd X continelitur erit
  20. id ob X aego pxq erit aequ. p in p. 2 -q seu pp: 2 -q
  21. 273 Videamus quid tunc X contineatur sit aequatio X + bX + c aequ 0. pars rationalis contenta
  22. ui x est pp: 2 = q mullipliceter per 2+ dsiit X3 + bX + ex
  23. (9)33494. - (9)32.34. a) 32. 37.84
  24. quae
  25. X +G)32. 33X 4(9) 312X. GBC. 33 si sit aequalio X + pX + r aeq. 0. quae scimus in X contineri rationale p: 3
  26. 1 +db + de
  27. quaeritur quid tunc
  28. x +9 rix
  29. Ca3
  30. es
  31. in se continentur, divnentur eu per X fic
  32. se jam sit aequatio quaemumue X X p X aX qNr
  33. rationale
  34. erit aequatio pro N,
  35. X
  36. 2C-2
  37. p X.
  38. 38-3
  39. X E p R
  40. ambinatoria
  41. Quos terminos sumsi ex tabula alias
  42. +29
  43. +5p9
  44. SpY
  45. 4.. .. X -4 ... XY -6 etc.
  46. i
  47. 509
  48. + 5pt
  49. +5qr
  50. concinnata unde etiam termini
  51. -5’esse rationalem scilicet
  52. Unde patet summam omnium quadratorum a radicibus, esse rationalem, scilicet p - 24
  53. relicti vacui suppeeri possent
  54. cuborum
  55. quadrato quadratorum
  56. 9. r. F. v. sunt combinationes radicum, nempe unnum summa uhiduum, qenuma
  57. surse solidorum
  58. Y summra ternionum, +quat summa quaternionum, V, ipsa quinio unica
  59. Hinc po Hinc jam sequitur partem rationalem unius radicis esse p: e.
  60. et po
  61. binionum,
  62. pp- 29. NC
  63. posito scilicet aequationes X etc. vel x etc
  64. vel X etc. non esse tractabiliores quam aequationem,
  65. Si valores isti bene inventi sunt, succedunt inveniendo in aequatione data quadratica
  66. ipsam X. Quod de generali intelligendum.
  67. cubica, aytica, surdesolida id quod rationale in quadrato, cubo, seto, sundes olido
  68. continetur, perinde ac si id non jam nossemus. sit Xx aequ pX - 9 cum rationale contentum
  69. (nam e eo caso valet 2) erit rationale in X contentum p in p. 2 - g. seu pp. 2 -g
  70. qui valor consentit cum priore pp- 24: seu p pp+ 29: 2 seu pp C2 - q
  71. sit aequalio, X3 aequ p X = gX +Y cum rationale in Xt contentum sit p: 3, in X sit pp: 3 - 29:3 ideo
  72. rationale in X3 contentum erit P :3 - 2p9.3 = pg: 3 +Y seu p: 3 - p4 + Y seu p - 3p4 + 3Y, : 3. ut aute
  73. in X sit p: 22
  74. to aorius que que am strite pui t neu is iu incares pote
  75. pro d
  76. C
  77. 36=9
  78. etC
  79. 2c. 4
  80. ps
  81. +4p9
  82. apr
  83. -299
  84. +4+
  85. 4.... 7
  86. A A.... X
  87. 4C = 12
  88. ete
  89. se- 15
  90. ete
  91. 4C-8
  92. Se-5
  93. 30-10
  94. p- 3p9 + 3Y
  95. P - 4p9 + apr 429q. 4L
  96. P - 5p9 + 5pY +5p9. spt. 5qu
  97. quadrati
  98. cubi
  99. jgti
  100. dicet p- 344+3,. 3bC
  101. Cp- rpotaprtq. at: se

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 18, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068231:0015?run=74