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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 275r

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: 0.78.

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. 276v); this page is its right half.

The machine reads it as

  1. Duns oportet comminisci radices quadraticas tales, ut quadrata singularum, et cubi, et facta sub
  2. ipsis. sint rationalia, si certis modis mnttiphiata invicem jungantur:
  3. 1 +m + s0, 1 + n +hum m. seu n+ n +3nn +2na aequandus quadrato:
  4. (5) bc + s0bc. Ejus cubus: bc + bc + 3bc
  5. F19bc + 0sObc + l.. unte quad. . 86 sebc + fb s0b + 1
  6. e sit alia L s, bc + + (b + m
  7. erit cubus inde.
  8. ponendo 9pf. itemque teph. et
  9. componendo fient aequationes:
  10. f + 3h m 1, 0. sive n A
  11. 1. 1
  12. ritit tc
  13. etem
  14. +3n h
  15. +.14
  16. 3t be
  17. +3h bra
  18. 2m t
  19. 1259bc
  20. R3 B
  21. bc
  22. 1bac nbe
  23. demque 11f 2t 3hibc (+3 mi L 35 0 er ponendo: x eel: fr v h. Rej: 2Iv + 3 hEbc 0
  24. 9h4
  25. quod si adtum ponasBp h hd fiet: t lino si jam hponas v fiei 2l + 31 bc +V3 4
  26. H sive Et + hY bc + h2V. et faciendo Y ∞Y. fiet 2 + hbc + h A, et aursus faciendo
  27. +) _h. fiei. 2co + hp n ed: fier: 2 + bc + ∞2. Sed ut haec muttamus
  28. sufficit fieri ber, . 54 - 18IH. sive faciendo 1g Af. et hp e f fiet: - 3 - 18s n. sed satius ista ditferre
  29. 19h0
  30. ad finem. Erisque pono b+C⊓) = 12 ( 2f bc) + f a + st f bc
  31. fiei bter 15 3+19d e
  32. 27h
  33. 27 ∞ - 45 - 61 fp +, Nf n 41
  34. 303
  35. 95 23 +54 A
  36. Hinc s ut obiter dicam videndum an effici possit in numeris ut habectur numers rationalis cutus
  37. qui non sit quadratus, et cujus cubus sit quadratus B. sed hoc est impossibile. Imo eodem argumento
  38. video id in irationalibus quoque fore imposribile.
  39. Videndum an tales fieri posiut irrationales quadraticae, ut quadratum eatum sit rationale et factus
  40. quoque sub ipsis rationalis, et tamen cantera
  41. a qVb + 56- c + 4S +b- B E + qu 1IX.
  42. pX e1 pb nac 20S6 C pb (, Y6- c) +2 Cp +pu + inj sb+S. + npsb - s.
  43. X +2b+2c 1b + 5... + n
  44. Are Y
  45. sb - F..
  46. + b n + 3 n Sb + 5..
  47. Sb - 5..
  48. fier: 2b + 3n + 2np + 9 B et rursus n + 6 ba + 2p b + pn + gn + r
  49. b- bac, H + 3n + 2np + 4 + n + pn + 9n +, sive 9n +6n + 2gn
  50. X, 3n +p
  51. +2p2.
  52. Hn +ptgnur
  53. 5 125 n + b4
  54. soc pro 2 N scribendo _, N
  55. fier N + 2p N + 9N + p9 B ponamus et X.
  56. fiet: 4b2 + ac +8bc + nt + + 4b n + 4t 45 2 b ne sib. + F. + ab n p XE
  57. b- si
  58. sed hini semper ad aliam uscendetur cubica, apus est ergo irutionalibus quadcaticis cubi as neludentibus
  59. Nihil. hac.
  60. notabile
  61. Exemplum hic rraninalis in speciem, nempe Sb +J6- C + Sb-sB
  62. 17 2b 42c. Itaque etsi sit majoi quam b. non tamen rdeo quantitas tota erit
  63. imaginatia. SXx nsy e b. Lxy n c quo ( x + (3y 1 Z.
  64. BxV ei 1DC quaeritur Z.
  65. 10b. 5b = c + sab - s ex
  66. mb +21 + 2b - 2c + 4 S C Y 2b + 2c
  67. ReculX + cy 3
  68. X2 + y +
  69. omnis si irrationalis ducatur inseipsam, multiplicatur fractio quae ejus est exponens. si in aliam adduntur expo–
  70. nentes: Exponens ab (3) est Z. exponens à SD est = 4 L +: 3 b 1 2c. si 3 postet componi ex
  71. dinita quantitate numerorum progressionis Geometricae duplae, possemus explicare sic Cubamam ipsius
  72. umagmariae apparentis radicem. Sed infinita ad eam rem serie opus. Nam:
  73. 3B + N 4 ist 116 450
  74. dC 5 + 1rg + f- 143 Y 1 2+ + 1415
  75. crisg. s
  76. +hi =( 2e m3 = 5 5

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 275r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0549?run=74