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Leibniz-Handschriften zur Mathematik LH 35, 4, 1, fol. 7r

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: 0.69.

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. 8v); this page is its right half.

The machine reads it as

  1. (4
  2. Aequatio Quadratica duarum incognitarum conglata
  3. in Numeris exequenda:
  4. X + dx TE yX + e y + f9 + gl. p0.
  5. X + d X + d H ~ C y 1fy - gl
  6. + 1dy
  7. +cgre
  8. e
  9. +2cd.. + q2
  10. unde fiet:
  11. (seu
  12. Invenienda ergo Y talis, ut - e ∞ fy y -gl sit que uadratus.
  13. re
  14. +c.. +2cd.. + aV
  15. a
  16. 1
  17. nde ab Aequatione quadratica completa aem traduximus ad incompletam
  18. Jam efficiamus ut multiplus iptus y ascendat ad quadratum
  19. Huus aequationis
  20. y (- f Y (= ob 0. tollamus terminum secundum
  21. +2cd . 7+ duact
  22. 12
  23. 1- f y
  24. +ned
  25. E
  26. ∞e+
  27. (+ 52
  28. -4cdf
  29. +4cd
  30. C
  31. l
  32. +8 - 2ec c4
  33. 1 13 1
  34. e
  35. t
  36. Asgrationum
  37. Re solunio ergo omnium robematumvadraticaum in Numeris,
  38. Resolutio ergo omnium Z0 eorum Constorum sive quadraticorum
  39. in numeris huc redit ad resolutionem hujus laequationis:
  40. -et y -el gl +f12
  41. a
  42. +c gl
  43. + et qr
  44. e
  45. -4cdf1
  46. (9)C4
  47. Sive invene generalius.
  48. v2
  49. hy mt v.
  50. c
  51. si m l’ absit, necesse est h, esse quadratum, alioqui problema est impossitile
  52. si h sit quadratus, problena solutum est, etiumsi ul adsit
  53. Artiq ergo fuerit saltem ab initio statim ita formare aquationem
  54. propositam ut hl sive et + ci, fiat quadratus. Quod an commode
  55. fieri possit videmus. Si c2 le
  56. si C2 = l sit quadratus, tunc enim inverso modo progrediemur incipiendo
  57. ab y; ati num incepimus ab X. Nunc ut appareat quid fieri possit,
  58. ponamus X p _ B n Z n co + p.
  59. eat 2it
  60. 1
  61. e
  62. C0 + En CP + p2
  63. = + drs p, e2
  64. et fiet acquaitio talis. co
  65. 1
  66. , et y H 20 + 1p +5
  67. et ey p C4 co + 29rco 29 seco tY
  68. l
  69. Et CyX Cnqco + cnr CoV + ens co+ cp 9co E Es
  70. 12
  71. 1
  72. +er X ahr C0 B, 29 se C + cpr V
  73. n 1s
  74. nx
  75. enpt
  76. 1c4
  77. i
  78. +57..
  79. 2es.
  80. 12 C
  81. es 0
  82. d - 2 + f= 4cd 5+ed
  83. + cxs 1
  84. e
  85. opl
  86. lita
  87. sive faciamus. 1y

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 1, fol. 7r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00067996:0013?run=73