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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 187r

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: 0.79.

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. 186v); this page is its right half.

The machine reads it as

  1. conditio deest, ut ad daas aequales
  2. radices determinetur, toties duo maximi incognitae duos aequales valores
  3. l habentis, tolli possunt ut esto aequatio X +BX MaX + nae X + ple ro
  4. determinanda ad duas aequales radices: ergo
  5. et jungend prima multiplicatio dabit.
  6. 17
  7. + 2ma X tna X + 4pa r.
  8. 4X + 3lX + 2mak + na 0
  9. Ema X +3naX + apa
  10. ma
  11. nar
  12. 10.
  13. In aequatione alibi inventa circum hoc problema:
  14. v
  15. et pro p, ponatur 15 y, fiet s -y
  16. sive ranco
  17. Et pr fiet:
  18. sy
  19. axfax pat
  20. uq
  21. +I et So
  22. ++ yf (+ +) XX
  23. d (+ +) .
  24. pro X + P, ponatur V. quam V necesse
  25. m7
  26. 2
  27. posterior dabit.
  28. Ergo
  29. Elegans satis observatio
  30. de (
  31. Jyp
  32. (1DYf (t F) yx.
  33. 45a = 29x f + y X
  34. Ly+ 12dy + y
  35. ax
  36. C
  37. reddendo
  38. tso
  39. Et pro 5 =y ponendo B,
  40. rax +aX
  41. pro V ponatur ejus valor fret:
  42. de () Srax + ax et qdrando.
  43. ++) f(t) X (+ +) p
  44. (
  45. est esse eanum, et
  46. possumus considerare velut eandem, etsi quia puncta A. et P. immobltia sunt, utcunque duo
  47. sint puncta X et Y quare ipsam p explicare utile est, est autem pa + a X fiet:
  48. da + dax
  49. sI
  50. 2ax a e et quadrando per 15-y, fietus.
  51. Nimirum FPp, (+ +) ((+ +) W dSo-
  52. (+ +) F)V dssE
  53. (+)
  54. -dse
  55. haec
  56. aequatio tantum unam habet incognitam duarum radicum
  57. as
  58. Lis
  59. dgu sive
  60. 1V -y
  61. 10. conferitur cum simili duarum gudicum aequalium Y y, e y -Y
  62. 2+ W + d
  63. multiplicetur per y + mconferenda cum u- re +C
  64. I locum X, subpiluatu 2ax f a X, fiet:
  65. Nry
  66. +y
  67. ytyrys
  68. + +29 X + 24d15 un 510.. juio nondum conferri potest, qua
  69. +d nondum satis deterim nata, est, u nulla atra
  70. a
  71. restet deterutnad quam ad duas aequales radices, pros, substituatur ejus valor petgr
  72. pro p, fiet a 4 2a X + L X et pro y, fiet 2aX + a X sed nec sit procedere
  73. puto quia ita mimium determinationis affumtum est, videamus tamen, videtur enim in nostra esse
  74. s
  75. potestate, vel s explicare, vel WV: Ita est, sed non debrisset puto explicari p.
  76. An sie, habemus. Venit inihi in mentem res notablilis, nimirum aequationes simles
  77. comparari posse, etsi non sublatis signis radicalibus: ut ecce aequationem superiorem
  78. 2d rax + ax +ZX bX + ta. A10 si jam alia indeterminatu, duashabens
  79. radices aequales similis propositae haberetur comparatione facta solvi posset problema
  80. licet non quadraremus aequationem, quinqe cule coleatitios adert tubus opus incopuitis pors
  81. El

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 187r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0375?run=74