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Leibniz-Handschriften zur Mathematik LH 35, 4, 7, fol. 2r

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: 0.82.

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. 1v); this page is its right half.

The machine reads it as

  1. Utile autem erit commemorure qua via ad rem penitus
  2. ernendum excitatus sit animus:
  3. in duas aequationes ejus modi:
  4. 2N 2E
  5. X
  6. Incideram aliquano
  7. n + n p b et memuri
  8. Fy 1Ab et XY B acc e quarum altera est
  9. circulum
  10. ad lineam rectam, alterm ad Hyperbolam cit ca
  11. alymptotos. Unde sequebatur:
  12. et yt -Oy + ac. sive
  13. et VH 16+ 5-.
  14. Xp) a. adeoque dc +y b
  15. V H + + Y - tE L-3
  16. Ergo pro X2 + y ( b.
  17. ergo substituto valore ipsius y, Scritebam
  18. X + b + f- et p b., sive X1 Yb - 1b- c
  19. Erat autem C major quam b, adeoque Sb2 -e erat
  20. At vero
  21. et aequacuidam linea a
  22. in quod me valie serplexum rediidit
  23. praecedenti
  24. Cum enim ex calculo praesenti deduxissem,
  25. TX + y + ~ b + 1B - c + lb - sV 2, non capiebam,
  26. quomodo ejusmodi quantitas posset esse realis in qua exprimendam
  27. imaginatiae imete sive impossibiles ingtederentur. Relegere ergo
  28. calculi restigia coepi; errorem suspicatus. Sed frustaa: e eadem
  29. enim perpetuo prodiere.
  30. Tandem venit in nentem calculum operationema
  31. instiluere quam hic subjiciam;
  32. d
  33. P3
  34. b + 16 -c + sb - sb
  35. 4
  36. Ergo quad rundo atrobique,
  37. +Fb-e + b + e, = sie dp, A+ B. Ergo quadrande utot
  38. aeque d + A2
  39. t
  40. 5.t
  41. ub +
  42. rectungulum
  43. + Be
  44. b - st .2
  45. + 2 AB BIBLI
  46. + 2C
  47. ipsius d, fiet:
  48. mam
  49. ac nenerre
  50. erit ergo ergo dp b +2c adeoque
  51. Aeqtando ergo inter se duos valores
  52. b H b. + -C + - 1
  53. BLCa L A
  54. comecio ed
  55. Nam (AB, sive sb + B- et in SB E facit c
  56. it calculus ostendet.
  57. a p)
  58. une
  59. Yb+ 2C
  60. stende si in numeris faciamus b p 2. et C etiam p 2. fiet:
  61. n se
  62. Y6ni
  63. Si + s- 3 + S1 - 5 - 3
  64. Servation farite
  65. Qua Therremate nullam in tota analytica singulare
  66. natatam
  67. magis et paradoxum a me nemini est egrvatam et nam me
  68. primum me arbitror quatta pi radices irrationales
  69. in speciem imaginarias; adreales etiam sine extractiones reduxisse
  70. aes
  71. Er notabiles iest, no sextum nos habituros Operationis sive
  72. grithmeticae hoc analyticae genus; nam praeter additionem, subtractionem
  73. mulsiplicationem, diisionem, radicum extractionum habebitur Rednctio Reformatio le
  74. Reductio.
  75. deu pares so tolun Additio et
  76. v
  77. subtractio composita reducunt ad simplicia; multislicatia mpliita a
  78. expressai Multiplicatio es causas ad effectum: Divisio et extractio contra-
  79. Divisio fractos ad integros. Extractio surdos ad rationales; e denique
  80. Reformatio imaginarios ad rationales reales.
  81. Cincognitarum XtX
  82. aB

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 7, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068004:0003?run=73