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Leibniz-Handschriften zur Mathematik LH 35, 3 A 5, fol. 1r

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: 0.85.

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. 6v); this page is its right half.

The machine reads it as

  1. sb + HC multiplicari debet per formulam aliam, ita ut in producto tollato sublata sit irrationalitas
  2. b + C in dee aequ. bd + bd + be + ce, aequ. b b + mc. sit daqu. b.
  3. fiet b + bc + be + ce. fiat e aequ. = c. et habebimus: b2 ( b0 ( bc) c
  4. b ed vel carius: b+c in 1b+ 2c, fiet 1b4 1bc + 2b6+ 2C. fiat Z aequ. ()
  5. et habebiious: b et 1 aequ + ( et fiet b= c. Hinc si sb + sc multiplicetus
  6. b+ per sb - se habebitur b - c. sed et si b + sc multipliceto
  7. per b - sc. fiet b - c.
  8. =. b Vb + sc+ Id mustiptican formula multiplicanda per aliam formulam, ita ut
  9. productum sit Grationale. sit b + c+ d multipl. per 1b + 26+ 3d. fiet:
  10. 1b + 2 bc + 3 bd
  11. 1 bc
  12. +2C+ 3cd
  13. + 1 bd + 2cd + 3dd
  14. erit 241 aequ. 0. + 1 aequo. 3+2 aequ. 0.
  15. Ergo 2 aequ. - 1. 3 aequ. - 1.
  16. sed et 3 aequ. - 2. ergo 3 aequ. + 1.
  17. a aequ quod est absurdum
  18. lig dodratilum
  19. itaque hac multiplicandi ratione Ctrinomium ab irrationalibus liberari non potest
  20. Ergo assumamus: 1b faciamus ergo solum 2+ 1 aequ. 0 et 3 +1. aequ. 0.
  21. fietu et 1 aequ. fict b 5- d - 2cd, factum ex b ++d in AsC.
  22. per compendium: b- c d vocetur A. et - 2cd vocetur - B. fiet A-B ducenda
  23. in A+ B et productum erit A =- B. seu b +c+ d - 4bc- 4d (2Cd9 - 9Cd
  24. Ergo si sb + +c+d ducas in Ab- tc- sd in b.cB d sed
  25. porr Ergo b+ c + d in b -c - d in b2 - c= d + 2cd dat b + c + d - 2b C 2
  26. jam: b- c- d ared dabit b 1- 2bod
  27. 1 =c = d
  28. b + C + d - bc - bd - bC - bc - bd +Cd + ed +2bcd
  29. rgo +b per 4b = bc - 2bcd dabit b - 2b
  30. per + b per + b
  31. d
  32. d2
  33. - 2bc dabit +b - 2 b72
  34. polile per - b + 2bc
  35. cet
  36. + d.
  37. 4 ct = 2 b d
  38. +d4 - 2 cd
  39. dabit. b 4 26
  40. 25+ + 2b1g
  41. + 2 ct d
  42. idem prodit si pro d ponas bvet c.
  43. sin facias
  44. b per + b per + b +26d etiadabit + b+ - 2b
  45. d - d
  46. +c9 26242
  47. +d4 201
  48. Et generaliter quia:
  49. quia +b per 1b3- brc +2bcd dat +b - 2b5
  50. patet
  51. =Es
  52. +c4 - 2b4
  53. +d4 - 2c2d2
  54. -2cd - 2cd
  55. Le per dat - b +c
  56. ideo facil etiam per quam formmlam multiplicari debeat +b+ c- d, vel + b - c - d.
  57. Hanc methodum prosecuti habebrinus resolutionem omnium aequationum
  58. Nam ponamus exempli gratia loco + b - c - d ponamus X - c - d aequ. 0.
  59. et spalturio tne aquatiarem dum C et d estrogaus a potert au debitam
  60. b + b2 + 2b cd
  61. = bc - 26cd 26

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 5, fol. 1r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068218:0001?run=74