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Leibniz-Handschriften zur Mathematik LH 35, 3 A 23, fol. 8r

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: 0.83.

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. 9v); this page is its right half.

The machine reads it as

  1. de quolientibus replicatis. Scheda 1V.
  2. proratione a ad b
  3. Tit series quotientium replicatorum e 1. v. Wv v. v. v. er
  4. quaeritur Erit aequatio exprimens relationem inter a et b.
  5. a - 1 b. aequ C. b - C vv aequd. c - vd aequ. e. etc.
  6. a = vbaqu. 1. (a) - v (b) aequ (C). Et generaliter:
  7. (a)- v2 (2(b) aequ (2(C)
  8. sive (Z(a) - (2+ 1 (4) Eequ (Z ( a)
  9. quod si aequatio
  10. (A (21 (a) - (B ((7, (6) aequ (211 (C)
  11. (2 v , (6)
  12. vel (Z (a) 2. v (Z() aequ. (Z + 1 (c)
  13. vel denique: CE (2 (a) = v ( (a) aequ.
  14. Eodem moda
  15. (211 (a) - (2+2(a) aequ (2+3 (a). Et pro (Z +2 (a) substicuend.
  16. volarem ex aequ. 2. fier:
  17. 23+1
  18. (7+1 () (2+1(a) = v (a) + v (2+1 (a) aequ. (((212(a)
  19. Ergo daegu;
  20. seu c aequ a - v b. Erga d aequ b- vc aequ b - v a + p b
  21. seu
  22. + B1 2b = v a
  23. p
  24. +vo1.
  25. fiet: e aequ. +1 a - v 7b
  26. 10is
  27. = verdt
  28. fiet: f aequ - v a +.
  29. - 1 7
  30. pis
  31. +voH
  32. + v
  33. + vor. 3 B)
  34. f. aqu d - ve.
  35. vel genepaliter assumendo quotientes
  36. l. m. n. p. g. 8. et faciendo: Reis quantitates. a. b. c. d. e. f. g.
  37. a - lb aequ. c.
  38. b - mc aequ. d C - nd inqo e. d -perequ. f. C- 9f aequ. g.
  39. erit c aequ +1 a. - l b. daqu. b - mia + l. m. b
  40. d aequ. - 1.m. a +1 b equ +1. a - l. b. + 1. M. n. a - 1. n. b - l. m. n. b
  41. e aequ. + 1.
  42. +1. M. n..
  43. faequ = l. m
  44. +
  45. + l. m.
  46. a ct1
  47. + l. m.
  48. a +1.
  49. = 1. m. n. SP
  50. . +l.
  51. Pa ego qu 1 a
  52. + vel Y
  53. + l
  54. +
  55. um
  56. +
  57. ut
  58. b aequ +E a + y
  59. C aequ. +V a + 5
  60. -nl
  61. e Et il porro
  62. faequ. - 1m a + 1+ l. mb - 1+ 1.m. n p a + l+ 1r Lm A B b
  63. gaequ. B - gf. est autem C aequ B a + A b.
  64. et f aequ. B a + Z b. Ergo 9 aequ. +B a + A b
  65. ergo coefficiens residui sequens fit ex
  66. qu. =95.
  67. sequentis (exempligratia D- qu. coefficiens cum a. pro
  68. residur ipso residuo g.) it conflonitur ex D
  69. resic coefficieate refitii verultium respontente cum
  70. a scilicet) residui penultimi e, et eo efficiente
  71. respondente in residui ultimi f ducto in novum
  72. quotientem q. et subtracto. Habemus erg. regulam
  73. proprediendi.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 23, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068236:0015?run=74