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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 131r

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: 0.81.

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. 132v); this page is its right half.

The machine reads it as

  1. ac + b
  2. b
  3. e
  4. bd +c
  5. Ebc sa cd cd
  6. bi ac+b
  7. cd vc Xd
  8. acd + bd + bc
  9. bcd
  10. In tali ergo casu, cum fractiones summendo sunt, q ita comparatae, ut
  11. se nommator praecedentis sit numerator antecdentis, fiat fractio, cujus
  12. nominator, sit factus ex omnibus terminis demtoprimo numerator compositus
  13. ex tot terminis quot sunt fractiones, et quaelibet pars ex omnibus terminis ita
  14. it
  15. ita componato, ita ut prima constet ex omnibus terminis, demto se secundo, secunda
  16. ex omnibus terminis demto tertio, et ita porro. ita terninus pri pars prima numeralori
  17. differet a nominatores quod loco termini 2di, habet primum, (quo nominator caret)
  18. pars 2da Ao, quod loco termini 3tii habebit idum C.
  19. dam ut talia: acd +bd + bc 4 + h +E
  20. d
  21. bcd
  22. breoder symnes ita orinor agendum erit: differentia imer acd+ b
  23. uud sic potius; nominator habet ses demito primo, primus numerator habet oes
  24. demto, ido reliquinumeratores habent suum terminum bis, et carent praxime
  25. ante adentet proxime sequente. differentia inter acd-
  26. summam ita investigabimus: acd + b d = ac + bd
  27. bd + bc = bd +E b
  28. Hini apparet si b. sit media proportionalis inter a et c. vel C inbib et d. tunc
  29. ad summam inundam, tantum primum terminum multiplicari possi per numerum termonorum
  30. et facto velut numeratori subscribi posse nominatorem factum ex omnibus terminis
  31. dento primo v.g. acd + b d + b facilius perveniri posse, quia ac = b et bd=
  32. 1 2. 4. 8. 16. et sit q l B ibi mendi poterd oes temminos esse
  33. Quid verd si temini siil Arithmeliae proportionales, ita stabit:
  34. a + 2aX
  35. 1+37
  36. act, t a a atir, 4 at or atr, atn aror, f an acin atx
  37. a + 2 X + 3aX +6 aX
  38. a lax + ran = 3a X + 3X 6aX =
  39. = a2+ 3X +5AX + 7 ax
  40. atx a + 2X a+ 3X. (bd) arxat
  41. Ar + = + + . sintque a. b. c. d. e progressionis arihm etiae.
  42. a + = 4t +b (B huc aequita ulilis observatu ad reduchines) i
  43. B+C
  44. ee
  45. a +X.
  46. a +b, 1 ab + bc + ac + - abe + abd 1acd +bed. Et (hoc schema unversalcest
  47. ab NC abc.
  48. abcd
  49. in omnium fractionum additione, in quibus Numerator Unitas. Cum jam numeri su pr termni
  50. sint progressionis Arithmetuae, sunto a = a. b- a + IX c = a + x d = a + 3x ex
  51. 1+ = = a + b = a + a +X 2a +X
  52. ab
  53. a aIX ara
  54. +
  55. 1 E
  56. L. abtbetac. arax + a + Er FSax F a trax (3 a 1 6ax 1 2
  57. abc
  58. quod si jam X- a. erit 3a X Ha et si a = 1. erit 1
  59. ad + 3a X F 2aX 9 a +3aX134
  60. math. X1B 2 131
  61. ac + b +, bd + c acd +bcd + +b d tbC-
  62. cd
  63. DCd
  64. acd +bd + bc
  65. bca
  66. Ca a a +2K =
  67. a + 2aX
  68. abc a aFL atEs
  69. = a + aX a + 2X.
  70. + a X + 24
  71. F ax
  72. 30

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 131r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0261?run=74