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Leibniz-Handschriften zur Mathematik LH 35, 4, 17, fol. 10r

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: 0.89.

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. 11v); this page is its right half.

The machine reads it as

  1. De summa factionum quarum numergcs constans, nominatoes, Numeri polygoni
  2. Ex Goselino de arte magna sive tgebra lib. 1. cap. H.
  3. Dato latere restigandi polygoni ratio generalis ac facilis:
  4. Anferemus 2 ex numero angulorum; auferemus et monadem a labe
  5. residuos multiplicabimus invicem; facto addemus 2; summu ducta
  6. in lateris semissem, dabit polygonum quae situm
  7. e
  8. v. g. vestigemus. Alum a latere 6 quia triangulum tres habet
  9. anguloe, subductis 2 restat 1, ex 6 aufer 1. restat 5. sjam
  10. 1
  11. 5 adde 2 fit 7
  12. Triangularis numeres quaesitus
  13. Ego id analytice ita enuntio:
  14. si Numerus angulorum sit b.
  15. latus sit y. Erit polygonum
  16. - 2a Y 1+ 4 aV
  17. s. 10c
  18. C ba..
  19. b- 2, 0 y - 1,, + y 3
  20. si esset Cy rely + el - βC
  21. iniri poterit summa; fractionum
  22. ab ipsis denominatarum, ut
  23. alibi ame inventum est
  24. sunt autem e. d. B. datae; jam
  25. termini conferantur, fier:
  26. =2a + b,, 2e, et 0p - 2a +b
  27. multi plia per E 3, fiet 21.
  28. L eac HelBC2. Et in polygono peo ypone L XA21257+
  29. jam ut termini ubique conferri possint
  30. scubatur: 2C 92
  31. et jam ordinando: a
  32. e F
  33. 2a +b
  34. -2a72 - 4faZ- 2af conferantur ter minitem
  35. l - 4f a + bf + 4a - ba
  36. minis.
  37. +b. + bf. 1b r
  38. 44a.. +44)
  39. -ba.. baf
  40. 1- 2af + bf + 4a f - baf + 2B5. Quibus valoribus inter se qunctis habebitur
  41. 2 er 2a + b
  42. valor ipsius f. eademue methioit paritertl. Quibus obtentis poterit invencri
  43. fractionum omnium a Polygonis denominatarum, numerato rem con-
  44. stantem habentium summa. In Triungulo ipsa f necessaria
  45. non esst
  46. + 3

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 17, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068014:0019?run=73