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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 417r

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. 416v); this page is its right half.

The machine reads it as

  1. sit
  2. bd
  3. + Ed = C+ C d quae a me reta reperta
  4. quadralor embituum
  5. vel sectori.
  6. est relatio polygonorum inscriptorum circulis
  7. respectu
  8. b, c d
  9. posito sequentem esse numeri laberum dupli praecede ntuse
  10. quaritur relatio inter b et C eadem quae inter C et d.
  11. sit
  12. 16
  13. 1618
  14. 25 26, 2728
  15. betro-b el 40. b 4 b ac 4. C + ee t b c +bC et
  16. e
  17. 16
  18. 2526 27126
  19. Eigo similiter 0- B5C+ 7C ecc + 6d +3d. et +5bC d + 78c d et
  20. e
  21. 17
  22. 18
  23. multiplicetur utraque per frmulam arbitrariam addantur
  24. in se invicem comparantur datae giam performutam
  25. cubitrariam multiplicatae. Generaliter et compendio
  26. sic fiet data aequalio b d +C d = C3- cdE =0
  27. BL + CM + BNC = 0 ta eodem modus CL + DM + CND =6
  28. (ubi nota librus B. in BL, non esse Lia B divellendum, et ita in caeters)
  29. multiplicetur aequ. 1 per B2 + C2 + D, + BTC
  30. BL + CL + BLC = 6 et Cs BL + CM + BN C = 0 et CL+ DM + CVd
  31. C
  32. non
  33. quantitates, sed notas modi tractandi .
  34. Multiplicetur jam ag. 1. per B4+ C4 + B + B4C+ B4d + C+d + BCD4
  35. seu per formulam 4. Inde siet aeg. 4. Similiter per aliam formula
  36. similem ubi tantum (5 pro 4) multiplicetur substituendo 5 pro4)
  37. Csrullem formulae 4
  38. milliplicetur 0g. 2, fiet aeg. 6. denique per aliam formutam
  39. similem formulae 4, substituendo 7 pro F mulliplicetur ag. 3.
  40. habebitur ae g. g. addanta aequationes 6 et 8. composita
  41. comparanda aequationi ut ita inveniatur 8g. 2, vel 3.
  42. sed hac methodo non invenietur relatio tant extrua
  43. nana transcendens seu indefiniti gradus. Se si des solvi
  44. pt. semper solvetur, ut potentiae per solos numeros deter
  45. minatus inveriantur. Igitur necesse est cote
  46. esse aquationem ut B ingrediatur in exponentem
  47. lipsius A vel contra
  48. sit igitur ec
  49. p B6C +7B+9C + C
  50. sit igitur B
  51. = C et D = 5C6d17 49D + C
  52. sit n numerus latem ipsius et anno et qquadratu–diametri
  53. et 4nng = h, fiet hb + cc = hC
  54. fnsi potius B BB(BC+ 5B + 7B) = C et D = C Te+ SC +7 C. seu D=
  55. seu DC et B teF, V+7B repertisum valores ipsius Cat ipsius d, per Bsolam substetuantur
  56. B(2 er , B 1208 + D + B
  57. n aequave
  58. 602+ cd=C2+ cdd

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 417r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0829?run=74