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Leibniz-Handschriften zur Mathematik LH 35, 10, 3, 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: 0.93.

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. 7v); this page is its right half.

The machine reads it as

  1. secta, modo non situm sit ut in intervallo inter
  2. A et B, erit AB pervenietur ad ab A ad B, tendendo
  3. ab A ad B F et ab F regrediendo ad B, imo
  4. seu hoc codine FB + BF
  5. Si Hamen oelimus rem ordine punctorum semer
  6. desicnare em directionem sic dici potest
  7. universaliter FB +BF
  8. Imo etsi cadat F in intervallum, tamen
  9. universaliter dici potest A F - BF = AB. Nam cum
  10. BF progressus ad easdem partes cum A, est negatious pocasu
  11. cas et ita moles addendo fit AF+BF = AB.
  12. jam inveniamus ZA2B ex 1A1B. Q
  13. (2d0
  14. Nempe () 2AF - 2BF = 2A2B et 1AF - 1BF = 1 A.B
  15. puncti, addendus est motus regulae et puncti si ferantur ins 1A2 A = FA- ((A) A 1AF- ZAF. Et (po) 1B2B = 1BF- 2BF
  16. 1BF =1AF 1AB Et per 2 fit 5to) 1BF = IAF- 1A. B
  17. Et per 1 fit (6to) 2BF = 2AF- 2AB quibus valoribus 5 et 6
  18. substitutis in 4. fit 1B2B = 1AF- 1A1B - 2AF + 2A2B
  19. ubi pro 1AF- 2AF substituendo A2A per 3, _ altique ex
  20. seu si a progressu
  21. ipsius A auferatur progressus e apsius B, idem fit quod
  22. sotus Regulae sit 1AA 1R2R . erit 1A2A =
  23. poprius
  24. et fiet 1R2R + 1A2A = 1A2 A motus puncti A totalis
  25. 7mo fiet (800) 1B2B = 1A2A = 1A1B + 2A2B seu
  26. fiet (9n0) 1A2A - 1B2B = 2AB 1AIB - 2A.B seu
  27. mosse 1A2A + 2A+B = 1 A1B + 1B2B
  28. pascitur
  29. motus puncti in Regula sit 1A 2A. firt 1AEA
  30. C sit centrum gravitatis commune ipsorum A et B
  31. sitque et AC + CB = AB. hinc 1AIC + 1C1B = 1A1 B
  32. et 2A2C + 2C2B = 2A2B. 1A, C + 1C2C - 2C2A = IA2A
  33. seu 1AIC+1C2C = 1A2A + 2A2C at 1CEC+ ECLBC iCrB
  34. et 1C+B + 1 B+ 1BdC, = + 1CB+ 1B2B - (1 C2C+ 2C2B
  35. quae duae aequationes differunt relegando, vel quod eodem
  36. redit pro A substtuseo 2B et cntra et pront C substat atur 2C et contra
  37. redit pro I substituatur 2 et contra; et pro A substituatur B
  38. Omnia ergo redacta sunt ad A2A + 2A2B = AB+ 1B2B AC+ CB = AB
  39. 1AIC+ 1CZC = IA2A + 2A2C et 1C1B + 1B2B = 1C2 C+ 2C2B
  40. Conjungamus jam duos motus situs novus 2A3A + 3A3B = 2A2B + 2B3B
  41. A 2A2C + 2C3C = 2A3A+ 3A3C, et 2C2B + 2B3B = 2C3C + 363B
  42. comparando A2A = 2A3A et 1B2B = 2B3B ex hypothasi seu A(2) est constans et B(B) estg
  43. C2C = A. AFEAT C- 1ErA Ergo 1A. A 3A A = 1BEB- 3B- B
  44. Ergo 1A2A - 2B.B = =BB 2A3A - 3B2B. Erqu seu A(A) - (B) B est onst.
  45. ergo B et AB - (B) A) est const. Ergo AC + CB = (C)A) - (C(B) est onst.
  46. est autam AC ad CB ut (O(A) ad (C)(B) Ergo AC - (C) () est const.
  47. et CB = CAB) est const. jam 1C2C est = 1A2A + 2A2C = 1C1A
  48. 1on
  49. const.
  50. Ergo 1C2C est const. seu 1C2C = 2C3C
  51. Hactenus phorographia de de libavimus
  52. nunc ad Pynamica nomnilit transeamus. Reperio
  53. ascripto
  54. omne punctur signo
  55. omnis linea positiva
  56. scribatin
  57. rum
  58. egto
  59. ordine contrario
  60. hoc prius non ob.
  61. servatu
  62. Fin uno motu
  63. adhibits soli
  64. punctis mobi
  65. A, B, C

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 3, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068156:0015?run=74