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Leibniz-Handschriften zur Mathematik LH 35, 10, 3, fol. 8v

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. 7r); this page is its left half.

The machine reads it as

  1. autem ex Phorographicis dynamica definiri
  2. invenim. Nempe regula haec est, quaecunque
  3. theorematalocum habent constanter in etphorographicis,
  4. in quibus, ita ut et aequali jure tractant utrumque corpus
  5. et eiusque progressum, eodem et locum habent in dynamicis
  6. Reperietur autem semper aequal et prcontinuatione vel
  7. retro sumta, vel porta (quasi dintius pro arbitrio durasset
  8. apraesens motus) vel porro sumta (quasi diutius pro arbitrio duret,
  9. seu cocursu; non impediuntur. ea etiam in dynamicis, locum
  10. habent Talis est constantia ipsius progres sus centri
  11. gravitatis, seu ie, C(C) et constantia mutatio
  12. nis intervalli sive velocitatis respectivae seu AB - (B) (A)
  13. sit stotus aute ocursum 1A, +B, B; et post concursum
  14. 3A, 3B, 3C; et +A, 2B, 2C sit vel ante concursum vel cocursum;
  15. vera manebunt nostra theoremata dissimulato etiam con-
  16. cursu intercurrente. Exempli gratia sit A per se quatur fugien
  17. sitque concursus in D. sumatur paula anteocarsum Repraesentetur
  18. tempus per motum aequabilem ipsius C, itaque temp momento 2C
  19. respondeat t 2A, 2B ante ocursam. Patet cum aqualiter decrescant
  20. terro C procpediente usque ad 3C, ut sit 1C2C = Z
  21. tempore, fiat sit
  22. a aequm
  23. seu tota mutatio facta tempore 2C3C aequatur eidem facta tempore
  24. erdo
  25. +C2C. Nepe tempore C3C duo finat primum mutatur inter-
  26. valum 2A2B, donec concurrant A et B, quantum possunt, seu donec
  27. amalius sibi accedere nequeant, quamutatio est 2A2B, demto
  28. tamm spalio inter centra gravitatis ob motem corporum intercepto
  29. quo intervallum sit H Ergo mytati quae maratio est est 1B
  30. hoc intervallum vacetur H. cessario reliaquendam vocetur X
  31. et it t et itarmutatus tempose y d erit 7A2B = K. Rursus
  32. matat poste rursus a seinvicem necedere oportet mobilia, et mutatus
  33. intervalli tempore D3C , 3A3B K. ergo
  34. tempe 1A1B - 2PA = 3A3B - 2B2A. Ergo fit 1AB- 3
  35. ac proinde infigura alia sit 2A2BZC, cocursus, et r sed retrotrahatur
  36. quarta parte temporis, ex iC in (2C) retrotrahentur et A, B, pro 24, 2B in (_) 2p)
  37. et 3A, 3B, 3C, similiter in (3A), (3C) (3B))rAB = 3A3B
  38. A+ B= D (EA) EB) et ifa A A) _ C iC(C) = 2C3C) ja m
  39. 2A3A 2ABA)L
  40. 2 2ABA): 2A3A:: rCBC): 1C2C
  41. BABB) = 2CBB = 2C (A) sit 2, 2A, 2B, ide. Ergo 2BBB] 2ABA)
  42. EA, : 2B3B = 2A3A : 1CFC): 1C 2C seu (3ABB): 3A3B: : 1C(2C): 1 C2C
  43. sn (3A (3A (3B) = 3A3B. 1C(2C): 1C2C. simiiter A( A). +AeA, et
  44. 1B2B A(2A) = 1A2A, 1C (2C): 1C2C et 1B(B) = 1 B2B. 1(2C): 1C2C. ergo
  45. et 2C(A) = 1 A2A = 1AEA) = 1A2A, 1C2C= 1C(C) : 12C et similiter
  46. 2C(2B) = 1B2BD 1C2C - 1C 2Ch: 1C2C jam (2AEB) = 2(2A - 2AEB).
  47. Ergo (EA) (2B) = 1A2A = 1B2B, 1C2C - 1 C): 1CIC
  48. est autem
  49. 1AEA - 1B2B = 1AIB, et fiet 1AIB = (2A) EB) = 1A. B, 1CEG): 1C2C = BA) BB)
  50. sed quod senfit 1A. B = EA) 2B) + (3A) (3B). Ergo similiter
  51. in oraecedente figura fit 1A1B = 2A2B + 3A3B. Sed haec
  52. aliquando accuratius elaboranda, et universalius
  53. concisienda
  54. seu non obstante
  55. concursu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 3, fol. 8v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068156:0016?run=74