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Leibniz-Handschriften zur Mechanik: Dynamika LH 37, 5, fol. 114r

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: 0.78.

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. 115v); this page is its right half.

The machine reads it as

  1. (1) planeta circa solem A, fertur in Ellipsi D PEXI, ita
  2. ut areae PACA PACp sint temporibus proportionales.
  3. irca ejus axen
  4. (2)Centro B allipseos, diametro ejus majoro vel Ax, pX describatur
  5. circulus pdXF. Et LC ordinata
  6. Ellipseo) ad axem, producatur dum circudo occurrat in K
  7. erunt areae circulares PAKP temporibus proportionales
  8. Nam LC ad LH, ut BE ad Bd. Ergo PL CP ad PLKp
  9. ut BE ad Bd. Rursus AL C ad ALK ut LC ad LK seu ut BE ad BC
  10. ergo PLCP + ALC id est PACP, ad PLKP + A ALK id est ad PAL p
  11. ut B ad BE ad Bd
  12. (3)at (3) dato tempore quaritur locus planetae, seu data area PACp, quaeritur
  13. angulus pAC, vel aliud quiddam determinans sit radius circuli BP, sit Y. BC, C
  14. BEsit C, AB sit f decter locus planetae C ponatur datus, adeoque BL, X et By et L, LC, y. est
  15. autem LK = fr - XX et y = eFrr. x: Y et PBKP s sit BK = a
  16. fiet sector PAF PBK P = ra : 2 et triangulum ABK = LK, AB: 2 =
  17. Vrr = XX. f: 2 ergo Area PAKp = ra + fYYr XX, : 2 = ZY
  18. Somex
  19. et fiet Yysdx + f Vir = 2YZ seu rdx - Xdx = 2rdz
  20. X
  21. srrxx
  22. seu rix dx = 2r errx dZ unde rVX -ZnX = 2Y (srr. dX dq. sint PX vel 27
  23. sinus frr-XX et PF vrlX Q sint tempora erit PTZ = prrxx dque = 2rX (XX, : 2+
  24. quia dx r-x a,: 2Y = dque hinc quaeratur per seriem ex X, valo multi-
  25. Ver - xx = fit do = - 2X x sir x
  26. plicetur per r-X. jedies prodiens summetur. fiet secies = e dq 2rZ seu tempori.
  27. Trrx
  28. est hac aequatione doncatur radix per seriem, ut habeatur X per L
  29. (e at v = a + e a v + C. e1 a V + C. p. 116. 2 13 17 + al e. 2. 3 B. 4 4
  30. ax YI = 2r dZ
  31. vn
  32. . 2. 3
  33. seu q = x + p
  34. Vir n
  35. 1,23. 4
  36. set rr- XE 2 rE X - C r xx + C. C 1 p. 4 - P. E. 1. 8- 2. pre 67 6 exr vr a3, pe 8,
  37. 2.3
  38. + 12.3. +.
  39. Sit exai folse) rruxx = = = + + + Z. 5 H + 2. 2E arr 2
  40. er
  41. F.1.2
  42. Er
  43. 2
  44. inna Dro cu.

Cite

Leibniz-Handschriften zur Mechanik: Dynamika LH 37, 5, fol. 114r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068534:0223?run=74