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Leibniz-Handschriften zur Mathematik LH 35, 7, 2, fol. 16v

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: 0.82.

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. 17r); this page is its left half.

The machine reads it as

  1. si
  2. X: a = (adz: 3
  3. et y: a = AZ: V. siet
  4. dy: dx 2 dEH Z: V Fingamus: (dz: V de de et
  5. fiet dZ dv: v + Sdz. v ddv = o seu (dz. v= dz do: xddo
  6. sed ita posten in aeg. data res reducitur non fautum
  7. ad dv, dZ adv, ds, sed ad 7, n, du, az ady, adzu
  8. quid sic sic:
  9. X: a = Sdz: Z
  10. 2)
  11. et y: a = sdv: Z
  12. dy: dx 2 dv: dz sit s Sdv: Z dZ L de. Ergo
  13. dedque: Z = - sdv: Z ddzue sed ita in eandem relabumu
  14. difficultalem, nam et Z ad est. Itaque via paginae
  15. phaecedentis melior
  16. pro calculo lineae isochrone. Grave
  17. escn i bdam tegtemdi unformiter ucvedere purto A
  18. BY BC7.
  19. AH, b. AC, E
  20. sit Rda ydy + rAx: ytr = a Sop + y: Fa b.Y. seu
  21. S et reducento omnia ad y. a, et Y: a, et dyrdr, siet
  22. y: a dy: Y + r: a: Syia tr: 4 = S1 + dy: dr: Y b. a - r: a
  23. seu (2) y: a dy: dr + r:a 1+ dy: dr. y: a + r: a : b: a = r: a
  24. Sit r: a Sddz: dzu y: a = ( ddz: dv dy: dr dzue: dv
  25. et quia
  26. progressionem arbitrariam assumere licet, fiat E ad Z. d dv de et dde =0
  27. (12) V.a
  28. Ergo filtt Sadzue: dx dev = 0 seu Sadz: de aaZ: dv= ua
  29. s
  30. per 6 et 11
  31. ont
  32. Aequatio 4 ponatur explicate c et brevitatis causa pro3 Sia, y: a, dy: dx pune 5, 67
  33. e fiet sGri e 66.77 + 2. 6+ pone 4, 5, 6, 7. et fiet
  34. 6.7 + 2.5,6.7 +5= 62+5 4+ 5. 7+6.7: 4-5 seu
  35. 4.6. 5 +2. 4.5.6.7 + 4. 5 - 6, b. 7 - 2.5, 6.7 -5 = 6 +5 +5. 7 +6.7 Et differen
  36. C14)
  37. tiando fil 4. b. 7. 2. 6dy 4746 + 2. 4, 5. 6. d7 4 5. 7. d6 +6.7 d5 4 4. 5. 25 - 6.7 d5 - 2. 5. 6. 7. 6d74746 - 3. 515
  38. ( 2.6d6 + 2.5 d5 +5 dy + 2. 5. 7. d5+ 6 dy + 2. 6.746
  39. vel si placet, quaeramus valorem ipsius 6 ex aequ. 14, et differentiemus tollendo 62
  40. fiet aiquao (16) quam differentrando tollatur 6 in aeq. 17. ubi erit at, 5. ddv, daz du, d
  41. unde rclatio inter dZ et lD qua dploria 9
  42. Itellatur 5 per aeg. 12 et (irl aeg. (18) ubi du, dZ ddv, ddz.
  43. caeleum si exaeq. B
  44. tollas 5 per aeq 12, habebitur in ea ipsius sddredu seu ipsius yra vator per 1
  45. laeterum ty aeq. 13 gatur y: a seu 6 per 5, seu C: et dq idy n aeg. (10) ubi sbti
  46. sollendo dB, ope aeg. 19. fil aeg. (20) abi q: a per satz: dque et cognata a Z pendentia
  47. compendii causa i+ dy: dr sit , 8. et 8b. a - r: a sit 8g. et ex aeq. +
  48. sed aeg. G. etiam Y: a
  49. Ele)
  50. mer
  51. 6reibE fiet s g F(6. 7 +5 = 8 5 + 62: 9 seu 67 + 2. 5. 6. 7 +5 = 85: g + 8. 6:9. seu
  52. (16
  53. 612. 16 ru - 12411) 6. 6. + 2. 5. 7. 36 = 5 -9. 52. t. Ergo 8∞9. 9.7- 8. . 8 + 9. 7 b2. 9
  54. est
  55. 7) =8
  56. 72- 8. A
  57. sit ditluratiendot ta de compendii causa sit n- g = 10 et fiet
  58. 6= G A.g. 10+ 7.9 -7.9: 10 seu d6 = 10d5 = 5 d1o (8- 910 + 7.9 45 B- 9 d0 + 10 d8- 9. + 2,7. 9. 1d9 u. 9d7
  59. 10. 10
  60. et do = - d5 et d10 = 2.9. 9 d7(7.7d6 - dy. 5. Et ex11, 5== dv ddque: dzddv 7 = d2. dv,
  61. et
  62. 8= 1+ dg: dv 9 = b: a - lvadzu: dzado 10 = bs b: a 1Z: v - dz adZ: dvddv
  63. L10 = 2b. a dy. dv - dd2: ddv dv olaze- dz. dav: dv - dd qdq. de dd z. dv + d zddv. dv,
  64. si faciumus 2bia 1 fiet deo = 1. du
  65. b = FiLrII - 1V

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 2, fol. 16v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068074:0032?run=73