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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, 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: 0.80.

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. imo non suni eementa destepsus absolut rested en soluju
  2. Y et progressuu circularium ergo. seu elementa descensus ECG. nantulit ddO = a daf + nt fdd +2a f
  3. At eadem 2CG sunt in composita ratione velocitatum, 2 adioro ad
  4. sunt in ratione differentio differentiarum ab ordinatis, et radisrm
  5. progressuum circulariam; ergo demtis utrobique radiis velocitates
  6. erunt in ratione differentio. differentiarum ab odinatis directa
  7. sit jam curva sectio conica, cujus axis AB (an foill et diameter)
  8. Ho fet vertex A, fiet cu latus rectum a transversum b, fiet
  9. Paf+ = ff = eC. et B X~ + eC. et AP = h. fint PC seu
  10. X = L+ eeth - f + ec sin quod si AB sit auis et B
  11. sit curvae umbilicus prit a latus rectum primatium, b latus trensver sum primartum
  12. ger axis curapplicantur ordinata inter verticae interceptus, sit c distantia socorum
  13. 12) tape si AB sit agis primarius erit a latus rectum, b tatus t primarium, et
  14. aX ux
  15. blatus transversum primarium seu axis primari pars inter vertices intercepta
  16. nempae ASt =b. sit ju p e et sunt foci p eeentium curae sit +, et erit
  17. sin
  18. am g = Y bb - ab et bb -99: b = a seu a = b449. b jam
  19. ut inveniatur pB, de AP, de seu h debet, a dimidio axe b: 2 detrahi dimidia
  20. l
  21. qu2
  22. indissi ti elgo his substitaris
  23. distantm umbilicorum q.2 ergo h = b74.V
  24. fiet B - B9q. b f + l - 49: b6 fs = e,
  25. e
  26. sed ante explicatioaeu tollamus f
  27. ex aequalionibus 1 et 2, fiet ff + bf +. bb = + ee + bb, et adeo
  28. b: 2 +9. 2 - f + ee
  29. X = 1
  30. fiet f = bb + ee 4b:2. rursus ob ag. 2. fiet 1XX - ee = h -f
  31. seu f = h - Sxx - ee. Ergo bbb + ee + b.: = h - (xX - ee- ja
  32. H: jam a SO = seu d 92 = 1: 2 3 ad. Ergo aequationis D differentiali
  33. erit Fede: s1bb tee = - X dX A ede: Sxx - ee
  34. seu ee de. XX - ee = X dx + 2Xedx de + Cde. = bb + ee
  35. sed ex e, investigam aequo t. anvestigemus de fint _ ads trafas= de
  36. de Lads +4fds: 1af + aff, et dde. Od3 - 3dco: D.
  37. seu ade seu Za+ f4fd5 . de = e. = a daf + a fads + 4 d5,: e
  38. seu d adt +gfd5
  39. ut enveriome
  40. I.2 =
  41. ddeseu d d (9) 2 = 1: 2,, C
  42. 1: 2C
  43. - l: 2
  44. do et
  45. I: 2 sdC + d C
  46. 2
  47. 1: 2 dC
  48. dd
  49. i2
  50. jam d O
  51. T: 2, dC
  52. 1: 2
  53. 132
  54. = - 7:2C
  55. .3:2 si jam -
  56. Ergo ad O1. 2 = 1: 23, C ddC - 5: 2 C
  57. = tas e = (af + a4 fs fiet 6
  58. a
  59. denque
  60. = et O = a5 + 4f et dC = adf + 24f af et d0
  61. si jam C 1: Z
  62. 1
  63. et dO = +f. a + 4 a f + 49 s seu df. a + 2485
  64. directa. ordinatauum autem inversa; at eadem per superiora
  65. sunt i coproposita ratione radi velocitatum, et ratiorum et
  66. et ordinatarum ac progressuum circularium inversa.
  67. d
  68. es

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 16v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0032?run=74