Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 82v

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

The machine reads it as

  1. aequatione
  2. pr sectionis conicis transformanda in aliam
  3. corrdinatarum rectangularum
  4. 24 2aX + a Xx = yy. fiet:
  5. 2aGe
  6. Pra
  7. raro La
  8. sep Z= Tur
  9. 2 2t qu
  10. (1+ W
  11. 2Z + 21. Y Zu + vBi tr
  12. 1+ I: rY
  13. seu 2a. sitrr Z. rv + a qZ - 2r ZV vV = rY ZZ + 2rZV + vV
  14. seu 2a Sierr Z. W trriusqe + 2YZV + _, V
  15. 422 + 2ar5 + a irs
  16. haec deinde aequatio amplius variari potest, auctis vel minutis
  17. per constantes ipsis 7 et v. et hac est omnis variatio
  18. possibilis salvo eoordinatarum angulo recto.
  19. Ut ex angulo recto fiat obliquus sit ABX BC
  20. B, AP A PL c. et PL: LB:: ∞: 1
  21. ergo _et X = = H + co rec- 1
  22. et y = Cd: e expumto dato E
  23. minima ad sectionem conicam iL 2aX. + a XX = yG. Ergo
  24. Xa dx + Fa Xdx = fyay. seu dy: dx: : a + a X : y.
  25. Ergo fit BP= a + aX. sit BF = B b et EF = C
  26. fiet L ideo ob LG: GE:: PB: BL fiet b: C -y :: a + a X : y
  27. seu by = ea + ea: qX = ay + ∞ a: q X y quae est ad paa
  28. aequatio ad Hyperbolam, retentu jam aequatione praecedente qua emulavicuus
  29. directricem conicae, aliam pro axc substituendo salvo angulo recto coorti–
  30. natarum fi matemus similiter aequationem istam, fiet:
  31. o=eZ Ldgen + rr
  32. Auiurr
  33. Arim
  34. s
  35. rrZV
  36. seu o= = crrea su EC fgrantia Z + er + g arb: a V + rZ +, 1EV- rv
  37. Hanc aequationem prius multiplicatam per urbitrariam h addamus
  38. aequationi , et videamus an componendo fiat aequatio ad circulum
  39. et sufficit considerum terminos prodituros qe, vn, et ZV. et
  40. quidem pro ZV habebiinus et debet autem evanescere Zn, et fier
  41. coefficiens ipsius ZZ aequalis coefficienti ipsius DD, prorit collenda ZV
  42. 2r +2ar: q + h - h rr L 0. Ergo h h: F=
  43. h: 2Y = 2 =c 1 + aq: rr - 1 rursus rr( a: 9) + hr = 1 (4 a: g - trr
  44. prodibit aequatio
  45. ergo fit r Mrr+ MY+ th hh 4 seu Y = Atih a -r c ostin A
  46. h= rY CEV 1- rr: 2Y. Ergo sit ( c- Er = - 1 +
  47. nisi in Ellipsi ubi latus rectum
  48. mnjs tan verso
  49. in hoc genere fieri possit, quae amus ordinatas oblique
  50. sa cm po
  51. ut apparent quid
  52. et in +Gg. C et ex proZ ponamus
  53. mus co., atque inde qponendo
  54. lemus p
  55. quod
  56. redilent
  57. + lon feear et poro V poret seu 2hr = 1 - 1Y Ego I = = 1 a:
  58. ponem it. E a iarr et (5 er 1gq ) eni
  59. lyo
  60. aonem 3+ Tentandum in ordinatis oblejuis. ia mius proceo
  61. aibenta vn
  62. ibed eeo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 82v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0164?run=74