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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 28v

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. 27r); this page is its left half.

The machine reads it as

  1. A X, X. XV, y
  2. AE, 9
  3. BD, h
  4. vy: Zlh = AVE: ACE = AYE: L99. Ergo gu = hoh, gX - XX.
  5. Hinc si fiat rg hh fiet yy = rX - =XX. porro cum h, sit minor
  6. quam 9. ser h: q ratiominoris erit et r. 9 ratio ad huc
  7. itaqueY potest esse una ex upplicatis lipseos. sit FR,. fiet r = YX - XXX,
  8. hine quaeratur X fiet qx 74 -gr = XX - gX. seu 39. X-
  9. C494. ) 1d = (t H) = CF (L49 i hh) = CF = ( FH
  10. Cum ergo quadratum ab FC sit differentia quadraturum FB etBC, vel
  11. Quadratorum ab FB, et ab , erit FB, L9. Ergo F est focus
  12. CY _ est =9 - X Vocetur Z, et fiet Lx erit X = Lg -7 et, et ex
  13. gy = Lrq= et
  14. minoris quir r: q = hh. 94
  15. Et latus rectum est ordinatim applicatu ad axem in foco
  16. 2(+ E 42) - YZq = = r9 - X7 = tt - hiti
  17. qu
  18. si est esset B, ei Ex masto cpseos F agatur nolmatis in aer cd jngatum Bd normalis et occurens in V
  19. et x CV vocetur v erit D - 2h - y, et feret a Lhh - hv + bD = gy = Llit - hhZZ. et fiet Z2 = 4a v- 4qvD
  20. plu 22= h9v - 2 W. sed prostat uti literii y et Z, ubi coordinatae i agibus ve
  21. sumuntur, et a absunt simplices lariata. Poro Aris compug atus empue mineestidiveto e eutu an
  22. quaeritur fa tagay + dz d2) seu Elementum curvae Ellipseos, fiet: est autem ydy = -y dZ
  23. et duys dy = he yque deder ,: 12hb - sitqque, adeoque dpdus + traz - 1 2dq, bili 23 1 - 12 2
  24. itaque summore oportt AZ H 99- ∞e22,: 99. 94
  25. ht yn =gaco et et 7d7 = 2aded t d=
  26. = 9122
  27. dydus +, drah = + g- eez 2g
  28. Aadeo:, (3 laco s dz
  29. d2d
  30. F agged, aco Adesque de = a dco, ap ace + q 9972
  31. A Et fiet dn = a du C1G4 4 raeeto
  32. Y(aco, 99 aecco, +q aqqco
  33. ta
  34. az au
  35. itaque extrchibilis aedtenda est quadatice formula aco acoco-= aqqeo- vel ducendo invicem
  36. quqqo.
  37. 4qued +qBac, quod totum dividamus per ee qq, tint C-44 (eergqu) nacoco +
  38. Qarqus coco
  39. Uhius sermulae vallies sunt acal, acd- 4 99, aed -9. ee 60, h et cD, ibeC
  40. Ia Hypert, A5, 9, CA, G latus rectum Y. sit tih = ce AX g. X, y
  41. 19 = ry -Ixa LYyy
  42. yu = rX + YXX. sit Z - L9+X se fet - 24
  43. +F
  44. seu yy = XZ2 - L Yaseu gy = tih 2 + gtk
  45. jungatur AB, ejque paractia dualu aXG occurrer ipsi axi conpigato in e exsi
  46. erit X Y, seu y, medi proportionalis inter DG et GB, seu inter summam
  47. disferentiam ipsatum
  48. itaq generaliter yy=
  49. et
  50. CB, et CG. idque tam in Ayibola quam in Ellessi reum es
  51. 22Lth,. ubi in Hy perbola
  52. ydy = + tih 7dZ et dZdZ + dijdus = d2d2, Z2 +th F B F, in Cllipsi minas est-.
  53. seu d ez t ayaus - drc d N = p A a q + ee 2,:, + 4922 + B L 90 7 4 223:, nt
  54. Ergo generalis haec est construssio pro Ellipsi et Hexperbo lice curveatemento, de
  55. Z + fil
  56. aut sot
  57. s mbiguitate in valore ipsius
  58. n
  59. e in Ellipsi es distantia focorum quod sic ostendo; FB qu =- BCqu = FC qu, ident est quod 294 - L hh = FC qu.
  60. Ergo oC = 49 - hh= AFC qu = FO. qu.
  61. ad quaeramus distuntiam focorum generaliter, tam pro Ellipsi quam pro Hyperbola
  62. in aequatione si sit generli gy + ln q2 + lh, sit y= LY, siet vr + hh d Z ( hh. sec. 1Y = h: 49,
  63. et fiit Zhh = + 22 + 419, seu 47Z = 49 F hh. Poro 27 = bis CF _ = FC
  64. Ero FOqu = 49 + hn = ee, seu C = FC. itaque in . Hyperbola non minus quam in Ellipsi
  65. e = YCga =+ lin) est distantia focorum
  66. ape directo, seu latere transverso
  67. Haec in Ellipsi est minor, in Hyperbola major
  68. aa : 7 = 9 fi de = - a ly: d8 d 5 de 1e = des s (a + 84): B 3.t 2Z = A at, fiet X- f ak
  69. et dus idh L et ft s(d 9des + d3 de) = d dX sC at + aaxK, - .a d(at tate)
  70. eK
  71. quod aequandum Rk tatu = KK WV fit ( siet a + akk = k10c0
  72. 1
  73. RK. = K. WW + . W0
  74. Zl -aa. = qua) W- 4 Ergo rest redit eo
  75. ut. 15 - 4 a aequetur quadinto quo sit si aZ + ak qu Caa + K K) suit aK AA = a M L XK aa
  76. 44 4. sit 19: e = f et sit 4 = 3 a f - 4 fint 99+ f = 25
  77. H= Apura +.
  78. sin H(2
  79. + ff.) =. 5
  80. Sit +hhf9e - ee
  81. 11

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 28v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0056?run=74