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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 172r

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: 0.75.

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The machine reads it as

  1. ydy = adx - 4 X dx
  2. dx = ydy
  3. a x
  4. XX - 29X +94=
  5. yy +49, et
  6. q qux =
  7. qy Lgy
  8. seu
  9. X= q f99
  10. yy
  11. y= R2aX = a XX
  12. sit Ellipsis A BF cujus axis AI. Centrum
  13. in ejus medio C. duo Foci S, F
  14. FL semilabus rectum a AC, q
  15. SL + LF = A 24 Ergo SL = ge29- a
  16. FF Et SL2 = LF = SF
  17. V
  18. = 499 4gataa aa
  19. ergo SF = 2199 - a9 vel si SF sit f
  20. fiet 49q - s,: 49 = a seu a = 4 - (: 49)
  21. seu differentia 242a = f: 29, seu differentia inter latus
  22. traus versum est recte seu distantia focorum est media
  23. proportionalis inter differentiam lateris transpersi et
  24. o recti ipsumqus latus transversum vel latus rectum
  25. truusverium
  26. es differentia inter latus rectum, et ipsi nte
  27. latus transversum pilateri transverso, distantiaque focorum tertiam propor
  28. et
  29. et ax= a-as ationacem.
  30. Honale
  31. strea AI
  32. et . ax = a 1 21) Area in Ellipsi est sit AB, X et PB, y, fiet
  33. Vaa = qy
  34. sx
  35. AdB
  36. yy - 2aX - = Xk eritque area ABP = (rax-xx dx
  37. SA
  38. sut s qu- 2x Etu A5
  39. sa est
  40. ACA SC = 1
  41. qu yf+sy dx, et quia ydus= ax quax quaereus per y
  42. XX . 29X +99 = 4 94 - 2 HH fit X = 9 - Y9q - 9 H)
  43. et x = a - 3gg - 9 xX = a - Yaa = = XX)
  44. ergo ydque = (adx = adX H raa - Hy Ax seu de- Idy: saa- yy
  45. Angulus exprimatur ASB exprinatur per rationem SB ad. BP, seu
  46. 4+
  47. S
  48. Area vero
  49. 2 (9+ =
  50. qtas seu SA vocetur 9 fiat 9 - X: y= Z: a et E(g - X) y + sydx =coa
  51. quaeritur relatio inter Z et co. Tollatur y fiet y - X: Trax- A xx = Z: a
  52. et L(9. X) rap - Xx + (Scax. a XX c) = coa prioce mod. Ex priore
  53. aequatione habetur
  54. 2. fel enim g9- 29X + XX :, 2a X - a xx = ZZ: aa
  55. ZaX - XX = g. X, a: Z p
  56. et
  57. fint Z(99- 29X +XX) a. Z) + seXa: Z dxida
  58. sed (g- X)) aa = 2 aX ZZ = a XX Z
  59. +ggaa seu XX - (daa +2
  60. la 2Z
  61. aa F a
  62. (l Cait a 7417
  63. e
  64. X
  65. sen aaXX+ a ZZ XX = 2aa9X - 2427
  66. +
  67. paq
  68. sen XX - 2 a c
  69. aa ta
  70. aagu aat qu
  71. aae (4 au + 4 2
  72. aa +.44
  73. s
  74. aat
  75. aata aatra
  76. (l lang + a35) daages an
  77. 1

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 172r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0343?run=74