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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 349r

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: 0.81.

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. 348v); this page is its right half.

The machine reads it as

  1. jam ope aequ 12, 5, tollantur 2X et 2X
  2. in Ellipsi vel Hyperbola sit L centrum fietus LG AGAG ad G
  3. ge 2rx + pXX = yy sit XA Z X +4 seu X- (. 9 fet 21 Z 19+ 7 (2 4r
  4. Hinc
  5. seu yy = xZZ- Y9 seu AG. AG = r (LG. 1G) - r
  6. Ce= sint LG, LI, LN, LP, LZ, Et GA, 1B, NC, pd,
  7. W X 3 Z
  8. (V), (1) (X), (3) (0(v) 00- r
  9. ee = qut B = vv + W01 - 2∞WV + Y vD + ruI 29 - 2 ((rVV - (, 19, Y 0u -r9)
  10. qu. BC = qu AB= WW + XX = 2WWX + Z WWW+YXX -2r9 - 2 +(rWI -193 Z XX- 19)
  11. LGe. D tG + LIqu en G. La) C . 2. 15) - (15 - 1A) (2E1 4 7 + C)
  12. ff = qu AC = vo + XX - 2 Vx gF 00 + Z XP - 2rq = 2 +(Z vV - r9, Y Xx r4)
  13. ope harum trium aequationum tob debent W. et x
  14. Ex aequ fiet Cel c v irq at vrrrvo- 2
  15. ee = (1) v0 + Wo - 2VV + (V(V) + (1) (10) - 2 f 11)
  16. ee = (2) WWW +XX = 2WX + (o po) + () () - 2 () (X)
  17. ff = ( VD+XK = 2VX + (v (V) + (X) (X) - 2 (V) (X)
  18. Oste rarum trium aequationuu posunt tolli W0 et x; sed
  19. remanente v. sed video jam praestare omitti tertiam aequationem
  20. solis adhibitis prima et 2da ita ut maneant v et X, sublata
  21. H
  22. vn F W0 -2u +(V(V) ((10) 20) = 2(∞(10) = (Wou XX BrWOX ((o (Co ( (a) - 2 ) (X)
  23. 1) + (V) = B
  24. et 2 C ) -1
  25. vocemus am
  26. sum solum media W. Erita
  27. int n 2p () e et q posito
  29. seu un-rxho+ (V ()- 2(∞120
  30. compendii causa vo B() () + XX + (X) (X
  31. Wo esse radicem, fint aamm- Jamno + annioro = ap uto). F
  32. V) - 2(X)
  33. in Hyperbola est (1) (10) = Wco = rq et fiet aamm -4amnuo + annioco = apporo
  34. 3C
  35. o) (u)
  36. e5lX=
  37. =4 pprq compendi causa aa seu Ce W0W + tamn W = aamm + IPX YI
  38. op. 4n pV
  39. pp - nn =(X) + (vYV) - 2(X (V) - XX -vn + 2XV
  40. seu (XX - r9 (t vD -rg = 2(4) (V) (XX vV) + 2xV
  41. App ann arb
  42. in =IL 2rg - 2XV)
  43. et am = - vv C∞ - v) v) + Xx + () () = vv + 2XX (= r9 Frq
  44. am = X+V, X- v et =amn = ~ + v)nu X+Asi
  45. sit fiet: itaque positis X+V, l; Et X V, n; set (X) -(V), p. et = am = 1a
  46. seu am = 2 (v0 -XX)
  47. Inn
  48. 2rg - 2Xv + 2() (1)
  49. fiet oi
  50. W
  51. +) Una + rg que ) rare
  52. 814 _ 8, r9 - X~ + () (1)
  53. lavenietur e per alterntiam
  54. 1 vel 2. ita datis punctis extremis et et C, habetur medrum B
  55. inte invento ergo valore ipsius. W, per a g. 4
  56. sit jam tertius valor ipsiis ee aequatione sta
  57. adeoque et AB et CB aequales.
  58. nempe
  59. ope harum trium aequationum 1, 2, 5 tolli debent literae W et X. jungantur aequationis
  60. ee -5) Xx + gy
  61. =Eyx + () + (5) e3) - 26 (s)
  62. 2 et 5, fiet 18 1d + XX ad instar aequrtionus 3, Wov - 21oX H(o ) (1) - 2 (0 YX) C y - 2 Xy ~ 1) 17)-
  63. d = jungatur aequ. l et 5 fiat eeraroro - Wto 4 (r) C~) H ) 10) 2(1) (o) = XX 49y - 27X + 1Y) (Y) es) () 2B
  64. unde Wno + (1) (1) = = VV + 2vW- 1) L 2(V) (1) + XX +yy. 2yX 2(1) CX) + (y) Cy) txH)
  65. + 210X 4 2(10) (X) + gy - 27. 9 + (1) () (Y) (7) q 3
  66. Ex 6 est (20) = (X)+ (9y- 2Xy +(XX + (7) (7) = 2 (4) (7) = 1010 + 210X)
  67. qui valor conjungatur cum sore aeq0 (((3)
  68. Aequandoque duos valores fit:
  69. hinc quaratuo
  70. valor ipsius ro
  71. V 2v0 + (n) (n) - Xx = 2op C (X) (∞B - 2(X 1V) +(3( 6) L (yy - 2p7. etc)
  72. Pro V, 10, X, 9, Z scribamus 12, 12, 13, 14, 15 etc L. v + X = 113 X B = 13) -
  73. 2, 23, 24, 25 et 5- (∞) (X) - 213 (∞ (∞) = 231 -
  74. Ex apo Ex arq. (3) fit nB-2MId,: Ep = (ut seu substitulis numenis
  75. 21
  76. 2(∞) - 2 (X)
  77. (1), (20), (X), (1), 2)
  78. Ex 1et 2 e L 113. 131 Y 213. 231
  79. Et ex 2 et 5
  80. similiter
  81. mus
  82. 12t. 192 +224. 242 - 2. 132 1
  83. 135, 1534235, 253 - 2 153,14
  84. = 2. 131. 12 - 2. 231. 22 -0
  85. 2.292. 27
  86. 2. 262
  87. 146. 164+ 246. 264- 2. 164. 15 - 2. 264. 25
  88. Co
  89. qury qy 1
  90. 349

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 349r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0693?run=74