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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 7r

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: 0.71.

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. 8v); this page is its right half.

The machine reads it as

  1. rx - rraa fia vv 2AC + a~D = ec= 2aC
  2. divitatta induu veraa =ee, seu va 2= C
  3. rentamen pro dimensione curva Hyperbolae primariae
  4. Uet pFVD-EfC seu V = H
  5. y= aa: X Ergo dy =- aadx : XX Et ax + dy = a FXt: xx. itaque si
  6. possimus efficere, ut a + X aequetur quadrato, indefinitis, solutum est problema secundum
  7. nomnovas methodos meas. A sit La + (x + a a oxraa d 2xx ac
  8. et fiet Xx aa eemaeu raatae 3ec. ate vo fit an C- 2, a exv. at e
  9. S sit X = e1AY + 12: 20y+ 4. fel + 1. y + 4. un 9 7 6 1. 1512 + 4. 11. 129+ 137 651 4 9
  10. FR3y +2 363, X + 2. 3a 39
  11. +97. 3) +2.59. 34] +34
  12. ar st adio ust 6a io yt 4a 20y ta 2, + = a tx
  13. (9) 20y +21
  14. (4 Proy +21
  15. conferatur numeretor cum formula 44y + 45y+ 46y +479+98, fiet
  16. (seu 1448- 27. 19
  17. 32 = (+4 34 = (48 33 = 45: 2544 = 47: 214 et (445: 47 = D4: Pa5
  18. denique 2(44. 48 + 45. 47: 4 41. 48 = 46. seu 8. 44. 48 +45. 47 = 46 141. 48
  19. et quia et et pro 48 ponendo nulorem, fit 8. 44. 47: 45 + 45. 47 = 4. 46. 44. 27: 45 )
  20. seu 8. 44. 47 + 45. 47 = 4. CB 44. 45. 46. 47. fit 48. 44. 47 +45 = 9415. 46
  21. 4. 44 = 4745. Set = 47. AB. probemus in numeris G+ 4. 8 + 6. 4 a 4. 2 +1 su q rep
  22. 32:8 = 8: 1 probemus in numeris (2 3) + 2 +1 = 94 + 12y3+69y
  23. 148 = 70 9: 1 et 8. 81. 4 + 12- 4. 9. 12. 10 e + a Gy+ 4y +11
  24. (7
  25. Calculus est s
  26. Leque 16127 +4.25. (2I, 113. 12+ a. 2021 = 1b 11 + a. 26. (2)11. 123 +4. 20. 25.
  27. itaquex ag. 8. fit
  28. 4
  29. seu 12 in aequ. 8 442. 47t457 = 4. 44. 45 46
  30. eud 12+ a2 in 1512 + 2. 11312. 4 28. 21 = 11 + a. 20, 11. 12 + 2. 11. 122a. 20. 21
  31. int
  32. . 12)+a 13. 12520. 21 + a. 11312. 217 + 2. a311212. 20. 25
  33. 1)1 6. 12)+ 2. a7 11312.20 21 + a 11 12 70 + 2. 48. 11. 13. 20.
  34. nidividendo per a. 11. 12. fit 2112127 28.21 + 11. 12. 2142a+ 112 282
  35. 18
  36. e
  37. 211. 12. 20. 213+ 11. 125. 2042. a7, 12. 20.213 ubi patet
  38. esse -2. 13 13, 20. 21 122 20 - (2 21 + 11. 12. 11.20-12. 28 + 20 28.21 11. 21 - 12 2
  39. d ode modo habere 11, 12 ut 20 21
  40. a aequatio dividi potest per 12. 20 11. 21, itaque haec quantitas potest haberi
  41. e e
  42. 1
  43. s
  44. 40
  45. qualis nihilo, et fiet 12. 20 = + 11. 2) seu 12 = 4 11. 21:20, ergo fieret
  46. uy L11. 21.20 et debel poni + =- alioqui fieret X determinata.
  47. 209+2]. seu fiet 12. 20 - 11. 21
  48. inc perest ad huc altera aequatio, nempe 9 explicanda:
  49. e
  50. a
  51. 26. 11. 12t a. 204
  52. ( + 42. 20 19. 8. 11. 123+91. 20. 21 16 (3, 1. 19+ a. 20. 21 = f. 114a. 20. 4. 1. 2t a B 16
  53. servetur lexjustitiae, siel 64. 44.45. + , 6. 99. 48. 45. 97+ 45. 17
  54. 114s
  55. Cutrmue
  56. 16. 46249.48
  57. p seu 64, 1+ 2. H. a. 20 + a 20, 12 4 2 12. a. 21 4 a. 21 16, 11 +a. 20, 12 ta 21, 2 H. 12 1 a 20 21, 1 rG
  58. +16,1 12+ 2. 111 a2V4 +a252I, p. 12L 2 1. 12 a 20 2 + a320. 21
  59. e
  60. e06, 36, 11. 127+ 2. 11. 12 a20 2 1 a, 20. 2. 11. + a. 20B, 12+ a 21
  61. 45. 47 =2(16, 114. 127 +113, 12. 29. 21 +1, 123 20.2+4202 , Et quadrando fit
  62. horaiicranonta oauta nona o2
  63. sic
  64. Aa4
  65. aIO2I tSaEn ruvatui uo
  66. +Bai t taci rouio ainou (a 2 2 A
  67. 4a112202 Staad adiinnom daia a i ou
  68. 6
  69. ux
  70. 4. 8. 88
  71. Et ordinando ac sollendo fila Be u
  72. u (+9420 2 _2.6, 11125 2025 3.145, tnEoZiraI
  73. A
  74. + q.
  75. ad e
  76. ab11220
  77. o hea id
  78. 1220 +a l 1, 220 21
  79. 2.615 1 21 28 5, 31132628
  80. 3i6 48,1. 12 23. 45 8- 34 202 44 11 1221∞ 4a 1 122128 = 0,
  81. 4411, 1 20 V g 11p 2024
  82. n 91no 2 quro ut 2batnuu
  83. 48. 1515. 20.2 1.22+1528 +2. 6. a11, 2. 20.21,o 1 2031. 21+1220- 3482525(12 1h8 L 1I. n E +12O
  84. a (32 B et quia 12 2= 15. 2 p S9. 12 hins omnia ingi possont per L 11 F21 2g2. 12
  85. a . M 5+2.642623
  86. aeao
  87. ab ac at
  88. bc 1
  89. e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 7r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0013?run=73