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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 85r

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: 0.83.

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. 86v); this page is its right half.

The machine reads it as

  1. C
  2. Aequatio ad curvam (onicam neralis est voce = p
  3. _ H. v= fiat Z = 31X + 32y + 30t et v = 49X + 4 y +40 b
  4. EZ
  5. aq. (4)
  6. 2. 40. 42y
  7. = = 313 XX + 35 31. 32 Xy + 2. 30. 31XX + 30. 30HY
  8. Z-
  9. F32.37 97
  10. 12. 303rfy 4.
  11. 400. 31 YX + 3or t
  12. 00. 3L 8y
  13. seu transferendo omnia membra in unum latus totumque aequando nihilo
  14. 5
  15. =
  16. fiale Z=LXL 3K + 329 F30N. Et substituendo valores iat
  17. Et substituendo 41. 41 XX + 2. 41. 42Xy + 2. 4D. H1 fX +40. 40 f
  18. VV = 42. 42. 9y
  19. I
  20. +X 31. 31XF + 732. 31 yy + 2Y3132 Xy + 2. 30. 31Y X +2 3032Y y +30. 3ort
  21. -41. 41 - 42. 42 = 2. 91. 42 ..
  22. = 2.40. 41t = 2 40421 - 40. 40 H
  23. + 1. 00. 31 Y +1. 00. 3t Y, 4 00. 30 rt
  24. iden fificetur iatae aequationi multiplicatae per 50
  25. soL NXX + rgu ta 13Xy + 00. gitx +eoprty +50. 10tt
  26. identificatoriarum
  27. Harum artlrarum Gex aequationum aps in seniamus 31, 32, 30, 41, 42A0. et erit
  28. Et opo
  29. ni fallor aliqua super numeparia 50.
  30. si sit Rursus ex aegq. 2 et 3, inveniamus X et y per Z et V)
  31. X = 00Z = 32y - 30t, : 31 = 00V - 42y - 40t,: 41
  32. 00. 41Z = 4 32. 41y - 30. a1F = 00. 31V - 31. 429 - 31.40t, et firt y
  33. Fiet y = 00. 31V - 00. 41Z + 30. 41 t, :, 131. 4L. permutam 0 3. et 4. item Z et V
  34. _ manet idem
  35. - 32. 41
  36. = 31. 40
  37. Nam eodem modo Y = 00. 41Z = 00. 31V. + AV. 31 t 3:, +41. 32 quod est sindicium
  38. 41. 30
  39. = 42. 31 Calcili probi
  40. Hiac pari jure per mutando. 1 ut 62
  41. ex valore ipsius y, fiet valor ipsius X = 00. 32b - 00. 42 Z + 30. 42t,: 132. 41
  42. 2 32. 40. - 31. 42
  43. (sol
  44. Hinc pro. N, Et duoe valores ipsius ipsorum X et y, habent uundem denominatites signo disserentes
  45. vel accipiunt
  46. seu habent eundem denominatorem, signis numeratoris etdenominatoris in alterutro mutatis
  47. Hinc si in valoribus X et Y pro 30, 31, 32, 40. 41. 42 substituamus valores
  48. im inventos ex aequationibus sex identificatoriis, A
  49. Habebitur modus datam aequationem generalem localem secundi gradus seu ad
  50. Conicam reducendi ad formam aequationis 1.
  51. superest ergo tantum ut sex illas aequationes absolvam exequamur.
  52. sint binae aequationes 1AXX + 19yy + 15Xy + 12 ax +13aG + 10aa = 0
  53. Locales ad Conicat
  54. 24XX + 29yy + 25 xy + 22 ax + 23 ay +20aa
  55. Videamus an X et y sic explicare possimus, ut _trobiue tollantur L, et xy Xy A et X, et y
  56. Hoc succedit in omnibus p ex Conilis eacoppta pprabola
  57. sit _ _ X = 31X + 32 + 30a et y 41X + 42 +40 a
  58. a Hincaou
  59. Excepo. 1. fit 14Xx = 1. 31. 31. XX + 2.1431. 32X+ 2. 14. 30. 31af + 14. 3u. 3uaa Hinc fit 3 3 pro tollendo Hb aZ
  60. 1. 32. 33
  61. Ct + 2. 14. 30 32 a)
  62. 199y = 19. 41. X17 F +2. 19. 4. 42 + 2. 19. 40. 41 ax + 19. 40. 40aa
  63. I9. 42M1
  64. 2. 19. 40. 42a
  65. 15Xy= 15, 31. 9122 + 15. 31. 42+ 15. 31. 40 ax + 15 340ay
  66. 1532. 42 W 15. 32. 41
  67. 12 AX C
  68. 12 ax =
  69. ay =
  70. 20aa =
  71. 15. 30. 41 ax 15. 20. 92 ay
  72. 15. 32. 40a) 15. 30.404a
  73. 15. 30. 42 a
  74. 12. 00. 31 aX + 12. 00, quaa
  75. c2. c0. 32 av
  76. 13. 00. 41 aZ +13. 0v. 4u aa
  77. 13 00. 4247
  78. o 00 ua 10. 00. 00aa
  79. pt 2. 14. 30. 314 15.31. 30 + 12. 0b. G =c
  80. 2.19. 40. 91 15.37. 41 13,. 0. 41)
  81. protollan
  82. . 14.3031 + 1732. 10 + 12 0032
  83. 2. 19. 40. 42 15. 30. 12, 13, 60. 12s
  84. pro tollendo XV
  85. 2.19. 31.32 4 15. 31. 42
  86. 219. 41142 + 1G. 32. 41
  87. Eadem ad aequ. 2
  88. per mutando tantum l. et7.
  89. Autg, 2 et 3
  90. anenta
  91. a
  92. aqus
  93. infertm a
  94. s
  95. a resisim.
  96. G3
  97. 1
  98. 5

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 85r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0169?run=74