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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 350v

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. 351r); this page is its left half.

The machine reads it as

  1. itaque ex coefficiente ipsius m facto o in aequ. 24, fit it2. 71 2 = vel 123: 213, vel 223: 123) Ex duabus harum trium
  2. id est 112: 212 =, vel 123. 223 vel 223: 123
  3. et ex coefficiente ipsius l facto 0 in aeq. 24 fit 112: 212 = vel 113: 213 vel 213: 113
  4. a44. jam sequitur tertia
  5. et ex coefficiente ipsius n facto O in aequ 24 fit 113: 213 = vel 123. 223 vel 223: 1233
  6. Ex his ita eligere poterimus, ut fiat 112: 212 =13: 213 = _B NX 223: 123 O, Unde 112 = 113. 212: 213
  7. simili calculo institut ex coefficientibus in aeq. 29 nihilo aequatis
  8. 123 = 213. 213: 113
  9. nihilo aequatis, eodem modo fiet 312. 212 = vel 323: 23 vel 223: 323 2 Ex duabus harum
  10. (31 mo)
  11. 312: 212 = vel 313: 213 vel 213: 313
  12. 313: 213 = vel 323. 223 vrl 223. 323.
  13. trium aequationum
  14. jam sequitur tertia
  15. Ex quibus eligere potrimus ut fiat 212: 32 = 313. 213 = 323 : 223 5 unde 3n = 212. 213: 313
  16. ita in olectione priore, Doerunt prisa nempe 12 respondent mediis nempe aB
  17. postariore 31. postrema nempe a 2y respondent ... ..
  18. . i.
  19. - 113. 123.213. ~ - 112.213
  20. (21 ) 4, , 2. 22 22ZM + 113. 113. 123N, : 3=12
  21. 2069F - 12. 1(2. 123 = - 1(3,. 213. 225.
  22. ( 12. 119 20 m + 219, 13 7
  23. 309h= = 212, 212, 223. =313, 323.207
  24. 312. 312.323. =313. 213. 213.
  25. 312.-13
  26. - 312.1212
  27. g 313. 23. 213
  28. .
  29. . 1 23 m + 112. 213. 213L
  30. susobs =32. 223 . - 112. 113. 213
  31. aus 1 in 20n + 12 l5. 1B l
  32. uo
  33. 11(3. 22
  34. Valores ex 30 et 31, substituamus ipsarum 112, 123, 312, 323 unde
  35. seu fiet 100f = + 212. 223. 12 m
  36. = 213. 213.22)
  37. +123. 213
  38. +323. 213
  39. =22. 223. 23 = 312.313. 21313.)-313. 223
  40. 312.313,325. 313,41713313. 233
  41. n : + 113, 212
  42. ita patet omnia evanescere, idem enim in caeterarum iteratum valoribus continget.
  43. = 212, 212, 223
  44. 21
  45. Et tagus . 169 -- 112. 127. 123. = 1(3. 22. 213. 31) -13. 229
  46. F113 (212: 213) 223 (213: 115) 212 M + 213. 113. 21,
  47. 100f = LHZ _ 212(2I. 213) M
  48. 9
  49. Itaque non licet aequationes 24 et 29 divellere in tres alias unamquamque. sed paulo prolixiore
  50. calculo utendum, et coincidentiemus aequationes 24 et 29. vel ponendo, esse
  51. aZm= + 6N et 5m = 4 l+tin, fiet m - Z1Fon,: E L 7 l + tin,: D
  52. fiat 8 = d, et fiet 2l + hn = Zl+ 6n seu F (9 -7) l + - t) n = 0 et ut
  53. evanescant l et , fiet Y-2 =0 et 6 -t = 0 seu fiet
  54. Harum trium aequationum ope quaeratur. 21Z, 213, 223
  55. = 212 (112. 123. 123-313, 313. 323)
  56. 223 (H2, 12. 123- 313. 312. 323)
  57. 1
  58. f= 2 et 8 2 ut G - 8
  59. Ex his aequse unam consiieemus nempe cum = B, fa sit 212, 213, 213; X, y, Z fiet
  60. +212, 213, 223 (123-423)
  61. a 212. 243.223 (112-812)
  62. 0
  63. compendio 1201XXZ + 1102 X2Z + 110OXlaX + 1001 aa Z = 0 = 9- 5
  64. +
  65. 2210 XXy + 2120Xyy + 2100aaX + 2090aa =9= 8-2
  66. 3021 99Z + 3012y77 + 3010 aay + 3001 aa z= 0= 5- 6
  67. =Yy = 22IOXXG + 2100a aX + 2010 aayC3: 2120x
  68. = 3011y2Z + 3001 aa z + 5010 aay 3 : 30217
  69. quos dues valores aquande ipsius gu aequando fiet y = (2100. 3021 Z + 2120. 300, ) aax Z:
  70. : +tE2IOXX + 2010aa uti notandum temper qudivabre eX a piontere
  71. -301277 = 301044
  72. ubi notandum semper
  73. posse permutari simul
  74. X, Linitiat, antepenultima, notam
  75. 2
  76. 3 inital, ultinam notam
  77. compendio y= E) C ex 2m: a 12. 3o) XZ
  78. Sed sumamus prius aequs 2 et 3 pro tollenda y, et compondio scribamus: 1
  79. 12 27 + Byy + nay + 124450 et 20yy +21 ay + 22 aa 20
  80. fiet - 10. 20yy = 11. 20 ay + 12. 20aa = 10. 21ay+ 1022 aa, seu erit
  81. Alitor 10. 109y +. 101ay + L II. Vaa = L. 11. 11 a a = 12 a a seu y = - = 11 a t a 4u 12,:10
  82. fiet
  83. seu a y = (10. 22 = 12. 20) a :, 11. 20- 10.21.
  84. = (pari jurC) = L 2a + a Y + 21 - 22, fr: 20
  85. fiet 21. 20 - 2 10. 21 - 20 ( 112 - 12) - 10 ft2-22),
  86. C202 10. 21 + 11.25-2. 10. 1120.25 -a 721Z 422 - 2. 10. 20p11. 21 - 4 11. 12
  87. FII, 2F = 4112. 22
  88. 2. 22 4. 1V21
  89. Senz. 10. 22 + 220 2. 12. 20 = 10. 11. 20,2] = 10. 201+161222 4. 12. 22)
  90. 4. 10311. 28.21. 22 = 4. 10. 11. 19. 20.21CC 7,10. 711. 20. 21, 10. 20,. 12. 22)
  91. ext
  92. 4. 10, 22 22 + 4. 12. 12. 20 )3. 10. 20,17. 22 4 10. 11. 20. 212
  93. Et divisie omnibus per 4 et ordinatis fit =10. 112. 26. 22 - 4. 10. 12. 20, 21
  94. 0
  95. 18. 23 10. 22
  96. =4.10.12. 20.22. +10, 113 20.22, 103.11. 20.21. 32
  97. 10, 12. 2021
  98. 10. 11. 12, 20,21
  99. seu (2) (10.22 - 12. 28) + 18. 2D (1. 22 + n. 21) = 10. 11. 20. 21 (182 22 + 12. 20) =0
  100. 12.209
  101. 12 = 2100aAX
  102. 1 = 2210Xx + 2oaa
  103. 20 = 30212 2= 30122Z + 3010aa 22 = 3001 2a 7
  104. 10 = 2120
  105. Unde fiet:
  106. voc

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 350v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0696?run=74