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Leibniz-Handschriften zur Mathematik LH 35, 3 A 5, fol. 3r

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

The machine reads it as

  1. X + a
  2. Si a radix quadralica
  3. X teu si a radix enbica
  4. c
  5. ex+a
  6. X +1aX + 12a
  7. +iaX + 124
  8. trax +.aX
  9. +ax
  10. Pone a b. trrationales quadvaticas
  11. X +12a
  12. ponende l aego un et
  13. ponendo. 1a + a aequ.o. et F124+14 aequ. 0.
  14. ergo 1 aequ. - Unit. et 12 aequ - 1. seu 1eaqu + unit
  15. adeue X + a divisibi per aeta
  16. uti 2∞ = a divisib. per X- a
  17. X + a divisib. per X + a
  18. + a k
  19. Uende ponendo ab quantitatem
  20. rationalem, seu duas irrationales ,
  21. b
  22. inde teqgritur in impanidus etiam x-a Stales esse, ut factum ex ipsis sit rationat
  23. 15= a. etc. dividi puse
  24. a
  25. ponendoque praeterea 10b + b aequ. 0. sive
  26. 10 aequ = unit. et 1a + a aequ. 0. seu laequ -unit
  27. Ergo prodibit:
  28. a. b. radices
  29. quadratice
  30. X +1a + 10b
  31. Fetgenentibr ita
  32. potest per X-a
  33. a dindi Et ita porro in infinitum
  34. 1obX 4roab + 10b2
  35. 1a, riax +b ab
  36. bX
  37. Hic ut omnes formas ipsarum a. et b. Follamus
  38. praeter ab. quam pono esse rationalem,
  39. erit 1aqu (1) Eaequ - 1. seu 249 +(1)
  40. et 11 aequ - 2 seu 1 aequ. 2 seu 11 aequ. - (1)
  41. N X - 3 ab X + q
  42. X+ _ abiradicas
  43. X +, aX +24
  44. +1aX +24X
  45. +nab X
  46. 4 1ae X
  47. +(2) 1abX
  48. + vab
  49. +24
  50. +2ab a
  51. =naba
  52. Eodem modo res semper procedet etiamsi a. b. sint radices quadrato-
  53. quadraticae, sundesolidae, aliaeve altiores, quemadmodum jam alias
  54. ostendi.) si a+b vituissemus esse ponendo semper ab rationalem
  55. secissemus atb esse rationalem aequatio vel etiam apso
  56. alius prodisset calculus
  57. Y +VyAC. Ergo 5aby Ab e bu X +1 a X+ 24X + 34
  58. A aequ. b+ s
  59. fiat 1. aequ - 1) - raequ +11
  60. 2 + V 16 ab
  61. ta (sib. (etab qu
  62. suspectus calculus novae enim
  63. Baequ. 3 () 2 + β aequ. 0.
  64. 3aequ. 3.
  65. eit
  66. arbitrariae (vitentu esse debere.
  67. inutiles
  68. Zu quo ) )
  69. 2
  70. V’agys. + 3b C -31- 2bC + Y erc
  71. (9)B aequ. Ergo 3 agus el2 aequ
  72. 21 - (2) B. V aqu. 0.. Ergo Y aequ 21 - (2) + (2)2
  73. 2) ab + 1 ab +) ab + 9 uqu. 0. Engu ()ab radr na s sad (abra luus (17 ab X
  74. un
  75. en
  76. +(2) 21 - (2)) ag +( aequ. 0. Ergo (X(2) 21- (2) 21 (2)Y- (4) 2 a gu Vabae
  77. denique E 1 rap cus suqus
  78. b
  79. et cum duae tantum restent
  80. aplssunt solum itenent ab. 2. 21
  81. X X a (2) ab
  82. +X +ax
  83. cubisae
  84. + 11 ab X +21ab4
  85. tX +q
  86. +24 X +34
  87. + aX HaX
  88. +(24bX
  89. trabax +21ab
  90. +14 x
  91. tnabax 32a6
  92. +24X + 343 X
  93. Lβab4
  94. 6at
  95. v
  96. dia
  97. +nab X
  98. cul suptronmelarier et habemm omnta per u adeoque qispcabiaa

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 5, fol. 3r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068218:0005?run=74