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Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 10v

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: 0.73.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. in priuntivis
  2. Tianguli rectanguli
  3. latera
  4. latus impar
  5. X
  6. 1 y
  7. qDE
  8. Xt Golsitat
  9. atque par
  10. Triaamuli redangili y
  11. secudi latera
  12. latus par
  13. 2XV
  14. 20072
  15. inzempr
  16. lcuu
  17. E
  18. m e
  19. 2 mn
  20. mn
  21. Trianguli rectangulitertii n
  22. Latera:
  23. Emm
  24. m-n
  25. me
  26. n
  27. 3+V aequ X
  28. W + N aequ. Z
  29. Ergo Z aequ. m +n Ergo mn aqu. C0
  30. Ergo Trianguli area ma quadratus.
  31. et Z minor quam x advoue et minor quam
  32. e Xey2
  33. ato ergo triansulo rectangulo ninumeris, cujus area sit quadratus, dabitur
  34. aliud striungulum rectantulum in numeris cujus area erit etiam quadratus
  35. hypotenusa autem minor priore; et sic in infinitum. quod in integris
  36. est absurdum.
  37. Ergus in integris impossibile est dari ud
  38. rectangulum en numeris cujus area sit quadhatus. Hinc demonstratur
  39. iem etiam impossibile esse in fractis.
  40. L-3 = X -y X xty
  41. ∞2 12
  42. E
  43. S2
  44. 12
  45. 22 5+0
  46. 22
  47. iuvemre tres numans
  48. invenire tres numeros integros quadra
  49. progressionis anthmetrcae quoruque
  50. sumun quadratus differentra quadratus
  51. X equ. st. _ X2 - y eq 5. yrego 82 51
  52. Eip
  53. 3
  54. 25
  55. 1349
  56. t 2E - h aequ 2 seu 252 aequ s2 + 3 seu ponendo st aequ2 + β. haequ 5+)
  57. fici (18) aequ (E2β5+ B + (3) 275 +V fier 5 aequ 3+ quod
  58. et
  59. impossibile est in integris. Nam: Za B e + 2
  60. BL
  61. 3+V
  62. 2(3+2)
  63. 26V
  64. β+Y. sed impossibile et
  65. sin 22 aequ. 6+)-
  66. 67
  67. sed iumpossibile est (Y esse integrum nam B+Y est fractus nempe +
  68. + ell. Nam (37 aqu Y - got. jam Y est fractus
  69. le
  70. q
  71. 2C
  72. 3+)
  73. β+7
  74. (+)
  75. (3+)
  76. 1 1 V
  77. B) e+) s est fractus incdncibilis. Ergo et inversus ejus.
  78. demonstratu m ergo rest dios netres numeros quadratos integros
  79. quiat
  80. progressionis arithmetriae dari non posse. Quare nea
  81. multominus dabuptur ties quadrati integri progressionis farthmetur, quorum
  82. differentia sit quadratus quod tagen ad problema resoliendum
  83. quod tamen postulabatur; ad habendum triangulum rectangulum, cujus
  84. arta esset quadratus in numeris plegris
  85. mpossibile est ergo dari striangulum rectangulum
  86. in integris cujus, area sit quadratus a
  87. R a
  88. x
  89. 5 5hc
  90. 4
  91. X = h 2Y
  92. G2
  93. 2
  94. 5=G
  95. n
  96. st
  97. 22
  98. X+hV
  99. cnca
  100. 2
  101. 52 y aequ h2. vaejuos = he
  102. 524y
  103. ergo impossibile, est, quadrabo quadratum ess differentim
  104. ductum quadratoruu summam
  105. ∞2+y aequ 2
  106. 5 Mua 2E aequ 22+ B2
  107. S. Bt et aeque B
  108. 3 aequie 4Z
  109. E ( C(x
  110. 45 aequ
  111. l817
  112. +6(
  113. Hypotemis
  114. sit a y in exy quadratus erit ste
  115. yr aequ v
  116. X + y sitt quadrusi Xtq k g X. y xaequ 32
  117. X -G Z WoY Y aequ. co
  118. m
  119. c
  120. m+n
  121. =X - X
  122. D
  123. C

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 10v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068001:0018?run=73