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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 137r

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: 0.80.

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. 138v); this page is its right half.

The machine reads it as

  1. (1
  2. y = 10 LX = m + 11 Ex+n
  3. gy = 1010m + 1. LK = 10. 10 F 11. LIX +2 01S, X+ m. X+n.
  4. sit v OX+m +2 EXEn, et VV = 202om + 20. 20 X + 2. 20. 21 Tx + m, X + n
  5. 31. 21n 21. 21.
  6. Et qL 30 sxam + 3) IX+n e ZZ 303o m 4 30. 30 X + 2. 30. 31 b, x+m, Xtu
  7. 31. 31 2,, +31. 31.
  8. sit jam a+bgy Zv0 et etRyg = 22
  9. ubi a, b, c, f sunt data
  10. Ex aeq. 7 per 2 et 4, ut omnia fiant identica seu X maneat in determinata fier
  11. a + 10bm + 11 bn 2 26m + 21n et 10b4 11b 20 +21 et f 10. 11b = 20. 21
  12. Et ex oq. 8 per 2 et 6 similiter fiet:
  13. (14)
  14. (+ 16fm + 1fn = 36 m +31a et 10f+15F 30 +3 et 10. 1f = 30. 31
  15. 2
  16. Ex 1 fit 21= 10. 1 b: 20 unde ex consit a FYSbm + I1bn= 2omet 10. 11B 20. Et ex 1opr 15
  17. Et ex 10 peris (2t: 10b + 1 b Z 2d + 1 10. 12P 20. Aequatio 17 multiplicata
  18. e
  19. per =n addatur ad aeq. 16 fiet: a + 18bm-n= 28 m-n osimiliter
  20. aeg. 17 multiphcarta per - m addatur ad aeq. 1b. fiet a + 12 b n- m L 10Vb n- m
  21. 21
  22. i a18 fit 20= a:mn + 10b et ex 19fit = a: man + n b = 10. 1 b. 20
  23. (22)
  24. Cergo per 720. 21. fit = a: m. n. 4 11b= 10. 11b: a :mon 10b d
  25. (24)
  26. sit a iman (per conpend) = p et fiet - pp + pb. 112 - pb 10 (+ b 10. 11) = (10. 1 b
  27. 23
  28. 63
  29. a est duarum
  30. num
  31. 1d
  32. Pari jure et H - 10 0 = C. f Sed pari jure 11. 11 = 10. 10 = C: fm- fn. Ergo fit a: b= c: f
  33. eris
  34. i sunt vianeta
  35. quod est absurdum, et contra hypothesin, quia a, b, c, f sunt datae imo in easu talis proportionis evanesceret
  36. indeterminata. Ergo haec via succedere non potest.
  37. interim notandum hoc theorema: si pro y sic assumi debeat
  38. Si pro y sie atsumi debeat 10YX +m + 1 extn ut a fbyu aequetur quadrato
  39. et
  40. unde patet non posse ta aliam
  41. a, ab(a 20X+m +2HXIn) fore _11. 11 - 10. 10 M - n = a : b
  42. el aequari tali anto, velut C+ fyy aeq. cgto (a 30 Trtm +g1VXFN)
  43. 20. 20 =, g; m.n + 1010b et 21 fore 10. 11 b: 20
  44. nam fieret a: b = c: f. Ergo si formula C+ fyy seu af. b + fyy, coincidit priori a+ byus
  45. m
  46. talem formulam ad hui
  47. martiplicatae tantum per f: b
  48. a +bgy aequari conto a 20 exam +21 sx+n,
  49. et et Lun aequari onto a 30 sxtm +21 tran
  50. indefinite,
  51. potuissent absolute aequam itri vationati
  52. a numeris rationalibus; quia X+m et X +n
  53. simul possunt aequari quadratis indefinite.
  54. Video igitur confugiendum esse
  55. nanc nt
  56. ad compositam ex tribus irrationalibus
  57. sed quae in se invicem ductae nunquam sub vinculo
  58. contineant plus quam duas dimensiones. Ita enim
  59. idem fiet in lateribus quadratorum
  60. quo facto ilti na et entractiones
  61. si res processistet, seu si simul potuisset
  62. quod sufficit ad scopum quadra turarum. Nam
  63. formula summandam constabit ex Hc partibus,
  64. varum quaelibet per se quasi sola esset revo-
  65. eabilis est ad summationem quantitatis.
  66. IX = 1C L. _X F. 1
  67. yy = 1eM 10X
  68. possit explicari. Rem ergo tenta
  69. Y I. X AR
  70. - 210.
  71. Or
  72. 3x
  73. Da Rorkum +D. Exin, ut pauso antet
  74. _ a 30 l.. +3) f... ut dite
  75. 3c
  76. +byy = VD, 32C+ Z2 fX 1-2C
  77. 22c +28b10m (I1. n
  78. = 2 0 I + 2CZ
  79. re + 22(1d 1 + 32f10r2 1,
  80. 22b(0 + 2261 a 262
  81. rationalis, etsi tota formula composita per nt r
  82. rationale non aequetur indefinita non
  83. bimus pagina sequent
  84. s
  85. 12 p A It X
  86. p 23
  87. A
  88. sed video 2
  89. 22 et 72
  90. quae considerali
  91. possunt t
  92. 22b. Z. 10. 11 fF. 20 2, Bluna
  93. 32 f. Y. 10. 11.= X- 30. 31
  94. nhil
  95. Adese
  96. Ex 5 sit 2Y- L2b1c.1 e 20 CF tinc p7
  97. AE
  98. e
  99. fit _ B10 b11 AEB + D 1Y b: 20
  100. Ex 7 etst sit
  101. 3
  102. C R + bloME L bi n Dom + 10= 1, VH. 20
  103. multiglis etut _ 9. . P = 1. et pred iunstio
  104. addetur ad aegq
  105. +cetL 21. et, et
  106. AD
  107. n V10 + a +b10 M = - n
  108. 20m Vt nubetur q es
  109. ractio. 10 h per A et 9 habi tur
  110. alter 20.
  111. abc abd, acd bed

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 137r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0273?run=74