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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 34r

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: 0.79.

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. 33v); this page is its right half.

The machine reads it as

  1. at
  2. Invenire tres Numeros, ita su ut summma duorum
  3. duorum
  4. quorum vis sit quadratus, et summa quadsulorum ab ipsis quorumvis
  5. sit etiam quadratis
  6. La qx + ly = fusi
  7. 1x+ 1Z= gg ly +Z = R
  8. yy+22 = pp
  9. I XX + Gy =msa XX +ZZ = nn
  10. ly = ff lx = hh Z (Z = gg - lx = hh -ly fit ly = ges hh- g9 + 12
  11. = ff- lX et fit 2lx = ff + gy - hh et Ely = ff + hh =gg 2tZ = g9+hh.
  12. AllXx = f4 + g + h = 2H99 - 2shh- 2gghk
  13. allyus = sa + g ati 4- 2 H_R + 2f sit - 2 tih 99
  14. 4UZ2 = f+ G2 + hd affgu 2ffhih + 2g9tit
  15. AllXX + AUyus = 2f + 29 = 4gghh = MM
  16. fiet fa +9 + h - rghh = uUl mni seu gth- 2gghh illum
  17. flrg- 2f89 EUpp - ho
  18. Ex 1 et 3 fit AAgu = Cyghih = pllpp. furum fhi ssht = Ellnn-
  19. seu sit gg - h
  20. 99, tah, 5 -h Il, p + m p. mtt, fag, 5- g, = Il, p F m, n- m
  21. Cpm=f df - dh
  22. ff, 9+h, g-h= U, p. + n p- m
  23. sit l,p - m des bf - bh l, n = m = cf - cg l, p - n = d9 - dh
  24. et ex aeggue. 12, 3, fiet lesfat lbpt m lyg. f. +h. = Ub, p + m H
  25. Ihhf +g UC, n+m IF, oth = Ud, p+n
  26. itaqusope a49. 4, 5, 6, 7, 8, 9, se loc non juvat
  27. aub
  28. Radicem extrahere
  29. subtractio melius peculiari plagula
  30. Generalis duadica
  31. Non potest generaliter, scribis tas
  32. ex fomunta dyadica
  33. nec sed Nac potis etiam generalita
  34. sed 1(b (+a et isu A d Ia
  35. sit ergo
  36. 11 + q quod et identicum est
  37. Aaus hine
  38. h = a + b- 2ab a takl- 2aK L= a nte
  39. ab ex R, nisi conset
  40. h esse 1, neq esse
  41. Kh, nisi os ele et
  42. nec ex vel esse
  43. ergo vel ex Y vel
  44. vel ex itkIh
  45. H
  46. isique ho hab
  47. M b dabit: 2b
  48. q
  49. b
  50. + sil
  51. -b
  52. EK
  53. ab +bh
  54. quaentum quantitus, quae sit b si b esto, et sit 0 sibus
  55. aqua
  56. x quaerantur X et y bi t but 102
  57. Ergo y= mhtnah+
  58. A Y (Et X = a si h sit 0
  59. 101
  60. A y-o EtX = 1 si hsit 1 et a sit 5 Y00O amplius variuni
  61. yX
  62. a
  63. si hsit o siet X = la + p = 0 quod de-
  64. similiter yla + mhenahtp bet esse = a Ergo fiet p = 0 et l = 1
  65. et sed qulop e
  66. minon
  67. E1
  68. lis
  69. sit Eod si h sit 1 et a sit 0 fit X = m h Ca)
  70. Ergo LX + m + n+ p = 1
  71. sonto, se seo f 1 orgo m + d -0
  72. erjog= inhenunt1 si
  73. 11 12
  74. ut oportet + y - 1 EtX = 0 si h sit 1 et a sit 1
  75. tah-2ah 2- 2t 2ah t a th rat) - rta. h
  76. =fi + h
  77. sublamono duadica generalis
  78. deu a = h - 2H - L2b
  79. non absolute fieri pt
  80. res non procediret. si pari ratrone non potest generalitar fier
  81. Ergo tandem
  82. a
  83. -1
  84. a 4 ha b, 1 - 2b
  85. isnga= R + L Fb. - 2bA
  86. scribi petibi bsta sed ilta namsibet a essent c
  87. fien C) b+a
  88. sublatis columnis,
  89. nam si
  90. si
  91. ab FL ergo )b Lakl
  92. 1000 ergo a n h tk
  93. lie d
  94. Subtractro Jgadica e etad
  95. et X = a + mh+ nati,
  96. quod debet esse Ergo fit
  97. et X= e nato quad debet essed
  98. Et X = Rat FInat sit jam h,
  99. pa t sit y = td mt et a, 1. fiet x = +n1. Eg 12C
  100. ax seu n= -M. tandem
  101. ii a o rit bal, n a
  102. n=1
  103. copi 1.L 1. p
  104. cup atI. _ p dta Ergp H
  105. o et (Erra = Eah
  106. ab
  107. xut
  108. ed e fgh

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 34r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0067?run=74