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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 14v

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: 0.76.

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. 13r); this page is its left half.

The machine reads it as

  1. 9 uit tres quadrati
  2. 2X 12XZ 1 2 y
  3. pone C B S Habernus valorem
  4. Ent enim b sf. 2. ∞2 + 3X2- .
  5. est autem b pX. L. H.2
  6. Rrectius factrer
  7. uit
  8. X X-
  9. L. quadvando: fiet:
  10. X2Z + X Z sive
  11. Pace ergo, hin quadrata: X
  12. ponendo 2 Ry. et C A
  13. 5 22, fet egoh
  14. seu ctp fr - XZf. + quga
  15. fa - 2 XZ f + q2 4
  16. 1) f+
  17. X + af. (4d)
  18. , ad ed quod (+)
  19. 15. Riet E qualio destnctis destmendis
  20. Het 5 9h. l e pa E 29ht 1
  21. et habelimus quu Eg 1C 41
  22. seu a2h
  23. nes 7C2 + 4
  24. pone X. 1 f 1I
  25. 3gh ponc r 91
  26. + 4 a 3
  27. d
  28. a +b p X. Cago a X - b.
  29. a -d B y Ergo a. p X + b. = y.
  30. Ergo X + X H. Yb
  31. Erit X4 b a etiam quadratus
  32. nempe X. Y + 2y
  33. re a 2Xy +1
  34. -X+ axb - b2
  35. fet . = 3 a + 2X y + y -Xb - b2
  36. quadratum estu imB L A p 2. b13
  37. deorema.
  38. a +6130 =, 9 B -
  39. est quadratus verum ergo
  40. Enficissimmia futurum
  41. ad destrnctiones. Imo execunda 6
  42. fiet 2 seu quod 2 et 2xr9 2Y
  43. a n a -. 5.
  44. Ego a p,. +x- git
  45. est quidem, sed imitile ad destructiones
  46. hodem modo:
  47. 15 3 + 816, 10 - o 25
  48. pet + d2+ ad 4 2d (4) 32 seu f 73 (4) or
  49. it aea
  50. (4) 2+ 1. seu 45 + 2 (4) X f 1 0. Emo (4) X 1 Y + 2. ponc sM 4
  51. P.
  52. pone neis det. + H +, e
  53. ta t
  54. 2 5 45 + 2f vel (1 e. 253 + 2f ponendig 2s fit 4X et (4) et esse, fier 5f 31 45
  55. et
  56. et s euit e
  57. ponendo f p 2. f’ erit 8 er 2f erit 4 fiet 4f3 + 2f5 36. ergo porendo () esset
  58. erit g76. et X73. Ergo 4f + 2
  59. Ergo in aequatione seu restat tantum seme bis ipsa d
  60. semel ingrediens in quoddam quadratum semet pura destruendum part est quadratum alteius:
  61. ex prout ergo vel g vel d, vis esse, dtum, alterius quadratum destines, explicando ad quod
  62. est dalum;
  63. pone quadratium este datum, culi aequari debet laberum summa; explrabis, et fretogo
  64. A 9. unde gr he + 2X d. + x d destnctis igitur utrobique pure
  65. d + X
  66. Possumus ergo problema solvere hoc modo: tres numeros ivenore
  67. di suuma sia quadratus datus, et quadratorum surmma sit quadrato quadratus
  68. alqaatitur vator ipsius.
  69. pato idem sic solvi posse ut quadrato quadiatus, quam quadratus sint dati. Ponatur esse datus
  70. ego sumatur quadratur so
  71. minus quod ab ex differa numero
  72. C, et fie pro cot porremus l+ on
  73. SH + m pone m B4r + m fiet:
  74. morm () pr+ ft + (2) erit me e 14 1. Latera jum erunt.
  75. + p +q
  76. p 1q0 + r(7t
  77. sa e la. +
  78. adug
  79. +p 14q Bs. ant fit. fr + p + qu + (4) l + 9
  80. quiia numtur pn esse muntius quadratus seu aeguaut F lonatur 5 n + v+ t.
  81. jen ponantur +r + p2 lam poriatur et L (++)
  82. fiet aequatie pr +
  83. () c p2 qe l + m + r- Ern (+ n) . Ergo n e
  84. sed jam video hoc non procedere si
  85. coa sumponitur datus, quia n rependet ex Y et m. F. nisi ponatur vig; (+r a
  86. et fiet aequatio: 2r A P 0 sed an forte rectius, in p n. ponetur
  87. u
  88. unde fet p2 + q H
  89. Erunt tuta latera: m. p. 4. pp g2 sumtis M et
  90. ut et g habetur +
  91. Exgrat esto quadrato quadratus 16., seu 2Y9.
  92. fiet (9) + pr a a 7 (. 9) Ergo P n 7 - q. seu PB 7 - qu
  93. proartitir habetur
  94. ladera. 3. S7-9 9 B g, sive 17 - 91 5 - 9 - 3.
  95. sive 7 - 4 t g -g q - bg4. + 9 +69+9.
  96. pone g1 1. fiet q H 7 + G - 1 - 9. seu erit 4 73. Absurdio.
  97. 1+ n fit l⊓ p +4 vel pr 4 l - q
  98. Resumerus quod supra C XA fa 2 Xf Z +d + B (0. pone Z A 5 + f. fei 2 X5 Z n 2Xf5 - 2X f pone XA Z
  99. n + p2 + qu p
  100. et fier X + d 1
  101. 2Xf5. et fiet XSr L+ d. Jan latera erunt 52 + + + 2d+
  102. explicata jum
  103. 8 ut sit pth, 4d, tar q +h 4
  104. 3u 3t
  105. 1o re
  106. + 2d +82
  107. ponc 5pd. tit Ad2) etc 19n B t +4to 4d) sumta ergo
  108. d hores
  109. suit d 1
  110. et b p ng atro quod verissuum
  111. Jam tria latera erunt
  112. 3s 10d

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 14v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0028?run=74