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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 122r

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. 121v); this page is its right half.

The machine reads it as

  1. Sipiora haud dabic succedo ut; videamus tantum nan brevius sic.
  2. t
  3. a sit unus numerus. deterhatio a quodrate, X, fiet ab eo detrahatur quadiatum
  4. X, fiet al = X numerus 2d9., a quo si detrahatur rursus quadratum, fiet
  5. al = X - 30 numerus otius, atque is iterum detrahatur a prumo al
  6. fiet al - al f X + Z2
  7. tan quaeruntur tantum duo quadrati, quorum summa sit quadratus.
  8. seu X + ZY (, W Ut ergo radix extrahi possit ex X +.
  9. fiat y + b 5+ X, et X + C,, 7 unde V + 2by + b
  10. seu X + Z1 F)
  11. 3
  12. + 27C +c
  13. + 2C + c
  14. fietque X 27C + c et pro Oponendo X + d,
  15. 2
  16. fiet X 2ZC + X + 2DX + d. Ergo (ZX + 7Zd + 3d0
  17. s Unde patet obiter, quomodo duorum quadrato rum summa fiat quadratus, nam
  18. si q sit A 8, erit Nam si datus sit X, erit Z e - + iideoque
  19. ponendo et dopro artitie, seua et minorem f majorem d t
  20. tivum, A seu ( - 9. et g majorem 2X, ponendo -23, et 2x -917
  21. fiet
  22. d
  23. idque exemplo probemus.
  24. eus
  25. 17 +
  26. 2X 2g
  27. +
  28. Esto X e 8. ponatur g 1, 10 erit d5 do, et, 2d p800,
  29. et = 2d2 + 800, ergo Z p 800 200.
  30. cujus quadratum 40, 00b. ergo 40064erit etiam quadcatum
  31. Si verus
  32. ponatur g F) 10, et v d 10, et Fd r, 100, et
  33. - 100s, et Z 1 = 100 17 150.
  34. jam
  35. n
  36. 2500 + 64, seu 2564, debet esse D,
  37. x 54 Erravi in calculo est enim 2ZX + ZdX,
  38. Hue
  39. sive -d
  40. 2712
  41. + 2X + 2∞ d
  42. a
  43. 27c + 20+ d e0, 8. pro
  44. C, ponendo X + d fiet 27X + 27d + 2d X + d ,0
  45. 7 = 2d∞ - d
  46. et ut signum negativum evanescat, ponemus:
  47. -adx d2 2d 5 - 29., et g pex
  48. jam ergo esto Z 0 X ( 8. et d B - g ⊓ - 20. erit
  49. vel 64
  50. +160 - 400-40
  51. + 16 = 40 17- 24
  52. 575+35 1 60+
  53. 5 5 Jam 25, 64
  54. o
  55. N= Z7X +2dX 1D X , Se 1 _ qL 2ZC + C H Ergo X H 2ZC +C. ponendo
  56. CCe X A d fiet ex ( 2ZX +- 27d + X - = Xd +d 3E
  57. et a Ergo ponendo X esse cognitam fiet Z e C-
  58. 20
  59. sit penim quadratus aliquis, 16 et alius eo major, 36 pC, erit Z17 2015
  60. jam 25 + 16.
  61. id
  62. 14
  63. 16
  64. ac
  65. t
  66. Eraf 1E4
  67. a
  68. 1Z, et 46 p, X et Z + X F
  69. 1
  70. 169
  71. 13 13
  72. 12 3
  73. utergo uniora resuamus quie Z ep C + X..
  74. erit yu pC - 2CX + X
  75. ergo ut habeamus propositum, id scilicet ex tribus num eris duorum
  76. quorum libet in tervallum sit quadratus, erit primus a. pro urbi trro,
  77. secundus al - X, sumto X rursus pro arbitrio erit tentius al X-
  78. erit tertius al - x A = C +2CXX et habebi; intentum.
  79. sumita C, rursus pro arbitrio et patet.
  80. 4
  81. differentias duorum quo rumbt
  82. se quadcatus. Num estilcicudum, ut et difflrentie quadhatoru snt quadrats
  83. Eodem modo Z
  84. Ergo -d-2
  85. 1d
  86. Ergo X
  87. si
  88. X
  89. d = 2d7
  90. +d
  91. d

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 122r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0245?run=74