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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 31r

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. 32v); this page is its right half.

The machine reads it as

  1. quaeritur an possit ex esse X + 3 = gu. ita et X sitractus fit a + Bs -. 1
  2. fit a 5 + q = vY et X 2 a vV : 9q
  3. 4 5 6 7 8 9 10 1 1 n quolientes si quadrati dpudantur per 3, sunt B 9 10 10n
  4. 1b 27 36 49 64 81 100 1ut 1193 0 1 3 5 8 12 16 21 27 33 40 4856 65 25 804
  5. 2 0 1 2 o en
  6. 1b B1 256 625 1096
  7. v - 4 = v
  8. 0 5 27 85208 64 - 16 4
  9. 8 -4, 814 3
  10. X =
  11. sit v = 8. et 9 = 2, g0 v = _ _ 4 :
  12. 12 + (a - 4 181 1
  13. V. + gu = D ag - 3. 1 v = ag - 49
  14. 8- 2 =53 8+2 = 3. 4 8- 2. 3. v- 9 = 5 8- 2 =
  15. 261 256
  16. si un et st divedentur per a, debent residui esse eqales t isi vet quidi
  17. si 4294 et B + dividan ter per a, iebent, vel residui este aequiles, bll simul facere a
  18. tantque q et primi inter se
  19. v+ q= v est major quam que
  20. 2 2 3 4 4 3 C 6 y 8 8 910 10 1 12 12 B 14 1115 16 6 17 18 18, 19 20 20 21 21 19 14 24
  21. 33 8 12 1b 21 27 33 4u 48 56 65 75. 85. 9)b. 108 120 13 H76] 175 192 28 125 243261280. 30 320341 36) q)
  22. si a primition fit
  23. va - : a est intere Cio fgg = a fi v = act + 4q n ∞ + 49 = V:cofiet
  24. ac, L 299 = 5: 9 1 4 299 = a8 Erg res d reodita est fucilior
  25. H v. ex SEB, 8= 2 prSE fini aptis ou per et
  26. vidend an possibiem sit 1 24q pos diviti per a
  27. sunt pudemi cuter se, fiot s
  28. f2 3 3. 2 = 2. 2 =
  29. quis
  30. b2 B
  31. Residui quadi
  32. quoidoh dim bex tut 6, 2 3 3 0292
  33. lon
  34. 1s07
  35. oc 0 i
  36. 125
  37. al
  38. Nucmndiidus per 2 078g. 10
  39. V, Residmi Numeroru 01 01 01, 0 1
  40. quadralam 0 1 0 101010
  41. dibplam Eonctula 0 V v 00b 00000
  42. biquadiatorm 0 1 0 P 0 1 0 101 0
  43. per 3) Numer, 0 1 2 3. 4 5 6
  44. Rresidui numeram 0 1 2 0 1 2
  45. quadulam 0 1
  46. diflaistam 0 2 2 0 2 2 0
  47. biqualtatam 0- 1. 1 0 - l--
  48. Resieni apadior
  49. quadralor
  50. 01 2 3 4 0 1
  51. 0 14 4 1 9 1 4
  52. duplor contorum 02 3 3 20 2
  53. biquabutom 0 1
  54. pr TRlesidii Nlama 0 1. 2- 3. 4.
  55. quadralom
  56. ducam qu
  57. tiquadratom
  58. 2
  59. 4
  60. 0 2 2 4 4 2 7
  61. E et 5 non possent esse a
  62. si postuletur, ut X sit fractus
  63. et sit X+ = = yy
  64. 9al2 822. 4 X = 4 sit 4 + 3. 19 - 1 -2. 3
  65. Resisui quadratorum per Sdibisom 0. 1. 4 4. 1. 0. 1. 4. 41 0
  66. sumira vel sisfeantiae
  67. per.3dale
  68. duplam quadrolam
  69. 3 1 11 1
  70. 023320
  71. ee Bimii R s Nen possunt componi duo retisui
  72. unn biquadrati per 5 divisi alter bini dupliquadrat per 5
  73. divisi, ut summa vel differentia sit S. Ergo. Aunem 5 non qula rat
  74. . 16
  75. I
  76. 256
  77. V, qu. primi inter se
  78. , et q pui, iem β01 9 prmm intli se
  79. 9 10 I1. 12 13114. 15 16 17. 18 1920
  80. 89 + 14 = 100
  81. 0 1 2 0 1 quia residut et duplo quadrato eum
  82. 0
  83. chesitro a biquadrato componit 3, etsi
  84. 0 2 2 ipsi sunt primi inter
  85. 0 1 1
  86. 0
  87. exeluditur 3
  88. 11641
  89. quia summa et differentia pesidui a biquadento et a diulo
  90. quadiato, non componit 0 vel 5, quamo radices sunt
  91. spiimi inter se, ideo non quadat 5
  92. on
  93. +
  94. 14 2 Hvisib. per 3 14 + 2 = 2
  95. q= 2 v = BB ab - 299 - a
  96. vn - 9, divisib per a
  97. 19- divisib per 3
  98. d
  99. vt q. l 10g2n -8 i
  100. H tus a
  101. 19-3 = 2
  102. Bv - q divisib. per a v 449 - a β v + Hi
  103. 20 = aB + A+
  104. +4 desta tab, aus pera, v+qq a bd v
  105. 108
  106. 29
  107. 2
  108. B = 34. - n
  109. resi ma a n biquadruli
  110. et in duplo quadulo non facit D1, Q
  111. quando non sunt primi inter se
  112. 0
  113. Residui duplolu
  114. 73+16
  115. 3

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 31r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0061?run=73