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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 57r

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: 0.82.

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The machine reads it as

  1. quaeritur an numemi 7 possit divedi in duos quadratos Tentemus
  2. in quisitionem dy per dyadicos
  3. = 11I = 1X + 1X + 1 posito X = 2L
  4. siat quadrati B 29 2Z, yy et vv: gy, fiet 7 = vr + 2Z,: yy
  5. seu ex 7yy = vN + ZZ. sit v = 10 +UX + M2 XX, 3 et Z = 20 + 21X + 22 AX + 23 X 1 2+X1
  6. et 7 = 30 + 31X + 32 XX fiet
  7. 23X + 3X+ 31+ 30
  8. 3X +32X + 31X +30
  9. +1 30. 5 X f 303+ b30. 3 X 30
  10. +243 Z. F +31X ea
  11. 3Ss 32X
  12. 142715X
  13. +2. 10BX + Z.BIX F AIX EB 2BIXF1 - 00
  14. EHI. 15X ,2. 1I14 2. 11. B 21. 12 lH. X
  15. 2.12 9L 2. 12. 14 2. 12. 13 12
  16. 21. 5X 21314 13
  17. 13X
  18. 24
  19. idem repesatur, secundum 20, 2, 2e
  20. CE v t2UB +2MX + 31 X
  21. 32
  22. +29033 +250 9rX + 2.0g X OX
  23. 2.313) 2. 31. 31. 31
  24. 229.3 32
  25. 2.30. B 2. 30. 32 230 H + 30X
  26. 2.31.33 2.31.32 31
  27. 23033, 230. 3t 23031 130
  28. (ag 147F +abX +4SF +44R +43Y +tia uN 14cl 2o
  29. 2 - 248 - 247 -246 -45 24 , 13 42 A1L
  30. 40 = - 10820 +30, :2 41 = 8. 30( 4+ 2. 30. 31 -1 - 20l - 2. 10.11 = - 4. 10. 11 + ∞3. 30l
  31. +30l
  32. =4. 10. 11 = 2 10 l
  33. 2t
  34. Meterodum hic quae sivi utum possit pervenm ad aequandam sorumtam du adicam quadrato, vel quadurti
  35. multiplo ut hic per 7, vut alium nundrm, essi non fiant additiones seu res non peduaetur ad
  36. membra haud excioentia 0 vel 1. Viditur tamam additiae illae nolae 40,41 et. esse quidem integri
  37. sed non ost necesse ut sint ovel 1, etsi 10, 11, 12, etc. item 20, 21, 22, etc. item 3031 3r ea
  38. huit c vel 1 sed ii fallor hinc con datur Tota ergas res hac radit, ut his ipsis sumtis utcaque
  39. 0, _ 42, et c. fiant jage integri
  40. incipiendo a summo levitaturdvis 1o et prodeunt integri per se
  41. Ovel 1, ipsi
  42. 49215 +25 48 = Z2154325 33 A9 47= 14 +2. 1451
  43. 2. le. 1
  44. 24 +223. 25
  45. 49 = 15+25 48 = 2. 14. 15 + 2. 15 -35722713= 14 2. 23. 25 4. 445 4. 13
  46. Be(svilalis c cusu tentemus ponendo 32, 33; 22, 23, 2e, _ 12, 13, 14, sc = 0
  47. 2. 24. 25 42. 25
  48. fint 44 = - 31 43 = -2.31 - 31 42 = - 6. 31 - 1. 31 - 2. 30. 31 = -7. 31 = 2. 30. 31
  49. 41 = = 14. 31 - 4. 30.31 - 30-2. 30.3] - 2.30. 32 4 2. 10. 12. + 11
  50. 49 = - 14.. 31 - 2. 30 = 12. 30. 31 - 4. 30.32 + 4. 10. 12 +2. 11 -30 -2. 30. 31 + 2.10. 11
  51. 2. 29, 22 + 21
  52. 4. 2022 +2. 21
  53. 2. 20. 21
  54. = 28. 31 - 6. 30 = 28. 30. 31 -8.30.32 + 8. 10. 12 + 4. 11 + 4. 10. 11 = 10
  55. 8. 20. 22 +4. 21 4. 20. 21 20
  56. quae aequatio est solvenda non solum in dyadicis, sed etiam in 0 et 1. seu ∞,t,
  57. sed 10 et I1 non possunt simul esse O
  58. 10. 1(1
  59. ut
  60. sunt 1 vet L
  61. seu 10, U1; 20, 21, 30, 3) debent esse 0 vel 1
  62. idem est de 20 et 21, 30+ 31 Ergo seu
  63. X = 10r1 10 + H1 X ~Y X - 201X - 1 = XX - 3X, f 2 ∞10+ -21041
  64. +1 f. (19 (+ 11) + 2. 10. 11 - β3)10-(3, 14 12 =0. ita 10 et U possunt esse ambo, a ,
  65. non amba vel unum 1, alterum 0, sod non possunt esse ambo D
  66. Habemus ergu aeqq. 1,2, 3, 4, et ope agy. 23A, tollamus 10, 2D, 3D ex aeg. 1.
  67. semulis asquatio inveniatur pro 4,21, et pro 3031.
  68. superetunt 1424,31 in aequatione ubi omnes literaee possunt esse 1 vel 0.
  69. nulla ab aliis dependentia; cum ipsae 10, 20, 30, non possint essie 0, nisi cn 1, vel 21,
  70. porro haeaquationes si haec aequatio si quadretur, et cubetur
  71. manent eaedem literae nec altius assumnat, Ergo s habemus tres aeqgu. securdum
  72. quas haben potemul tres valores; sed quomodo quaeso efficietur, ut quivis valor sit 1velo
  73. vel 31 sunt 1.
  74. Resus invenietur ope fractinis, cujus si numemior sit denominatur sit, o vel nomi
  75. denoninatur et numerator simul sit 0, ipsa ert 1 vel 0. si e numerator sit
  76. nominatur quicunque erit 0, si. Numator et nominator sint aliquid id aequales fiet 1.
  77. sed hoa. hoc inquovis gradu tentare minis prolixem foret
  78. ut habeatur
  79. d+
  80. n 10.1 - 10-11 + 1 =0
  81. s
  82. 33 X +2. 5134
  83. +33
  84. 2. 3237
  85. ex

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 57r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0115?run=74