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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 135r

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: 0.74.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. Lavenantius quotutat qualuor
  2. triz sunt faciliora. qualnor assurgunt
  3. invenire qualaor numeros progressionis
  4. Geometricae, sic ut summa quadralore
  5. summa cuborum sit duta:
  6. LeXG X y L
  7. XZ= yy
  8. X +s + Z b x+ yr BC
  9. +Fya
  10. sit xy+ XZ+ yZ = m. fiet: at 2m.
  11. (9)
  12. b+2 m = a. Ergo b + 2ya = aa
  13. X3 + y + Z3 + 3Xy ∞3XZ + 3 5Z = a3
  14. X)
  15. x3
  16. 93
  17. (11)
  18. seu C. + 3 Xy~X = 3XyZ = a
  19. Z
  20. seu C + 3am
  21. 093
  22. (n)
  23. 393 = a
  24. seu c + 3aa y - 3y3= a
  25. ex ex g et 10 inter se sunctis habetur aequatio
  26. pro y. vel si univis ex 8hraberi
  27. potest aequatio pro quod optime fiet collendo
  28. prigum a, fiet enius:
  29. y LaC b a: 2 - b: 2a, ex aey.9
  30. un in aeq. 13. fit
  31. a = C + 3 3a : 2 - 3 a b: 2
  32. - 3a: 8 + 3. 3 a b: 412a - 3. 3 ab: 2. 4 a 4. b: 8a
  33. 1b
  34. seu 8 a =8c+ 12 a - 12 a b - 3 a + 92b- 9 ab +, b3
  35. 2
  36. seu a 9a - ga b. a 9ta + 3b0
  37. et inventa a facile habetur y per aeq 9
  38. seu a-3b a +88c a - 9bb a + 3130
  39. 1N 729
  40. o is
  41. 2d
  42. 648
  43. problema duvena
  44. 5. 4x x
  45. sent ra + a + a
  46. Ergo V a N
  47. spril. b6ss
  48. ,X aN
  49. ax- 3aH, F + 3axX
  50. beE 108
  51. tam idem aN. ergo aequando
  52. a N= 3a X, X + 3axX -
  53. 1 Na
  54. b.
  55. E
  56. seut cubus ab aV = X X a
  57. seu
  58. E 1 10 nane - a
  59. Quod si summam cuborum a
  60. quatuor terminis. X. a x 4 X. a x
  61. putes equalem dato a
  62. tunc eadem orietur aequatio tantum
  63. pro substituendo a. et pro
  64. X ponendo X, et pro aN ponendo
  65. a B nempe.
  66. cabus ab a B X a X aB
  67. s
  68. r3 B cubus ab a
  69. eB aB
  70. X3II a cub. ab et.
  71. o sive
  72. à B- X3
  73. Unde:
  74. aB3 - 7a 8 X2 4 2 + 3a 8X 43 -x px a B
  75. sive saB- aB a D neoque conferendo aeq. Z et E
  76. sue areo avran f xaa )- a a
  77. d. (BB- 2 av 4 2- a uZ- 0 a
  78. EIta X + L X
  79. a X à
  80. a X + a X a N. problema davenant
  81. =b v + X+ isP = C. fiat v+xty+ Z =a et v exG=n
  82. (3
  83. fiat b + 2m =aa C+ 3am - 3 3n= a
  84. L aa - b
  85. 3(107
  86. fint c - 3ba 3n 4 3 da a. sent 2c - bn - 6ba + a -0
  87. n exy + vygt vyz+ xyZ fint Cexs per 1. E4. () X gng.
  88. x +Ky + xy +G = n
  89. b (∞)
  90. b
  91. ryt 2 a aβ t. Pn. lin m
  92. si suat quatuor R. y Z. v. X. y. Z ex v
  93. sit V + X+ y +Z2
  94. N Ay = XX ~Xy + gya
  95. uty
  96. 0
  97. 3
  98. . -729 +, 648 = 729 + 81 = 0 cubi X + a x + a x + a) a B ad lne 12 Apuil. 1695
  99. probatio per calculum posito X-y- Z =1
  100. G1b
  101. inge
  102. solvialibi adde ubi de homoeositotus ex. XaX
  103. ad gradum nonum
  104. tres
  105. m = ya, (per 4. 5. 1.)
  106. ton
  107. M
  108. X. Y
  109. P y
  110. py
  111. vvare a
  112. n et virav
  113. Ve a give: C)
  114. at
  115. X
  116. ixa
  117. sive d’ a
  118. adeoque: yak- atNax
  119. Xay 1
  120. sive yar-a xaya
  121. hioc V aN
  122. aX. XX a
  123. Ergus aex
  124. calriti
  125. + 3a V X
  126. XoaDaS
  127. unde conserendo aequatione
  128. C et D tollitur y
  129. (3) Xa NM 3a.
  130. Na X Z3 at
  131. Quaeritur X. et b
  132. istota oldenbum
  133. ex vetdstm= a
  134. ex
  135. 2y 39
  136. XX +Ny + hy + ex + 9Z + vZ + xy
  137. artut niutque
  138. vra.
  139. Ox + XX + xG Fgy + yZ = m = _ aa- b

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 135r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0269?run=74