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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 104v

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.

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The machine reads it as

  1. Huddonii inveniemus ipsam V.
  2. JX 94 + 3
  3. ope aequationis hujus quadraticae.
  4. V
  5. =SE 13 +20
  6. 24
  7. 121124
  8. sive Y +
  9. +S a
  10. y
  11. 4
  12. 2
  13. semt
  14. +gtX
  15. =Y:..
  16. Adioque yp
  17. L
  18. +2124 H. id
  19. +E
  20. um generali emuntratione est.
  21. y + L p _ A y
  22. r -912s.
  23. + ZZ
  24. p=2P+Y
  25. +2 P- 9+Z
  26. 110
  27. 2 23
  28. a
  29. 25, 47
  30. 8,4
  31. 17 (13Z
  32. 24) 27
  33. e
  34. +42
  35. ruzis
  36. itaque problema reductum est ad duplicationem cubi. Nam extruhenda
  37. est tantum Radix cubica de 2. qua inventa habebitur etiam Radix cubica de
  38. cuim sit quadratum prioris. Habitis audem 1(2. et +6 4 habetur 7.
  39. et habita Z. de catero tantum e cir Geometriae planae beneficio habebitur Y
  40. protiandi causa, ducamus Z + 4 in se cubiae fiet: Z + 3, 42 + 3. 6Z 64 (128) + 3, 16, (10) E, 4, (10 32) + 4
  41. sive Z + 12Z + 48Z - 164 24 194. et rursus cubando. sed ita ninis alte sspugemu,s 2st brevius ergrita.
  42. 132
  43. 214 B1, seu 2 +64, 13, 1Z27a ( (126d) (+34 (32 d) + (3) + 13+ p 132 + 3 , 2 3+ 4
  44. divisisque omnibus per Z+ 4 fat: Z + 2 AZ + 16 p7 132 4 24 3A, 2
  45. a
  46. Ai rectius quadubnmus ab initio, non cubabimus, fiet: 92 + 24Z9 1) 16 1 2 8) +O+
  47. B5 Sutus ita:
  48. ZF + 1(32 + + 4 + ergo
  49. t
  50. +2 pF4 + 5)1.. 4 ut d 3 164 1 3 3 2. 1 4+ 2+ 1
  51. 17
  52. Sid rectus ita quia Z+ ps + 4 + V2, ideo erit : 62 q+a = s(2 p 4.. Ergo Zd C, +4. et fiet cubando:
  53. 2 + 3, 2)
  54. et s
  55. 192
  56. 162
  57. 14rB
  58. 7 64 sivi 2 +6Z + 127)- 120 p0. error. Itaque aliter ron esse oportet,
  59. su
  60. 162
  61. scilicet valor ipsius e, est quantitas falsa seu negativa. Nempe C- + ) - s2
  62. H e 4 erit 4 10 - 194. - 4) hic Z+ 4 p. 4 + sD2 vel 7+ 4 - s a
  63. vel
  64. C4 + D( 4. Unde Z + 18Z 13, 16 Z5 ∞16 p0. 2. - 1B 2
  65. S2
  66. +NB)
  67. quo rursus erroo est, cum ei
  68. = (3)
  69. deprehondea ac quae rere
  70. neceste est, ec proinde primum omisso Z investigemus e,
  71. Nempe e p 4t2 + 104.. E eju e
  72. 10 2 N +. averque : et - 3A C) + 3, C 8 4 102 1 + + 102. sive e. - (2 p, 4.
  73. sue e - 2
  74. -128
  75. 132
  76. .o. sive e - 6C 412C - 132 50. Debet
  77. ergo -60 4 12C esse p - 24 e
  78. sive +be 13 quod est absundum nam foret ex 4. i contra hypothesin.
  79. epetindus ergo culculus extractionis: e - 24C - 132,0.
  80. C N 3) +66 +3844 + (0 66 - Ax 3824
  81. Eritque per regulas Cardani.
  82. sive Cp 3 28. + 13 4 vel epp+ 4 13) 2 + s 4. et quo minus dubitationi
  83. sit locus oprationem ipsam scipionis Ferai suscipiemus: e 14C + 132. sit er Z + v. fiet
  84. e712, + 3ZF 3Z Z+ v). Et conferendo: 24 , 3ZV. et ZH _. et Z2, 512
  85. et quia Z2 + v 1 12. fiet se + v 132.. adeoque
  86. 132f6b. 218
  87. 105
  88. o
  89. 396
  90. 356
  91. 512
  92. 3814
  93. 14
  94. erit ve-B. v2 (+6666) 435 ( (4356 3044. et v -66 162. et v 1966+62 3) n8 13
  95. 512
  96. et quia ergo sive v’e 6662. est autem Z2 132 - v. fietque; Z7) 13- 65 +62 5 66 +62
  97. adeoque ZY 13 4. sergo epi s3 128 + 1(3 sive C p + 4 s3) 2 + 1(3) 4
  98. 128
  99. cujus quantilatis cubus, nempe C 464, 23, 16,4 + 3. 4 s3) 16 + 4 seu d24 + 243
  100. aquatitur quantitia ettusm nul 24 P. + 132. H 24, + +3 2 + 24 (3 4 + 132 nempe -
  101. 12
  102. 192 + 23)2 24, 4 13) 2 + 24 ((3) 4 quae duo aequivalere necesse est: sivi 1925 4, 3 +(3) 2 + 24 104
  103. et diuidendo pes 24 fier: 8 13 +) 2 + 15 4 ergo 8 + 1D2 ei e quod quomoda fieri possit non capio
  104. vidiamus an satisfaciu calculo, an aequutioni nempe 562+2 + 396+C 132 + 3, 8, 1() 4 F 24 8 +24 (3)2 + 132
  105. Unde alia rursus compantio mira. Haec scilicet pertinent au doctrinam de arte ineundi binomiorum summas. Similiter quia
  106. C 121+e
  107. sive e = +() p 4 Ergo
  108. 16.
  109. (1 + H 5() 2. sive eri 4 e- sB. sui e. sin e,
  110. 1.
  111. 2 ( 4. Ego C. 3,2 + 3, 4 C4 -8 64 adeoque e 6e +12C. 136 49
  112. 1B
  113. et spu. C L -1nC. pao. Ego nit: oc ite + 4 pe + igC sen e. B + +.
  114. i
  115. e
  116. 512
  117. 6.
  118. 512
  119. 5
  120. 10
  121. Si
  122. 334
  123. 192
  124. Gt

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 104v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0208?run=74