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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 232v

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: 0.75.

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. 233r); this page is its left half.

The machine reads it as

  1. par b
  2. Operae pretium est, ut videam aneffici possit, ut duoe termini de ex Aequatione data Terminus
  3. secumus et tertius simul tollantur Habem qp in Aequaline quadrato quadratica
  4. habemus: ap C. 4 p FI 1.
  5. ejus valorem, fie
  6. e
  7. itemque p - 3lp F -am. et pro p substituendo
  8. iga
  9. Bl -am sive l am
  10. 240
  11. aequationis quad iato quadraticae
  12. +4 Sam. Antequam
  13. ego possimus utrumque terminum, secundum et dertium simul toller, efficiendum est in aequatione proposita
  14. ut secundus termini cognita quantitas, sit quadrupla radix quadrata cognitae quantitatis termini
  15. tertii. Quod an effici illa arte queat, videndum est. Si aequatio cubica esset foret
  16. foret
  17. 23
  18. + 2p2
  19. a
  20. ba
  21. + 3P
  22. =B3 Unde pei L. et 3p - 2lp pam am. vel
  23. -l .. - 2l p . = lx2
  24. am +amp
  25. +anp
  26. Aequatio data calica esto, ut dixi
  27. a 3
  28. k
  29. j
  30. 2d
  31. = 2l 5 - am, vel l 7 dam alvel le
  32. vel ldam. Quod ut in data aequatione
  33. efficere tentemus:
  34. yN
  35. +an) + an
  36. Ponons Z
  37. Pouamus ZB SXg. Quare id sit terminus secundus aequalis radici p se terti duplicati
  38. erit aequatu
  39. a
  40. v - 6pl + l
  41. alia ergo arte opus est, nimirum, ponendo
  42. et yn
  43. adi
  44. sive omnibus per divisis:
  45. v
  46. eritque 9ga-69al+
  47. s
  48. 9a-6lag +am
  49. op2 = 6pl + ham, quae aequatio identica, mutelusque
  50. t x
  51. 51. a + g.. EgoZ3 F
  52. + 39a X + 3agX + a
  53. Unde rursus mutilis inquisitio, patet, hc
  54. arte quidem ista, quod quaeriimus effici non posse.
  55. itemque 3agr
  56. er
  57. req
  58. ulag. lag
  59. +am..
  60. +4 3
  61. +an
  62. +dofrx
  63. Aey. 1.
  64. C+34Xrq
  65. +392
  66. ex
  67. +39a - 1ga
  68. e
  69. et fiet nova aequatio:
  70. +lga ∞am p 0 quae sirdae ps multiplicatae jugatur siet
  71. Aeguda
  72. dac
  73. da
  74. an
  75. AL
  76. ang + lgaaem ere sive g- an fg +D , +3a +D
  77. sive gF 4
  78. am
  79. 2l
  80. 2l
  81. assa
  82. 4C
  83. ga..
  84. HI
  85. ss
  86. cunque sit sge+ Ega fietque gF ex dicta aequatione 3tia, g am. ideoque at rursus
  87. g1 L ergo = ( am sive l ham,, ut supra neque quicquam effectum
  88. est tanto conatu dignum. A Nisi quod rationem deteximus ex aequatione qualibet
  89. X _-3m X - n ostensum est ab aliis secundum Regnlas Scipionis Ferrei
  90. s
  91. confera mu jam aquationes duas unemus
  92. quoritur valor ipsis
  93. sed m m fi n 15): poratur eggo m FJ A 1 N(3) L C, sive e M- R s
  94. A - 3m X - n 1 0 itam 72 X 2m Z 2n b(h bem N
  95. as nn posse rai applicars nnsi sit n6 m. ac proinde s H p Y ( B note
  96. poramus eam in
  97. ut
  98. tollendi terminum tertium vel antepenultimum. Bopum est certitudinis
  99. Si sit aequatio
  100. erg
  101. -1lfg .. 2 lg
  102. 2lag + am 10, et prore multipli aequatione multiplicata per d fiet:
  103. Acg. 3.
  104. e
  105. 2
  106. in
  107. +amf.. gang.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 232v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0466?run=74