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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 271r

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: 0.77.

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. 272v); this page is its right half.

The machine reads it as

  1. lonatur scilicet aequatio cubica assumi
  2. 3
  3. 2
  4. y3
  5. conferenda haic
  6. +pZ2 - 3aq Z + aY
  7. 1 +b93
  8. 2
  9. -3a9
  10. ∞ ac
  11. +a. qua collatus temnis perultims fieri mups aq. et npu ag
  12. +p m2
  13. = 2mN
  14. =a M
  15. + ac N
  16. L3In
  17. 3mp
  18. quem valorem ipsius n, inserendo in terminis altimis, fier.
  19. M +p M = ac M +ar M tacaque M +p a 1))
  20. Abq
  21. +3ab9 .
  22. u
  23. Acquatio sexti gradus in qua sunt arbitrariae numero quinque
  24. et quae ad Tubicamo (uno si terminus m3 desit ad planam) re ducipotest
  25. ubi si ipsum 9. non eyplicemus sed reserveruus, (modo alicorum artitrariarum sit satis.)ut
  26. quantum licet magnam assrmere liceat, erit Cybica assumta 23, etc. utique tractabilis
  27. hebet autem 9. esse affrimativa ergo bcuia etiam affirmativa, seu a A b.
  28. si scilice 4. liti hoc modo volumue.
  29. sit jam culua aliqua data intracrabilis atis t
  30. multiplicetur ter tractabilem, et excitetur ope trium novarum arbitraviam s
  31. + Ba
  32. bua
  33. ide conferendo, eri q ex term. ult
  34. ex perlt dn. qh patqut aile -a cqt 3 abq
  35. he . + a B m
  36. b. a d b=a d
  37. X atd. +ald m
  38. la abb- a
  39. Ahb-a
  40. aV acqtaqe habitas pla + p aeqlaat
  41. q dR
  42. aot aacnb BIBLADEAEBI
  43. +aem-ahe. + a le
  44. AICEL+
  45. EIANBOVBHAEEA
  46. Rectius sic aequationis prioris term. penult. ad secundo ut aq ad 1. idem ergo et in
  47. t
  48. posteriore, ergo de Pa ae qui
  49. +ac + 3bg
  50. b a
  51. b a
  52. a b9t vat ( qh + 1
  53. la2
  54. cut
  55. il
  56. +ah ad ap - aehd sustulimus erg e,) et c
  57. 1a
  58. b-a
  59. dei ahqebua - aelp p aqeh bua + pa t
  60. buan) a 9 - ae h
  61. a B-a,
  62. Ergo a q- ah Ergo Xq- Xh + a l que aeque dificius ac data
  63. cursus cupo clapsa est natura
  64. qu
  65. Resumamus ergo aequationem ex quadiato quadratica stusiana, et quadratica impostibili exertotam
  66. nunc tamen autem videanus un quaedu quadra trquadralic redncibilis sim erter
  67. excitari possit, sit aequalio plam: Y. Z cZ + da ponamus E, Z m= n
  68. explicando fiet: E H
  69. conferetm cum. Z p mid
  70. = 2m1.
  71. an
  72. bini
  73. -imn
  74. sit cubicu dH. uq y + aY
  75. +
  76. yA + - aqy +ary
  77. by2
  78. a- b7 f
  79. pro ma scribamus ea per: m tac m + da m eac M - fe 2
  80. Quae aequalio semper plana,
  81. 97. X -agg. tarm
  82. plana
  83. conferatur h oyorutica cum sensinua:
  84. et si d,o etium latioculis reddi
  85. e potest
  86. fea
  87. af
  88. si =en +. un + posibile: ut si Z e 4Z. quadratus
  89. quod facile, quando e aib hari erit etram rationais 2
  90. onflundo gB = Ca e = ac e - arf. quas duas aequationes
  91. a9f
  92. A explicare possum omnia habermus, ex primo et ultimo valore ipsius g
  93. erit cag - aCe B f idem ex imo et 20, fp, = caY
  94. aer et destinitur CAitq: C3 - 9 + Ya quae redit ad datum
  95. X+ + en X3 - 3a X -nan X anBo crit si -ac)) et. erx er a. du ac c. 3a - ac
  96. ano an
  97. imio vilo gparationem institui non posse quia uttrimus
  98. dratica plana est:
  99. in
  100. +pXrq p
  101. aum cae etrans oae nucn totue a pe. 1 e u i ft 1 1
  102. t 3mnz +m
  103. quadrato- Tubicu hmic similis:
  104. M X. Lah M + a
  105. +ad m + ae
  106. +pa N
  107. b-a
  108. X - ah M + ael B.
  109. X
  110. ad
  111. potito
  112. et ZB M = n.
  113. explicemus LZ3. + pZ -acZ fer
  114. +a 9

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 271r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0541?run=74