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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 115v

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: 0.80.

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. 116r); this page is its left half.

The machine reads it as

  1. C bX, ac
  2. + d X +ac
  3. X4 + bN LacX
  4. + d... + db.. +dac X
  5. tac.. +aebo eaeac ah. adeoque.
  6. X + fN 9X rahX xad
  7. et fiei novissima aequatio:
  8. ag - df +d
  9. agdtis ute a fo
  10. X H =x x n +_Y,
  11. + v f
  12. v f f
  13. f. e
  14. H erga haec ex priore suppositione eunt
  15. falsce q quatior falsae.
  16. Y +0X - X +0 X + X + Y
  17. f 4. falsa, unavera.
  18. X -0x = X - 0 X + x +
  19. v f f. v. f nes false due verae
  20. X +0 X = X7 - 0 X + X + r.
  21. f V f v f
  22. X - 0 X - X + 0 X + X +Y
  23. tes false dureverae
  24. tresfalse dus vers
  25. Hud sequatur ejusmodi aequationem ds habere
  26. radices reales falsas; unam realem veram, et
  27. unam imaginariam. Omnes enim positiones n
  28. consint dicunt tres falsas, et unam veram,
  29. etsi aliquae ad falsus aliquae ad veras unicam
  30. unam adjiciunt.
  31. X - ap X raer ar
  32. X - rap X + + ap N - ar Bo
  33. Tolteado terminum secundum fier: Scribatur ejus loco
  34. 2 X = 24Z + Ap Z a a po ponmus Z., s +P
  35. Co (+n co to +
  36. p at . Apco ip,
  37. lubg at P A 72B
  38. p 0 ap, 2t
  39. Xe sed na + 10 Ana
  40. XF) na 3+D = nat + 31) nt a + + na
  41. sive Xs na
  42. +3ans S0na +sna
  43. xnsona + se tna.
  44. X e na + na n a +3 nassiae
  45. hiic XH na + han X.
  46. Xes er
  47. + sq X
  48. sit jam aequatio dati:
  49. conferendo erit een ces curmmmis. n p T q. quem
  50. valorem secunda aequationi inserendo, fiet:
  51. aa , qu Y, nir g+ .
  52. N4 +3 _ qarf sr a.
  53. sive N 9ra s +
  54. 122 fugae) orra ria
  55. quod est redire ad scipianis Ferrti est
  56. pigno, atque ita
  57. Mutenda nonnihil scena est:
  58. ax cVona + d sona. Ergo
  59. ax ena + d’na +3edna vona + 3Cd Sina
  60. jam videamus an 3 cdna (3) na + 3cdna 1B) na f
  61. exare dividi posit per Ec 1 na 4 d na lcanca
  62. fer. 3ea 3Cdna 10 a 4 3cdna +3cdnao
  63. 8 c N9oa
  64. n a B
  65. procedit ergo divisio feliciter, et fita x Ca + 3cdnaX
  66. ex aruns colur. ). + aX aXH N ra + Naque X
  67. fiet Cne 1. N9. uq Ng
  68. quos valores inserendo in aequa
  69. oedtionem ex purorum terminorum
  70. collatione
  71. X APX - ar. hioc X p X apX ar
  72. snibam XZ -p X trap - ar 0
  73. C0 +, eZ +3 Z+
  74. 2 tat fat talga
  75. +rapYZ Acap La
  76. + rapr 20 t
  77. 1ga += p
  78. nerpe da + 4 a gea o ra p coe q 3d aga
  79. sive grac d se Cq s + dga, sive:
  80. Hac ergo mutilia sunto neglecta si fiet e Dra
  81. si possuissemus - Cd N, fuiesset n+ - 4. et n 4
  82. et fuiset aequatio. C39a + d a Cdera tcd
  83. v ponamus qu p 1. qu. erit 47 ta, quod semper
  84. est qantiodo egndiva. Sed pissumus etim facere semper
  85. in aequatio quae est. aequatio inter tres cubos
  86. Unum a c. alterum a d, tercium a cd Bra
  87. ponc iin se . e S3ra Sed e c - d
  88. fiet : C - d’ 2 - 30d + 3d - d,
  89. sed haec imutilia.
  90. CB ora + 81 Y a- n4a et nH 3
  91. sive ne
  92. gra = SBrra-iqa et virae 8ra 2qu
  93. gra + Spira = 12g a
  94. sat axe se =, oa Y su +4 103 1 ia forrariuria
  95. quae consentunt Huddeniaris.
  96. graduum ad hanc quae duos tantum habet teruinos incognitae X. Y AY
  97. quadcando reducituur ad altioam nium terminoram ergo per regossium
  98. exinmpli causa: X6 - 2a(XY a p St X
  99. Xe X + r. dant: X 4X + 2gY X +V
  100. jam xCp, qse X + X 29Y A X + Y5
  101. cu: X B B X + AC X + d. Ergo
  102. soita confrendo r N d. coanescunt mibitrariae
  103. +g s, Si radq 2d ga ut aute
  104. gra da , 4 +3d qa
  105. 207 a n arpN atr. X 3 obtineri potest in data aequationa negati i 4
  106. Xp
  107. ni adis nddilur
  108. ni nvatioaem paudami
  109. be) f - d. ex secundis.
  110. ac ag - df +d- ae extertiis
  111. BaaB. Erga ex quarti
  112. dag = df +d- dac, + aef- aed
  113. aets à h. dag 43 f.d
  114. adeoque res non procedet. Nota omnis aequatio quaa omnium
  115. duorum terminorae
  116. culius aequationis cundus terminus tulli potest: sed hunc credo tertius fici affirmation

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 115v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0230?run=74