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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 126v

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: 0.76.

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. 127r); this page is its left half.

The machine reads it as

  1. Data sit aequatio:
  2. q side 1ode
  3. + ge . ..
  4. pXe + ulf ode.
  5. agX p) aGs
  6. tar e
  7. X + X ∞ + aqX + ar 5. Sonamus X⊓ F 14C +1de
  8. e se de + 6s ide
  9. +92de 00.
  10. +3fgedl. ..
  11. ragg.
  12. psde
  13. P31d
  14. ubi tres habemus aequationes subsidiarias, exquibus
  15. duae priores una dividi possunt, prima perf, per f.
  16. secunda per g, et si post divisionem una ab
  17. altera ab altera subtradatur, habebimus:
  18. (3)fd + 39 e 0 quae aequatio promitit
  19. aliquid ob simplicitatem suam. itaque si ipsius g’e
  20. valor repertus. inseratur in aequatione 2.
  21. et ponatur de v. fiet:
  22. 55v d + 3 afgpV + aq fo
  23. Habemus ergo eti fd. et dF - a g - 3afg p V
  24. sic et - aq. 2at9 pr
  25. 553p2
  26. ope igitur horum valorum repertorum vel assumtorum, tollamus de, et d. in aequatione ultima,
  27. fiet: 2p 2pa 2. 3a59pV + 6v f92
  28. = a 4
  29. ar pEd0 Quae aequatio est semper
  30. posribilis, et si aersit quantitas negativa.
  31. Nseusaem rujus requa lionid ope nees Sed una ad huc aequatio construenda est, nimirum:
  32. er Y e9 sd. et v ) a 52 (+)- aq
  33. et fiet: d agpd 1 a 9g. l0
  34. unde necesse est f et
  35. 5fd+ 3a59P
  36. oblisa est liam
  37. quae aequatio semper est tractabilis, si p. et g. sunt ejusdem signi, aut si
  38. pura foret si abesset P plana si abesset g.
  39. debet esse t
  40. ergo pe
  41. 25 (19) 24
  42. sines
  43. 4 44 H
  44. Caeterum pro d ponamus cot
  45. Egae
  46. 100
  47. o fier.
  48. Q et debet esse vel p. et 9. ejusdem signi, vel
  49. 2s, A p sive q f 100 p3, quod atique semper freri potest
  50. fEo gu adeoque 22 (1)6
  51. 53
  52. in aequatione 10. fet: 29a c0t3
  53. :Quem vatorem inserendo 27
  54. I corsu
  55. t9Pa
  56. orfus L
  57. 82
  58. (23)
  59. ...
  60. et s
  61. asq...
  62. sive aspacop paq + 30a59 + a Yco f9) 0. quae aequatio cum sit puva
  63. simplex erit utique semper possibilis fiei: - 3 pa ap atq ab - pa a 9 +61395 a6
  64. sive + a Y C04- p a c02
  65. -2 paq ....
  66. = 6a 770.
  67. XN = 10 d’e + d 110 de
  68. H S
  69. qxri
  70. fa .
  71. + aer
  72. +itd
  73. 10 de + 1 10 de
  74. XH 219...
  75. PX,
  76. ascribatur qX fiet:
  77. +35919...
  78. +(510
  79. restat ultima aequatio:
  80. cor
  81. c04
  82. Unde jam patet non esse nobis satis incognitatum
  83. en aesde dre faghed ( de 2ohe de
  84. a 1 de... 113225d...
  85. 1 d ersge . . .
  86. a chie. . Atgd arghie e
  87. +g. d 19...
  88. Fd’e cut d
  89. de2
  90. 2de
  91. + ar
  92. +H. 7g de- tp9a
  93. es pta. et de 7 s’a
  94. sed in ea omnes incognitae ded -p3
  95. evarescunt
  96. 35gde + pg’ ea + 45 a B si esset dpe. vel sulter si esset DY e
  97. 39 f de + pf da + gg a3
  98. Unde novissima aequatio:
  99. fiet f9 y =P qa unde
  100. ge2f + g’e +2p9 e a 9 tatrf
  101. sive - ge 94 + ge (2p aq 4+ ar gat
  102. jam faciendo erit aet
  103. +yh de
  104. Adee
  105. gide
  106. 2753
  107. a fier. a 9a4 9a V - 2 p a6q 4 ar 28
  108. Sed supest adhic una equatio 8gas- d 2
  109. = N dre
  110. pons jam emines terminios aequationis, cubiae
  111. datae esse affirmativos quod semper fieri potest
  112. habebimus desideratum
  113. e oe aieits
  114. A
  115. alter.
  116. fl.v. Hrce p)
  117. nneren

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 126v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0252?run=74