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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 122v

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. 121r); this page is its left half.

The machine reads it as

  1. Tres numeri inventi sunt al.
  2. al - X
  3. in
  4. usa
  5. al = X
  6. rCX X
  7. +C
  8. quadralum primi, a l. quodrul Ergo al Na- ralX + X quadrato
  9. ito
  10. secundi, pro W po Wl, pons 1 (e
  11. x
  12. 1487 (4, 4d X+
  13. 4 df
  14. none
  15. seu - 1212
  16. et 2a lX + X+
  17. et ponendo Wl 1. X - dl fiet - W 2(2
  18. r
  19. iase
  20. - 2alX +X
  21. X7 - 2dlX + al modo scilicet
  22. quod sedulo notandum est, et habebinius idque
  23. ostendam fieu posse erit enim 2d (X +e X + d
  24. 30eo- fl3 ergo X - ol 5 Sd f (3, cujus possibilitasermanifesta,
  25. quia f pro arbitrio assumi potest. quare si differentia inter X et d, p
  26. minor esit quam d, seu si si X minor dupla dl,. seu X 52dl.
  27. Hinc jam aequati fiet:- 2d CX +d (
  28. _. 1 d1
  29. Fal +2dF
  30. vel ponendo X d , e + N 2al 2al + 2dl
  31. Et quaeritur Ratix ex 2al + 2dl, Ergo
  32. eritque
  33. Ego 2al + 2dI ( _ v et erit d B v - 2al, eritue
  34. X e
  35. v0 - 2al
  36. ax
  37. . Quadratum
  38. Ergo Terminus secundus est al
  39. ita
  40. + al V
  41. +v
  42. 2C
  43. secundi est ergo est a
  44. 4au2
  45. et quadratum ejus
  46. aQuadratum termini tertii est s ut habeamus pro Z adhibearus loco
  47. asat
  48. 16c a l
  49. =8C alX-gal valoris ejus inventi, fietque
  50. a(2
  51. opo
  52. =a l + 2atX + 2alZ +2427 ~ 94
  53. 5) X + 2flX + s et differentia quad ratorum termini secundi et tertui
  54. L
  55. entque tal +-
  56. 2(M)
  57. fiet t al = yV
  58. ( XfX + ( (ponendoque
  59. E
  60. +
  61. + 29Z, ponendo + D + hZ. perit GY Z + AY
  62. L
  63. dil a
  64. L + 2dhl Z + h 1
  65. vyr
  66. dl 102 4(2
  67. v4
  68. erit +2alZ1 + 29V X
  69. L SI W=
  70. 17
  71. t
  72. eridque
  73. u
  74. L e
  75. q + hl et g, erit
  76. d + do 2l
  77. I2
  78. Z, HAZ, eutue
  79. 1 1 est itd non hab ut sed ita d vix habebitur sine fracte ne,
  80. ergo suiditate; Ergo potius ponamus al-
  81. se contnet n.. sic ergo
  82. =h umo non succedit, quia g. in
  83. rectius effidemus ut h eva- 2
  84. evanesent, faciendo 2 al ye q - fX = p qtfX 2f al, et
  85. pionendo
  86. X 1 5 + f
  87. sive f
  88. z2
  89. X pu va ral
  90. pone
  91. 2 V
  92. fiet y
  93. e
  94. 2 N +f∞ 2al, sive f
  95. 45 et X ( 5 + Z X 2al. et supra
  96. fiet 8V7 16 als p(65 V + 2vZ aV al
  97. S( 2V + L, fiet 16 et _ ponentoque prBy e ponendo BV W ponendo scilice tp Z
  98. et pro 5) ponendo v + L pro W 2 P +4, pet 8v +8rt cb 7.. 8r Fvr 18r
  99. 6p 15
  100. jatum ponennde Y H 3
  101. at, pone set Y +al, fiet al, t 22 al
  102. ces pone s Z 2al + vel. ponendoque
  103. + dl fiet f
  104. et
  105. 5
  106. S 1 = 24 +292 - 9, et pro -g, ponendo = Z- 2hZ - h
  107. fiet al - qu
  108. H - Z2
  109. aesu
  110. h
  111. vet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 122v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0246?run=74