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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 16r

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: 0.72.

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. 15v); this page is its right half.

The machine reads it as

  1. ss
  2. seq
  3. 6h 1 46+ 12)
  4. Esto pp1. et 9n 10, et +-
  5. et ++ fi -. et 1+ p
  6. fiet V poi 2- 20- 100 1ini
  7. F4 =2- 40+61 732
  8. qura +g 12t semper veru est si p. 1. et +
  9. quantitas major binario; se cunda ergo ut ver succedai necesse
  10. sive 24 1e4 1292 49
  11. 1412
  12. 18 p 14
  13. 130 ep7 11 28
  14. cet (7 (t) ponendo +
  15. Aliter resumta aequatine ponamus r P
  16. et V 1 et +, et + F p + f 9. fiet equatio
  17. p. p) - aul + V. 2lp4. P∞ + + 1p4 (2p 7) + apuq- 1q m oprt po
  18. ligo + P
  19. 1+9- 1+7+
  20. +41+1
  21. 1C1)7)
  22. 14 -2p + + 1p al- 19
  23. + 4l3 + pp + +pgl +6pC
  24. 1 + p 12 1 + rp 4 2pgl + + Vqe
  25. 414 + + 2p l + apq1 +6p 12
  26. et S7 P, = t.
  27. Sr essiu -. et
  28. 51 2. Ergo 2 149+ 497 - 49- 69 + 41 4 ab B es a ex
  29. illude v
  30. 7ath + 10l +P xe videamque au tres conditions
  31. et ex
  32. 1 +9.
  33. atee
  34. 41 fop multiplic
  35. V do pe aintem, fiet. V + ta + +1Y
  36. ac Y) e t + Cx.
  37. P
  38. P+1 = + P
  39. Xex,
  40. Ergo X - aba ac, est . e. x - p (t C Ct) - Cx) 4. Y + p- p1
  41. sive X. ab - ac p C v - C p - 2 CX.
  42. ex ex pi at. qua ab. quantidas affirmativa
  43. Ergo C p Y exp, aC = CX. Ergo e p + 2Cx p ac
  44. ev p e p + 2ex l
  45. c ++ ex p 0.
  46. p
  47. Habeluus ergo tres aequationes determinatucesq a tribus silicet
  48. numeris quibus utimur nempe: CP + ex A Ct. ++1
  49. es
  50. C F + ex p. 0. et e
  51. p CF + 2exH
  52. 1 + P + 2
  53. pro et in prima substituatur ejus valor ex secunda) Eo B fr- Bp. 1B
  54. fier er p + ex B 0 = Cx. ergo C F + 2ex pio H(HLS . s + + L. Poratur
  55. pror ex, substituatur = A 2F,. seu Sp2p..
  56. Ergo vel Ep H 2CX vel 2CX 10.
  57. in Aequatione 3tia et fiet + D F ) V
  58. ejus valor inventus, fret: nempe B= e p ergo pro CV pC P + 2CX poms (4 aio
  59. ua
  60. 110. quod cum
  61. per se ipsa quantitate constet, quia omnia quadrata sunt affirmativa
  62. H e p + 2 ex. omilti, cum
  63. ideo potest posteria extis e
  64. sua sponte
  65. itm g p et en F
  66. C p + 28X p0. sequatur
  67. + B +1. fiet:
  68. 2+B + - B (+) (FP+t Fb
  69. Pmamus
  70. eno a p
  71. Rem ergo eo reduximus ut necesse sit vel ep p X sive p LD) B
  72. vel X p0
  73. Quare si tantum X 1 0. omnibus conditionibus
  74. est satis factum affirmative
  75. ergo C P B+ Ex po- ex
  76. et fier PH i C
  77. Nam si X po. erit etiam p 2CXpO. Fiat Pp D ex ut exaral
  78. Erralum est hic in eo quod conditiones (tem affinuntivam a
  79. diversasive aequationes diversas inter sejungi
  80. d+ Ex et d et LitXYD
  81. .
  82. 2e P+27X+
  83. ergo eX V - X +β. Ego p Y- 1 . p p + ((DD
  84. ergo e est quantitas affirmaliva. Ergo ep
  85. e + ex P + + e
  86. Ego oE
  87. t= + + + g P) pro H) sin
  88. p + 2x
  89. + 2x pP+ B.
  90. 2e0
  91. 1+ PD + +9 +C
  92. s
  93. (11 14 pr 1 4 + X F
  94. IIs
  95. sine etip attolem
  96. 2.
  97. Ego (Y e (+) 2 B Sp2 18 + 1d ael 2 41. - 2 +2
  98. et pC PV 2rP p
  99. ~H ()
  100. V + + 9
  101. 2+4+β-B
  102. aemus vatorem ipsius 4. nempe
  103. 114 + C - 1
  104. rc tppl- p L
  105. Aliter.
  106. ++2
  107. 7+1
  108. viBit
  109. pel- p
  110. +2
  111. fiet eividendo per
  112. et p fiat p et
  113. si apparent tesse quantita
  114. a ( n esptien
  115. et fiei Aequatio
  116. 1en + p
  117. unde fit:
  118. reeit
  119. D NB. Poneut
  120. scilicet (+) (D
  121. Ergo V seu v2t
  122. l a)b
  123. a aV VE

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 16r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0031?run=74