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Leibniz-Handschriften zur Mathematik LH 35, 5, 17, fol. 2v

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. 1r); this page is its left half.

The machine reads it as

  1. XN yy a1
  2. Sidendum an res sic probari possit. d x
  3. ax + 2XaC + coa y + 3y A + 3yM N.
  4. Exa
  5. 2 aa + 357
  6. auferantur hinc ax, illinc yt, aequalia ex natum curvae, item hinc 2xaco, hinc
  7. ByA, ex constructione, erunt oa GA t N
  8. onfido at eadem Es in dupli 9y. ergo
  9. et 3y)
  10. 904
  11. de
  12. + n 4Xad i
  13. Jann ce p 39 + 1.
  14. 3y + s Ergo 91
  15. exae a
  16. P L. seu 393 p 4 Xa ut 31 p 3X a. Ergo 3N a p4 X a,
  17. quod est absurdum.
  18. V Sumamus aliud exemplum sit natura curvae: aX p y fiet:
  19. a X 3a XC) + 3aXC+ cSF (y) 4575) + 10y A + 10y N +7 A+ A
  20. du
  21. et (x)y - 2XyB 3x(Y)e anferendo hina 3ao, illine a X, illinc ex nalica carvae, atem hinc 3ax c0, illinc
  22. seu 2()y+ x9, 3Ny) AGA ex constructione restabit 10A quia
  23. Ergo X A(7)
  24. 1D R2X43
  25. B 10V
  26. seu 595
  27. DH 53t Bet Co
  28. a v3ax
  29. 9a+ 3aXF a Co 9ar 3aXrao. C
  30. et = 3aex p seu 3a 3X + coA, 6a73
  31. 3aX 5y+ p
  32. 1) Erg. 3X+ Cd seu + co p. + 1xa
  33. 4) Eui
  34. Sed nondno
  35. est
  36. et
  37. f o r
  38. 3aer taeco
  39. p 1 + 1 x5 y5
  41. y pa
  42. ) Ergo co A Y B V quod est abferdum Ergo coly B A
  43. hoc satisfacit.
  44. Generale hoc Lemma. demonstrandum est:
  45. innumerae aliae imposibi Si duae potentiae ut diversi utcunque gradus, a duobus binomiis utcunque
  46. citates poterunt ex tamentibus diversis , du babeat habeant a duos altissimos
  47. duci et forte omnes propositiones terminos mus pominis unius potentiae, aequales duobus altissimis terminis
  48. impossibiles ex tangentibus
  49. habent orrginem suam itaque auus nominis alterius potentiae
  50. si general Terista ad tangentes) proximo:
  51. sapplicemus, generales sane mirus
  52. aequationum imposibilium
  53. formas dababin t
  54. 346, 2cd
  55. a +bp C+d
  56. ast
  57. es
  58. Ergo
  59. a+2ab +b
  60. inquam, id est
  61. cimis
  62. altissimum altissamo, proximum
  63. ipsas potentias aequatet esse impossibile est.
  64. a +4 ab16ab , aab b
  65. si a⊓ C ent a cpa
  66. C+ 2cd + d
  67. C+ gcdred + d3t
  68. + 4d 16Cd 1 4c8 + b+
  69. 4 ero apa
  70. atb p AC3d. cueu
  71. ego a p a embgem sit
  72. si a thaeb+habtb erudisus 84
  73. a a (2, b (2
  74. eut c+ d ea +b +A cuo et et jam a
  75. Ergo ap 3bC nmiB ate c+d7 a+ b +f.
  76. axtis: 3 ergo A+C+d A+ B+ a de b+fC
  77. entm
  78. 4C ergurum . C. pp C Bl
  79. co tmodura B C.. 4ab rcd s = a bp ac d) en de sta am 12 cid
  80. a +b c+d.
  81. voa + 4a bpC Ctdumm
  82. ae ccond,
  83. Ergofiet: ad a
  84. a x H
  85. a n
  86. a Es
  87. eon.t id st oduissis S aequalibus
  88. estb
  89. Ergor C++ b pi a Xa
  90. coadAZbC Satis video thcoremats de istrationm analytice
  91. Ruisu coiza
  92. quaerundam, idque procedendo didine, x
  93. 1a Ergo Ergo Analytica idemonstratio per calculum, ad
  94. sive 27 ad
  95. v 1 BC
  96. EB seu 27 b.
  97. Est autem
  98. EpV. Ergo Cp a
  99. et c+d p arb.
  100. a C. Ergu v t d H C +. b. Ergo dp b
  101. Videndum ergo, quomodo ad hanc
  102. a3 + ab x ia b, 1 +C + d C+ ad a adribB a. cad b, e
  103. Cporb M, C N 381 13
  104. decuoastrationem
  105. novum denique nos ducet theorema, et ita non dubitem ad simplicissimam demonstrandi
  106. rationem, nos denique perventuros.
  107. redibit aequatio pinst.
  108. Ergo +d+ 1b
  109. Eogo d . seu cd p ab. at ad pbc
  110. neua Eergo cd + ad H ab tubc.
  111. ciar a.
  112. c
  113. tictandem
  114. puliterime
  115. jam yye ax
  116. seu (Dyr X).
  117. no nuter
  118. seu fiet a ) P. E. d.
  119. co
  120. a tt
  121. Hy - 2X3p a(r) B xy ram ay. 6) X51 aB
  122. Ergofiet 3XYI
  123. imutatione hulus
  124. inventa
  125. 3yp A
  126. v (X) - X 4y
  127. Ergo (X) - X - 5 2
  128. ergo
  129. va atidem
  130. b7) a ccon

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 17, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068035:0004?run=73