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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 68v

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. 67r); this page is its left half.

The machine reads it as

  1. Ex aeq. 9 datur LM = NP. Ergo hoec aequatio sepanatur
  2. ponamns K = 0 tentandi brevioris calculi causa. Ergo ex aeq. 8. fiet S= - L fingum 1 - 8 L. E+ m
  3. imgo ex aq. 10 fiet
  4. 2a bcC 2 + 2 a 22
  5. ae hon eu tanchno + rachi p + raach RR
  6. -2a cts =qualt b n 42 - 2aabfi mn L
  7. ta
  8. ut follaltur L et Q, fint acc : b = bfll: aa se acc = bbfll, seu lI = a c bbf
  9. 0
  10. et m =0
  11. Ergo sit R = ep _f- . sed haec video postea nonlicere, quia ita LM et Np haberentur
  12. per mera in Z
  13. si tollatur geosen fiat aecc =bbfll, et ponatur reliqua aequalio extrahibulius, fiet
  14. tiatque
  15. 243L ab lfm g - 2a abtum G +RR7 et volia delemus esse extrahibile aequadem
  16. raact
  17. 2aach
  18. aubfr bfrum = 2R Vaac blsm
  19. hy aeq. 10 fiet (+2ab 24
  20. ahq
  21. =ra ac aXE)
  22. si
  23. - 2 acbs ll 42
  24. pi T= E ff L) R
  25. -4 abf.L n Q - rasibtum = 2aa cF h R)
  26. et fie et extractio per se procedet, fietque Abf. L.9+ m = cR Y.
  27. seu R fB+C F: h), L2+m
  28. Hic pro (contandis imaginaris, si b sit negatura prioieva, erit 3 posituva
  29. et si b sit privativa, eut fetiam prvaliva. Vicissim si, b sit positua, erit h privatua,
  30. at si b sit positiva eut f etium positiva. Itaque h et f habent signa autraria
  31. superest aeg. 11. in qua Ntiam K = 0 fiet
  32. R. 5) l 8 + 2 a h a b (.3
  33. afH 2
  34. RG l (a 3)
  35. -2af a m
  36. agbe
  37. an
  38. ah F bb (
  39. +Ed min 2
  40. =af mn qG
  41. Ex 2. sisi p. aaut. Aegebit, P, due
  42. b alicm - facch +Llbgl, L3: hac
  43. mosi, poaesrum a i erta
  44. + 6 agbb f I mns Z + a a g btst n Q + a
  45. ah ax
  46. Habenque ut luc extrahibilitatem efficiamus, habemus b L, et m
  47. da
  48. ace
  49. celia
  50. Si dastionemus 23, fieat H- (4 c5,: reg9bb: cehu C (1Z uetras ce haaf: 2 gffob. seu l-
  51. Hic toli sensu h et u hatebunt signa eadem
  52. aa
  53. b
  54. ec 49
  55. Pestesta
  56. les
  57. 29bb
  58. destmanus jam et 9 fiet cca - 7 f hcc + 9 fibb hh f -o ita evanescit ec, et deberet
  59. 2966
  60. in datis esse a = th + q fk seu 4a9 = 3th seu g = 3th: 4a
  61. b0
  62. itaque haec via non est permissid, sed sine destructione, tentetur an formula possit fieri
  63. reu trahibilis compendio sit, 10. 10 Z + 00. 1 aR + 00. 00. 12 aa 9q. + 903 13439 + 00. 14. 14 a
  64. un puoce aeq. fit hic gg 10. v. ni Z 14. 14 : 13: 13 Cs = 10. 10: 11. 11, fiet
  65. abgfm.
  66. att
  67. obilit aech
  68. dyb isfllm: Cttiaa
  69. seu acch
  70. bb fBumm
  71. ag bbstm =gu. gbb m al stl m es biclll
  72. acth- aThbbcell-aafh bb cell + gb Cna Bcchat
  73. ccta
  74. ahflam CC i affurm, a th + b g9 1 L 2a ab b ccghill 3: aBth et
  75. Ve- L = a th - 2a bb cct u + b Zgl
  76. atrae, aCh - 2a bbcc fII + (912
  77. 9. 14
  78. s esse A =P
  79. 16f a cthh - 2albbCC gn+ (2 g9 H
  80. +EC B. RR A2L = qu, be L. e
  81. gRR
  82. Moacoporeet u e
  83. norem LM, et valorem
  84. are icurant sico
  85. seu Y aacC, aa 2+ + abig R3 + atia 2ERR = bbcu qu CL M Xp)
  86. Hic statiu sucederet ex tractio, si esset 2a ahg: ) = abcr atiq. 5) seu att +a an (Hrg) iffiet taaahus: G = aahit trggui
  87. ser + agf = hf +hgg + 25gh, seu A = 4agf: fs +99 + 2fa, quo casu succederet extracdio, et fieret
  88. R((+) ag:, 9) vidiamus an hoc effici possit
  89. indatis, sit ad fa:Woid + aB, fiat W = A V, et siet apX VB + a5,:
  90. pa et fiet
  91. a
  92. LM - Np, _ 6+bb: q = a QZ A R AR ((9:f
  93. et divident nominatore vel mulspliando finctionem per _: aa) fint as_ + ad, ∞0 + ad
  94. ates pubi sim n ai ats e
  95. +
  96. qu, ropt
  97. R- q+ p

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 68v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0136?run=74