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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 52r

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: 0.78.

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. 53v); this page is its right half.

The machine reads it as

  1. quaeritur extractio Radicis quad inticae ex gytab, yytac, sit
  2. sit y = 1D+ seffict yy = 4619D + 20 10D, et yy+ ab, in yytac, b dabit
  3. 4, qu 0+ 5) +40D + 4 (9, D) 40. quod extrahibile reddendum est, quod multiplicatur per EG
  4. si faciamus e=_ constanti, et extrahendum identificemus quadrato a + 4 +0D, fiet
  5. +
  6. (b+C) (O+ D + bc + 2 (b+C)
  7. 1.. e al aa
  8. e fi
  9. = q = 2a (0 + D) + a Cbtc): 9 sit 0+D =X et btC = c et liet t rax + aC
  10. Aa
  11. cuper est qu (9+7) + (b+C) (et D) + 4 C. B + bc = aa YG +9905, vel reductis bumbus ad X,
  12. fiet aa XX + aa PX + 497 + bc = 4 a XX + 4 ex + ex +990 seu
  13. a Xx + CX et + Aqb. N=(DD= osa co)nn + seo iuaqu n naaeu identificando fit
  14. 10. ua
  15. Ex X fint quuto (00 = 10) aa seu 112 00 ie t _ =9 seu 10 L = do ra 1).
  16. aa
  17. qquiaa
  18. seu aasju - qua) XX + aa (99 - 4 na) ex + aabcqque = (99- 4 aa) 99 0) + a ee
  19. aa XX + aa ex + elD bc 9q - aaee pa = qqD et exeplicando B8, ciet
  20. 99- 4aa
  21. 910 (00 -18)XX 100 10) B1 ax = u. uaa
  22. . 1.
  23. a F ex X fiet 1199 A e eto et ex X fit 11. May = bi 99 - aaée
  24. 00- 2.10
  25. Eggo
  26. 4aa-99
  27. Ergo 1. 1 9t = a e = bc 99- aaee qq quos duos valores aequando, fiet:
  28. ca- 19
  29. 00 - 4. 00. 10 +. 4. 10. 10
  30. loo ta ee ( a ee qu) = 00 bc 00 a ee 40o 10be ∞t, 4 00.10 a eeque + 4. 10 vbeg. 2udaeg
  31. seu qu(qu (00 -2. 10) bc g + 4. 10 (00- 10) ad eequs = +00 a ee
  32. 00volaa, quem valorem substituendo in aequatione novissima
  33. fiet qu (00 - 210) bc gt + 4. 00. 00 e) = (2. 00 a ec) et fiet 00 = 2. 10 seu 10 =
  34. ae
  35. superest ex X, a 49= 10 (00- 10)
  36. et 00 -10 = 1 et 10 (00 - 10) = = et 49 = 4aa, sed ita 0. B 1199 = 90. 2,10 fieret
  37. ae = 0 siu C = -b_ - b. sed hinc ob n. n44 = bc 9q- aa ee, :, 4aa - 99, fieret et beg4 -0
  38. Haec via ergo exitum non habet, iqq sane si successisset
  39. etim nume rationalis extractio saltem quoad variantes ex yytab, gytac
  40. identifictnas
  41. quod non licet.
  42. Itaque quod supra extrahibile facere volueramus aequemus quadrato a 91aq+ r sD
  43. haberi potuisset, neglecto scilicet 8
  44. et fiet qV quod est 990G + rY DG + 297910D fiet G. Q-2aa ( ) raax aa e
  45. et XX + ex +4OD + bc = AQ (49O+ n5) = qqq (o rua) raax 1 a= ) + H( (ex 16) X ua )
  46. 10. (9q W) (t 2XX + 2. 1 a X + 11aC)
  47. 30do
  48. qu.
  49. 0ve
  50. +aa) sentqrXX + qr ex F bCqr
  51. Ex Xifiet
  52. +49r 0B.1o XX +toB. 11 agrX 11. 1Iaa gr
  53. -99r. 10. 10 Xx =8. 1B. I agrX
  54. + 10mC X
  55. +_ (BB. raaXy + 00 ruVer) 00
  56. 4700. 00 grC + (rr. 99) vo. 10 C = 00. 00 rrase
  57. 2 (yq- rr) 40 a 400 agr + 8. 10 aqY
  58. Plali
  59. 00 (99. 1r) ae)
  60. Ep X fit g. p. 1 aagu + (9. rr ) aeit = 00. 0b bc gV. sou 1. + oocqpor tae. 11 + qu ( quaqu.
  61. 4ua qu
  62. = 4 qu (00(99- rr) ae 0o bc q seu 11 + 00sq9 - 1r) ae = L-
  63. ouqgae- vorracrquoa
  64. Diagr
  65. Gaa 1Y
  66. Jon (q’anee _ 2. evogr ee + orrt aa ex L 4. cro dabc g9rr).
  67. Aaa q1
  68. 4 aagr
  69. Ex 8 est 10. 10 -+ 2. (9. 1) - 4gr + qu (14 11 - 2 1) 99- 1r - Zgr.) + 1699rr)
  70. = 90
  71. daaqus
  72. Y(4 q F r1 _ 299ur = 493 r + 4 9r7 + 4 qqur . 69gri) YY - 44+ 24
  73. ex
  74. si esset e = 0, fieret 11 =0 dbc : a et c, 49 - 12, : qr = 2 s00 - 2. 10) seu 10 - q
  75. seu 10 =
  76. 00squs - oorr et 10 = 2.0 qr vo qu 00, 29r + rr - 94, : 49r
  77. compendii causa sit q9. rr- at. et 00.
  78. et qu
  79. = 2at. 10, 05 -00. 00: 2
  80. Ex X fit o 00. 00 gr + 497. 00. 10 - 49r. 12 1010-
  81. seu X 00. 00 gr 42 (291 - at) 10 = 4 gr 10.10 = 0 seu 00. 00 gr + 2. 10. 10 gr = 4. 10109
  82. seu 10 = Y(1.2) = 29r + rr - 99, : gr. seu re + (2 N(1. 2)) qY + (4 -YC. l. 2)
  83. 10 - 2gr = a t, : Tgr
  84. H 2) qu
  85. et fiet Y = L qt (∞ 15 - 4 d -2) -. Z q C2 Y - XY + 2 sit 2 - + ( 2) = Bi a et fiet . 2
  86. sit gq. rr = dat, fie
  87. Yr + (P: a) rq al epi aa) - d 1( (na 4 BB + 1, 49 - BB + 2aaq fiet rt P g - q B+ 4aa) seu
  88. eB aaa = taa = l - 2 1) + raa
  89. 4a
  90. si P =0 erit ex X + 19) e = bb = Q (990 + 1r) =(10X F ua( 99- Wr) + vOrr X, 2a2 X, quia B - 2 aa x et C = 10 x tua et D2 1
  91. nec riq (β 42) a β,: 2a
  92. Si e = 0 = bac sit c = - b et bc = - bb et 1 = b 1. 1
  93. = (1. Haa. unde XX = 10 (00- 10) XX +400, 8. 10. 1. ax 1 =- 4. 11. 10
  94. tooaar xex
  95. tut sed nuitus ex X, lit 60: 00 gr + 4 100. 10 gr - 4. 10. 10 4r = (2. 00. B aD + 2. 00. b0 rY, et fit ov. 00 (gr. 211) = 4. 10. 10 - 8.10. 10 41
  96. =4. 10 = 00. at: qr. seu 10 = 2. 00 gr - 00 a t,: 4 qu, sed munjus reex x fit
  97. =a. 10. 10 qr = 00. 00 Cqr. 2n) seu 1. = 00. r
  98. Gorr 2 agrt + aaH:: 1649 rr seu 89Y - 499 ur -a 0ssr - 40 r + 49 12 4 + P- 299r1
  99. e
  100. 41 +
  101. 00. 10 a
  102. + 1 = 0
  103. 46r 47 + = 12 99t b
  104. seu OD - 10 (00 - 10)XX +(00 - 10) 11AX = 10. H a
  105. tur sii -erb: a) sE 1. 2) etipris
  106. aliaie conmittenat et i et . it a uterintut mnm at acripeesse
  107. is tum patullarum omprotendat etrae an letatie i doieis deis est putaria nels oam ateripaesse
  108. - b r -2 4
  109. 10.10 = 47 00. 00, 2rr - gr,: qr00. 00
  110. seu t + p - 1293r + 49r- 699 rr =0 seu Y

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 52r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0103?run=74