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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 210v

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: 0.80.

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. 209r); this page is its left half.

The machine reads it as

  1. biL
  2. c ac aac, seu compendio
  3. 302Z+ 314Z + 32 aa, et A0ZZ + 41 aZ +42 aa debent habere divisorem
  4. communem, A30. 402Z+ 31. 40aZ + 32. quaa. Ent hic divisor communis
  5. frat (- 30.4077) = 30. 41 a Z = 30. 42aa
  6. 30. 2Z +31 aZ +32 aa sividendus per 131. 4047 + 32. 40a
  7. 1+ 11 4b3 F3 2qua
  8. - 39. 41 2 -30. 42a
  9. 3072+ 31aZ +32 ad
  10. +31.407 +32.40a
  11. =30: 41 = = 30. 42a
  12. sed brevius b Z
  13. fiet Dandem 32le
  14. 30. 41Z - 30. 42 a
  15. + 36. 31. G1 - 31. 31. 40 (. 30. 32. 40 + 30.30. 42 a
  16. qu (31.40 - 30. 41
  17. (30. 31. 41 - ete) (32. 40- 30. 42)
  18. qu (31. 40 -30. 41)
  19. sn qu. (31. 40 = 30. 41) 3E (30. 31. 91 - etc) (32. 40 - 30. 42)
  20. + 3t aZ + 32aa, fit 2h+ 3 aZ + 31 11 aa = 31. 31 - 4. 30. 31, aa
  21. y L E 4 - C31 = (31.31 = 4. 30. 32 a
  22. 41 + + (41. 41 - 4. 40. 37)
  23. En his radieibus una alteri hebet e
  24. sunt binae radices prioris formule
  25. sunt binae radices posterioris
  26. 39 = 10a 20 et 31 = naa. vabay na
  27. fiet 11. 11 a = 2. 1. 21 a b + 21. 31 Jaabb = 4. 10. p2a + 10. 22ab 20. 2raab b
  28. 114a = 21 ab = - 2. 21b + 2( (tagi praeceo fin. Q habetur B) + 42 20ab
  29. et 21 = 210 - 216,: bAc et hic 10 21ab - bEB 4 b (1C - se
  30. eta firi 4 bb S + G - 216G = 4. 10. 12 - 4. 10. 229( + 4. 20. 22 abb
  31. sengo. 12 aol 0. 22 aclb. F 410. t2 aabbt 10. 2t abb abb 186 -..
  32. 4.20. 22 bCbb. 12. 20
  33. 42022 bbbb a12. 20
  34. - 41220.9a
  35. sedb Haec ubi tamen rursus adhuc quadrare; necesse erit, quod paulo prolixins
  36. sed in casu praesenti speciali rem breavius consequemur
  37. 4 st D- -
  38. Z et O. = 2 et b+C = , fiet b +c = cub -C = t
  39. 214( 8F 2r aff + 162 2 = 0 et 21. 51 - Bt 2 2f + 16th = 16 16b t - 1622
  40. seu 2. 21 f.= At +at (ab + 4 (tB 22)
  41. ergo tk. 27 = AOD pe fit 21 21f =, d +2 D + 2 15
  42. Pt 21 9+ t = 10 spersunt jam binae formulae
  43. quaquae deberent habere communem divissrem
  44. sirahatur ab alterafit nova formula 2
  45. 0 + 3) + +00 60
  46. +10a Z3 + inlaZ + 12 a, onZZ + naa Z + 12a
  47. -20b7+ =216Z = 22ab 630c2Z= uacz Fu2MC
  48. que +arae Z 20873+ 21
  49. eigdem divisorem debet habere cum altentra priorum
  50. debet etidem habere dvisorem cum altentra pross
  51. Ergo omisso eta
  52. dividendot fit (10. ) 410(a: (Z ua . 6) aZ + 12 (a: 6) aa. Habelmu ugo fret fommalest ex orima
  53. =2022 =2147
  54. secundafit +10A: L)LL
  55. = 22aa 11 diviendoper C 420 y
  56. +28 a2 T23 aa
  57. quas cnvicem addendo prodibit 10CZZ + 1C aZ + 22 aa e, et considerando formulas
  58. EC t aequaliones fit 1027 + 1aZ + 22aa, formula quarta. Ergo si a binae pria
  59. ced plinabae habent digisorem communem Etiam 1022 binae posteriones
  60. in a IZZ + Uaz f2raa, et 20Z2+ uiaz +. naa didissiem commupen
  61. a5 1e harebunt contra hypothesin. Ergo non licet efficere, ut binae ex formalis
  62. et eut unae binae ex formulis quatuor, quae prodeunt ex X + b, Xb XtC, XuC
  63. habeant livisorem communem. poperest ergo ut quaeramus an tres ex his formulis possint
  64. aaquan quadratis. duas jam aequabimus et habuimus valores. it et 21, aequemus et tertiam
  65. e= de alet velu rioa, 2Z + unqZ + n~,, et fet na=
  66. 214b2 = 22a a
  67. 20. 22bb 12. 28. seu nab224 2b - 28- 2b,
  68. E sit et fit b9 + C - b2 -c4 = (210 - 2b16 et fit (C- D) 10 seu 2 = Y4 ~41: ) L supra 2G. 2C,
  69. 20, 2266 - 12. 20 ac
  70. 4 = 10. 12 aa = 10. 2 al.
  71. 20. 22 bb = 12. 20 ab
  72. (b+927-268
  73. sit bic = h irt et b b+c = c.
  74. anQ + ec 4 b08 + 2H 192 = +bb 8 et h94 7 e24 + ahhec 9q hiet
  75. es e
  76. sit Au (hhQ = ect AAOV∞ (htQ teC H)
  77. V tis htr 9- ee
  78. hns ioces = rbor.ebB bcel abgu
  79. sed th e (bbr cdB= 4bc
  80. 28 + C4 = 2b15
  81. Catilbrec btra euborces sa nbe (ribest bbitca) ( vorce V_2b. BBrBV) - 2etorus sabeC
  82. Aal 10. 12a
  83. abe +
  84. bc p . o rabi ur , teicer B. b) a rabbC
  85. sit 2 = +)
  86. 0. 22 bb F1. 2
  87. am dt
  88. et hho = eeq = abb, a ion
  89. 11. 8) aZ T1a) aa

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 210v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0416?run=74