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

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: 0.82.

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. 209v); this page is its right half.

The machine reads it as

  1. Quod si jam adhuc alia sit aequatio velit 4ox + 4ax + 42 aax + 43aX + 44 redenat rursus
  2. binae aequationes, et t habetur duplex valor ipsius i1, fiet enim 11 = 10. 10. 12. 43 - 10. (2. 12. 41 = 1ro . B, 10 1. 21
  3. dividendo numcralores et noninatores per eo 1 sit V
  4. 10. 10. 44 = 12. 12. 40 102. 24 -132.20
  5. fit et firt. 10.10. 14 - 12. 12. 40 = 10. 10. 24 - 12. 12. 20 seu t16. 23. 94 = 10. 12.12. 27. 40. P. 1103. 2443 - 10. 10.12. 4. 41
  6. 10. 23- 12. 21 +123.21. 40 = 12. 10. 10. 21. 44 413. 20. 41 = 17. 12. 10. 20. 43
  7. scubatur deinde et aeqe, et aeq. 2, ad instar aequationis D, pro 10, 2, et, 29, 4 se ponendo 40, H, 1, +4.
  8. 10. 43 - 12. 41
  9. Habemus ergo aequationes adhic usuppandasD et 3, 7, et ad 6.. Et ope
  10. aequationis 4, caters simplicioris, habemus tollendo 12: 10 ex aeqq. D et 2 habemus
  11. binas aequationes quibus relatio exprimitur inter coefficientes bnarum aequationum divi-
  12. sed quid? nonne licbit pro aeq. N. assumere responden tem paris juris
  13. dudarum
  14. 12 20 1. 12. 11. 22 C10 10 12. 12. 10. 23 412. H. 1024
  15. 13.24 - 12. 12. 10. 22 + 12. 11. 10.23 +12. 10.10.24 =0 fiet 11. 11 = 123.28-10. 132224 10. 11. 12. 23716. 124
  16. 12, 10. 24
  17. + 12. H. H. 23 -
  18. = 11. 1I. 10. 24
  19. et rursus 11. 11 = 10. 29 - 10.12. 22 + 10. 11. 12. 21 + 10. 12. 20. Quos duos valores aequandi fiet
  20. ex N fit
  21. firt +10. 24 - 10, 12. 2224 (+ 13. 12. 20. 24
  22. =12. 20 +10. 13. 22.20 (= 10,15, 2024,
  23. seu 410. 24 q20. 24 -10. 12. 22 A0. 24
  24. -12. 20 5+1520
  25. 415. 24)
  26. et fiet qu h- 1. 205
  27. =13. 20
  28. +10. 12. 12. 10.23 = 11s
  29. 3. = 1. 10. 10. 24.21
  30. 1+ 12. 20. 23
  31. 1102.24 = 19. 12 7-10. 24. 21
  32. = 10.12. 22
  33. + 10. 12. 23
  34. + 12. 20. 23 = 11 = = 10. 12221
  35. 3: 10. 12Z - 10.24. 21
  36. +12. 20
  37. Vel explicite 118. 24 etc. et redibit aequatio H. 3
  38. +10. 12.27
  39. l- 10. 12. 21
  40. 410. 24
  41. absolvenda hic., aequaatio explicata
  42. absovendasres pro comprobatione
  43. Calculi
  44. 16427 25.24 = 10512. 22. 24 (3103.123 22. 20.24 - 10. 12. 20. 23 + 102 12. 20. 21. 22 = c
  45. +12.28
  46. Y- 18. 12.20.24 = 10.13. 22.20 (F103. 122, 22.20.24) - 15. 12. 24. 21 Y 102 12. 24. 21. 23
  47. +b. 28 u. . 24
  48. prosus ut ante. Itaque calculi possumus esse securi
  49. Xx+ ab, XX + aC = couadrato.
  50. sit X = Ga, fiet aa C O + ab DV, aa (B P + al V)
  51. quadrato se si b+c: e sit aa O + aubc V + e B0gD, quae
  52. formula debet habere quasdam ridices aequales
  53. corcipiatur, utae quatio x ab, exa ac
  54. Xx bb, XX - cC
  55. pro px + ab Xp + ac, ponatur potius XX - bb, XX - cC, et ponatur
  56. esse aequatio, ejas radices erunt X+b, X - b X+C, X-c, et
  57. sit X = 1a + naa: 20Z + 2a, erit una radix 10a Znaa + 20bZ + 21 ab
  58. seud 7 + aa +21 ab,:, 20d + + 1_4 = 0, et alia radix 17 + 1ac + a C , 20a + 24b
  59. quae duae si debeant esse in ratione data, fiet naa+ 2tab,: qa +2ob
  60. 2cbZ
  61. sea Z + na at C2, ab ixo +200
  62. v
  63. iaa +2
  64. = sit + 1ac Z + ua quarZ + 1aaY
  65. PaZ + uaa + 2007+21a67:, 20q +aa a
  66. 20 abZ+1 aV +20Y7 F 21aY
  67. et ficre t 10a F28 b = 10 ar + 20Cr seu X 10(aa = ar) = 20 (Cr - ab)
  68. similiter uaa = ar) = 2 u(Cr - ab) et ficret 10:20 = II: 21 quod non lices
  69. X = 10a77+ 1 a a Z + 126 O fiet X + b X +1, D = 10477 + nat + 12 a
  70. 10b
  71. a 2jabq 122aab
  72. et qu et X+C, D = 10aZZ + 11 a a Z + 12431 et ad huc duae
  73. 20ZZ + 21aZ +aa
  74. 20 _.
  75. et ac Z + 22 aaC
  76. coliae fomentae, ubi pro b ponitur Lb, et pro c ponitur = C
  77. vebent habere ies indices egotes tria paria radicum aequalium
  78. formura possum esse quadrati fieiet
  79. hae quatur formnle
  80. se prima et secunda
  81. 7)+ 114 4+ 21ab + 12a +2raab fre
  82. 10a 42b
  83. 10a + 20b) = Z ++
  84. firt. hrig= ann: app = fri seu nn = _ 4 ap et V. 1aa + 2 11 21 ab + 21. 2 bl. = 4 101ag tu o
  85. fit Il2 + 2b = 3 (10. 129a + 10. 22 7ab) - 21 b sed dem facendo inaJ. 2o.
  86. tic
  87. tC
  88. maais
  89. +21C, E b ponendo. C, iet 24 (+ Bl ) 2 + (aH . ad = 2((C + b)- ∞ ra
  90. 20. 22 bb F13(2. 2C
  91. si 40 c-36D diriene b et (D 2tdiatb
  92. -13.20
  93. rE. 20

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 210r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0415?run=74