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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 64r

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: 0.81.

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The machine reads it as

  1. via pro diresenteis per radics formularum
  2. in A sit = S, Xtay X+b :9, X+ C, X+C. sit X -gV+ l, :+n et per
  3. t
  4. DC FB X+ a = gv + hV 1 am: YEm. = at. Y uneu:, hV + m azoribus=
  5. Et. er ubi si duo ex lis possent aequari
  6. ph. cmts gV + C
  7. et y= Seit Y + anc ib anY B, V + 1
  8. pes esset in vado. vn sed video rem non esse possiblem ponamque essem
  9. 24+ qch = g + atr seu
  10. et q + qc m = l’+am
  11. T+ ah V + l’Fani 9, g+ch Y + V + im. sit
  12. g2 9+ ah: stch, l+ am: (+Cm
  13. 41
  14. fiet: 1) + abB+ cgm H achm = (91+ chi + agtr + Cac tm) fietque
  15. 9: h = l: mm. ed ita X
  16. procurare liael expari causa
  17. e
  18. L1
  19. G:h = A C- aH: c= a Mm unde seu
  20. ntra interende nec ex traribilitatem
  21. Eadem methodo altiqus: X = 11 B + RV + 13, 20v + 21V + 22. fietque
  22. sit jam:
  23. + 1
  24. 2: 20V + 21V +2
  25. non est constans.
  26. 1 - 20 a VV L (2- 21 a V + (3 - 224 = 9, 11 - 20b∞V + 12, 2IbV + 13 - 216
  27. 177
  28. +1 YV L
  29. X +a = -20a
  30. fiet q 1 - 20 api, 11 - 20b = 12 - 21 a, : 12 - 21 b, = 13 - 22a, : 13-22b
  31. 61
  32. seu (11. 12) = 1. 21B = 12. 20+ (10. 71 aB = (11. 12) - 11. 21 a = 12, 20b. f 20. 21. ab)
  33. et fit 11. 2C =. 11. 21 a - b 12. 20 a - b, seu 11. 21 = 12. 20 et pari jure
  34. exoqe. 17. sitet 1 2 = seu 11. 20 = 12: 21 et pari jure ex eq er fiet
  35. et pari juve ex aeq. 17 fiet 13. 22 = 12: 21 quibus substitutis in
  36. valore capius XC X aeqliore 2. set X HV.
  37. fB 1220: 21 VB + 12V + 12. 22: 21,: 20vv + 21V + 22
  38. tinc sed pari junc etiam fiet concidet reb. quus factae numeraloris
  39. cum relisfactoren aequabuntur duo factoret nonnaloris
  40. c
  41. Xe
  42. ans factor nomnaldeis alteri in artitariam Y, (ol supra
  43. ducta aquantur et fet p seu X 12nO∞B+ 12. 21V + 12. 22
  44. 20. 21 YV + 21, 21V + 21 22
  45. sed in fie X 12 et e ex 1Y 16 931 12 - 21a;, 12- 2b
  46. 21
  47. et quia eodem modo connesa sponte sua ex positis ob parita
  48. tem juris instar equationit 14 aequattur facto res. nomu.
  49. 16 raloris unus per alium diorsus relinquit Y loco g. ita ut
  50. fiet
  51. x = 12. 20VP + 12. 21 P+ 12. 2 =
  52. 20. 21W + 2. 2VF 2. 22 2
  53. sit Y = 12 - 21C,: 12-21C. Itaque caeteris omnbus existentions
  54. et et
  55. ubi tano 12
  56. extahicilibus santum q:Y aequatus est sub radice
  57. fit g: Y = S12 - 21a, 12 - 218: 12 - 21b, 12 -2)C
  58. et 21 = 40v + 41 e
  59. 20
  60. (27)
  61. quam 21. explicanto per V, ficret 12 = 31V + 32
  62. 122 -2. 21 a + 21. 21 aC = et 43, V + 2. 31. 32 V + 32. 32
  63. ta 40V+ 40. 41 V + 11. 41ac
  64. are 31. +0 - ate 31. 41 V - are 32. 41
  65. 12 - 21a, 1-2IC
  66. au
  67. et, si volumue tollere YD fec 31.31. + + aC - a Fr. 31. 40 20
  68. sed pulo tiustra in haec in quiri cum explicatio ipsius 12 et 21 per V scunde
  69. BC. 40V
  70. et sim part 31. 31 + 40 aC - R+ C. 31. 40 =0
  71. Non ergo aportet adhibere aeq. 1f et aequare
  72. integros factores quadalicos, sed tantum redtere 20r condirisibiles, parique jure in
  73. uit possit dare novi
  74. nominatore, et facere demunc unum tactorem, numeratoris condivisibilem uni fa-
  75. alis
  76. vide cmus Ergo an is- 204 vV
  77. + 1 -21a V = 13- 224 et p - 2cb v∞ + 12 = 21b V + 13 - 22b sit condivisibiles, per compendium
  78. rori nominatoris. Et ita haberetur venressio.
  79. si 30∞V +31 V + 3E5 condivisib, cum 400v + 41V +42 sit SC 13042 +39. 31.45 - 30. 31. 41. 42
  80. C
  81. 0
  82. 31. 31. 40. 41
  83. AV. 46 31. 40. 42 bis 30.92. 4042
  84. sitatis alibi inventa, vel etiam 32. 30. 4 - 31. 402-3150. 41 - 31 40, 30. 92 3L40103 n X)
  85. n ubi si unum gotum ingrdientium comprehensivorum sit 20. erit et alteruu tentemus unum sit
  86. per theoremata condioisib
  87. 31 =(- 20a. (Z - 21 b = 1 = 20b. 12 - 21a = 11. 12 = 11. 21 b - +2. 20 + 20.2 ab - 11. 12 + 11. 21 a f 12. 20b - 20. 21 ab -
  88. = 11. 21 - 12. 20. a - b = 30. 41 = 21. 40 et 30. 42- 32. 40 = 11 = 20a5 13 - 29b, 1 = 206. 13- 32a = 11. (2- 1122b
  89. Loa + 20. 22ab - 1. 13 4 11. 22. a + 13, 20b = 20. 21 ab = 11. 22 - 13. 20. a - b. Ergo hac cx54. 17 diusa per a b
  90. het O = 13- 22a, f111. 21 - 12. 20 4 17 - 21a . 11. 2] - 12. 20. 15. 22. p 13. 20 f 1- 20a F(11. 22- 13. 2
  91. substicuamus c et A in ag. c∞ et in non fnatore Herent esset condivisibilitas, renique
  92. similiter si pro a et b
  93. si in aeq. 18 pro a et b substi.
  94. habebitur qdivisibilitas in numeratore et nominat re adeo hic
  95. ubstituamus a C a et E simul concurrent
  96. aes
  97. u e souma

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 64r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0127?run=73