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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, 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: 0.82.

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. 69r); this page is its left half.

The machine reads it as

  1. m h, 2a + 2ohaa L, er5B M
  2. ov + ua 2 = 20V + et a 5 = 30V + 3a O = 200V+ -01a D = 300v + 301 a
  3. a=motu Zica i mote
  4. axx + am = ) a, ga t 2130Y48
  5. axx + a = L a, Dat 3130 16.
  6. denique sit
  7. aX = Ex6sit aXx = 120. k2 + 2. 120 20 2 _t6. quo valore suesituto in aeq. 2. et itentificando
  8. fiet 112044 et explicardo sigao aequationum let notas aequanonum l2,3 , f denique
  9. F1120. 1020 vV + M2D. 1an X +MO u2Ia = 2. 1120. 1920. 20V L f 5 + 2. 120. 32021a 1ti6
  10. 13c6 coefficientes ipsius
  11. Ex aq.2 fint
  12. + 1310 50.20.
  13. 2150 1 30
  14. 110. 3a 2120 +1328. 312)aa CL C. c. 2
  15. ei (10)
  16. 200. aa vV +220120 + 20i
  17. ns+
  18. +2200. 2130 aV 1+8 +2. 201. 21 30aa 1t6
  19. Quam equationem faciendo idetitatem assumendo ut identitatem
  20. fiet ex identificatis terminis irrationalibus 200a = 1170. 1320. 20: 2130 et 2014 = 1120. 1320. 21 : 2130
  21. E+ ex tatorulibus 26 200 a + 213, 5. 10. 30 = 1125. 10. 20p re d. 30. 20 2 138. 11 31 A C E m = 1120 121 20 321
  22. 2. 200, 201 a+ 2130310. 31 = 1125. 1021 + 1328. 304.
  23. valores ex agq. 11 et 12 substituamus in aeg4. 13, 14, 15.
  24. Ex 13 fit 1120. 1320. 20 + 2135.10.30= 1120, 10. 20. 2130 + 1320. 30.20. 2138
  25. Exerfit. rureoast. at 1128. 132. 2s + 2135. 1. 37 4 aM. 2130 = 1120. 1. 21. 2307. 1326. 31. 21. 2130
  26. Ex 4 fit 1120. 1320. 27 + 2136. 11. 31 == 1128. 11. 21. 2138 + 1320. 31. 21. 2130
  27. +a n. 2130
  28. 2.1120.7396. 17 + 2130t. 10.31 1128. 102. 2130 + 132 8. 30. 21. 2130
  29. Ex his aequationibus inveniamus ante omnia, per valorem, abque tollamus 21302
  30. A Tollamus aut inveni
  31. aequantem Aequatio autem 16 habet hanc formam e CX b. 238 +, r. 1130 + d = 0. unde
  32. bb. 212 + b. 2130. C + bd = 0 seu bb. 2130 + b2130. C + CC = L CC = bd. seu - C + Si cc- bd
  33. olaq exari 15 fit 10. 30. 210 = L. Md n + smonio pe nimo esie ( 10. B1o. 10 50 20C
  34. aa 9 reapse procedit extractio.
  35. tam Hinc pari pire qui valor substituendus in ae49. 17. 18. TatecyHaem autam calculus eut pro
  36. 22.1320.3020 451310. 30. 20
  37. Jide m antem calculus est pro aequ. 8 praestanda tantum pro 2136, 200, 201, ponendo 3130. 300, 30)
  38. sed quia valor ipsius 2136, adeoque et ipsi reo et ipsius 201. differre debet a ralore ipsis 310E, quia alioboi m et
  39. coinciderent si eadem esset aeq. in qua a, (nempe aequ. 17) cum aeq. in qua erit aer; ideo ex duobus
  40. diversus valoribus ipss ipsuis 2130, unus erit pro squ. 17, altera alter pro alie simiti qe laequatione
  41. 2etiam 6q9. 17 et 14 destrimi possent, ut repressa est aequib calculus foret tanto facilior, sed facile
  42. conlinente a.
  43. sed nec pro aeq. 18 procedit extractio nam fiet
  44. 10. 31 2136 = = 1120. 10. 2 + L1320. 30. 21 + 41120. 10. 28
  45. B3ed Gay) + L. 126. 13 20. 1030 n1 21 - 2 NE6. 13E0. 10 2 j r 21
  46. n. 30 it unde patet non succedere extractionem, quae successiset si in aeq. 18 pro 2. 1120. 1310
  47. slin in aeq. 20. sit +∞ et fiet
  48. =ae 12o. 20.30 Et exta quale
  49. Et exoq u per nefiel (120) 1320. 21. 307 4 1126. 25. 11 31 = 112. 20. 112I. 30 + (112591326. 303127 20
  50. Eexaep.i8 per 2 fitt (~(iuo 13io (u 30 + i ro an u dio + (120) 1325 ud 20 30
  51. E2 est 1316 = g2S. , BI 30∞3a2 - 31 20 1. ~7 2. 20. 11. 20. 3, - 71. 30 + ae g. 2030,:, 2.30 B 20. 3) = 21. 50
  52. quos duos varlores 25 et2) inter
  53. 120. 10. 20. 51 - 21307:, 30. 20. 31 - 21. 30 seu, 1320= 128. 10: 30
  54. se aequando, fiet: 112O o I_202 10. 21 - 11.20= aa mm. 20)80: 21. 20. 31 - 21. 30
  55. Si in ag. 20 sit 4 . -. pro 313 , i 513 Ex 59. 20. transmusa ypio aann, fiet 3130 = 1320, 20:10. Undi ex aeg. 17
  56. Et ex 24 est 1328 2
  57. 1(2 aamm. 204 X. 20.31 - 21. 30, -20. 11 + 21. 10
  58. transuntasa fiet 120 (132C) c 2I. 10 + (1320)1320, 20. 1. 3F= 1128. 11. 21 (1320. 2010 + (1320) 31. 21. 1320. 20. 50
  59. 1126 Cpi r2d. (Eo 0 +710) qa 1320. Ed10
  60. a n(32r0.10
  61. Ex 3 est 112O 1328. 20. 31. 20.M - 21010 + à n 20. ju, : 921. 10. R20. 1 - 2110
  62. coincidilcum aeq. 27
  63. Efex ayifit 1120 = 2920. 30. 20. n- 1. 10; 10. 2011 - 2110 seu 1120= 1310. 30: 10 quae aequat
  64. adeoque (quod utile est) ad nullam novam determinationem dicit dicit aequand
  65. p 20 olo D_ (per 27).
  66. Caxnn 20. 10
  67. quando jam duos valores 33 et 35, fret 13202. 21. 30 -20. 3]
  68. per 1320) 20. a n _: XP. W 2011- 21. 10. =20314 2130. 2x29 et37 fit
  69. sed in sed inde fit mpmnn seu duo quaprata in idem recidunt, quod est contra intentum
  70. taque res non successit
  71. adeo depressionem Aequationis 17 non prucedere. ob intervenentem am. alioqui procederet extractio prosuntuau, it
  72. iuteum si etiam
  73. ae (12920. 30
  74. (suplez 12d. 193970. 20. 21
  75. seu fiet
  76. 20 1-2110

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 68v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0136?run=73