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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 58r

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: 0.75.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 57v); this page is its right half.

The machine reads it as

  1. si omissa hypothesi quae aequationem tuctabilibrem reddere conati sumus, cogitemus de m: hfficiendi ut
  2. etiam 50 fiat 0, seu ut V exteminetur ex valore ipsius X, (.) et relaquendo v in vilore
  3. ipsius D, evitando tantum us fiat 20: 60 = 12:56, alioqui C firet consans; cipi sane hoc modo
  4. ita incipiemus ab aequatione fecunda per quam detem
  5. minabitur relatio inter 40 et 20, et ex aeq. 2. firt 20. 20 - 2. 20. 40, aa = 60. 60 ab = 60 169βB
  6. Unde fit 60.60β3+ 20. 20aa = (. 2040 a a seu 20. 20aa - 2. 2040aa + 40 40aa = 40. 4ua a 608
  7. seu 20= 40 = 1(40. 40+a - 60. soβ3) Tubi posito 20 = 40 firret 40a = 60β = 20a
  8. Et posset feri 20 = 40 = Et posset fieri 60 = a et 20 = β = 40. d video hoc non + licere nam ob
  9. Valorem ipsius 60. 60. hac aequatione repertum, substituamus in aequ. 1
  10. (40. 40 B(3(= 20,403(3) - (2)40. 403β (- 20. β() - 2. 20. 477 + 20 20y. ende tandem, fiet
  11. digmeni inter q
  12. 1oV, sequalisminao
  13. 2. 40. 20)B ir. 20do)(
  14. seu 40 - 20γ. β = 2(207: B8) (V . BB)
  15. seu 40 = 40 :20 = VC VBCt + y (V BB): BB
  16. ita pro d sumetur quae est major. ponamus 20 = ββ:)
  17. et, 2.qu 20 foret 2() + 2 (W - BB) PB, : 7 sed
  18. hinc deveret posse extrodicadi ut 60 fieret rationalis
  19. ho non ficta duulsione aeliquamus ronem 40 = 20) GStiss
  20. sia o bo B B A 2. 40 -20 = 20 ( 1)= ws B et = BC)) -1
  21. n casuparceu an
  22. 28+ 92 + 89 = 3 8
  23. Et ficiendo 60 = 20) fiet s) 2 = 2) (B + sC 1Y - pB) =
  24. ut quod videtur coremedissimum D = na aa BB
  25. fier 20 (V ((t SY. 18)- 1 eto 0 a:
  26. Tentem, aliquid amplius nempe videamus an liccat
  27. fucere simul 50= et 5b =0 quil aa ita extribus
  28. agrationibus 1, 2, 3, poteriuus invenire non
  29. sulum 6020, sad vitasse etiam vatorem
  30. ipsius a quiest adhuc ratitiar. Et 2c 60 opus
  31. Ex aequa, un 50= sit eo ol- 9 - 3
  32. 60. 60 ab = 20a4 (20 -240) Cx aeg. 2. ubi 5
  33. 690 aC = 40 a4 (40 -2. 20) ex s p. 3
  34. fi jam ab = -BB et ac = - 7)
  35. 20Y (20 - 2. 40) = 405β (40 -2. 20) Uende het
  36. X -2. 25. 40 βB
  37. 20.20)) = 2. 20. 40)7 = 40. 40 B 1 . - B3(2
  38. seu 20. 20)7 -40. 40 ββ-= 2. 20.40
  39. siu Z =g (3 + 1)
  40. et 5 = 215E:, 8-5
  41. 30 = E, 25, 5. 4: 3 - 125. 81 3) = 100.
  42. 2.4020): βB + 20267 (20 10
  43. fint 40 = β+ (9X (() Etato lo torete
  44. a W co -88t 5 y fit 30 = 2, 4 E
  45. 2H et 99- 55, H X
  46. guE, t218
  47. ee
  48. aequifieret b =c
  49. 3t 75. S1. SGA 3 Z, qu ( +5)
  50. sin 3
  51. fint 60. 60 = (20) 40 (10 - 20) aa ; quBβ - 2077 = (20(a, 240 - 20, :BB unde tandem fiet
  52. Er, qu ts) .00
  53. magnem in caleudo stragem dabimus.
  54. I= YH. nstace t 1. (rad Pa r fudi
  55. B 2. 10. 40 + 4040 = 2
  56. et 2ond 82 2040 (7) () +gosatulY. PC)
  57. seu 20 207) 1 2020)
  58. se prastat abstiere ab hypulles
  59. =4090+ 40. 4e qu (pr - 16)
  60. = 40,40, ( + t + 1 a sip eV
  61. et 20 20 =2.40 = 40 ( V- BBYB):
  62. 2e - H(VE 1Y)) + 277
  63. 20. 20 B-. 1 L. 20. 40 V BC + 40. deq u Y. A(B) = 40. u q u (B7. 11) 1 40. 4088 =
  64. 1 = 40 1(+ - Vee
  65. preniter fici t 50 =d
  66. - B2 + s ( 4 yiBB 68)
  67. 38. 71 + e. 1
  68. 1-γ1) = 2020 qu (8P. 17) = 20 2e p. (2. 7)) + 2020Y
  69. quaesissemus prodisset calculus talisa
  70. duc holop tin 40 = 20 BB = 20 rya- CY + () ber 1
  71. il fit sCB. pppy + G 4) = 2 s X eB a0 ∞B - no BP+ 20)) Ll7o)1. ros 1 190
  72. 40. 10 P1. 40. 29 (B
  73. fit ev. 40 ββ - 20. 40 ββ +20. 40 6) = 20. 20)7 - 20. 4017) +20.40 BB
  74. pV LY+ seri, Besto. (B. (Y B in 40. 40 (B - 2. 20, 40β3(3 = 20. 20γ7 - 2. 20. 40)) out ante.
  75. . qap
  76. =(1 ay. 2) 20 aa (2 40 - 20): B( = (ex a9. 3) quaa (2. 40. 40): . Ex (est (40. 10 20. 40 B(
  77. nunc etiam aequationem cum 2da vel tertia conjungamus. Ex
  78. a y H ed CC Y = (2, 40. 40 (353 4291207Y 20. 40 (3 - 2. 20. 40)). Er ex 1 et 3tio valorefer
  79. 2. 20. 403β3= (2) 20. 20)) - 40. 40β( ( 20. 40)) ita quas duas aecpation
  80. (6. 40Y) 20 20 uninagendo sit
  81. icafem ien fieret BB = V)
  82. pncrione ipsins 50. sa ex
  83. 1e 60
  84. c:
  85. baa (40020) ; (B = 20Y, et ceq. 40. 40 BB + 10. 1) 1 7
  86. 59 et c6 simal destracre
  87. r.
  88. e
  89. i
  90. 12 = 2, 25, 5. 3, : 4 = 125. 3: 2 = 325
  91. (1 20.46+40. 40a 460. 20)
  92. =2. 125) sungsia eq. ds o est
  93. aJ. 2. 50b0 7 2o) Hari jure si 2
  94. Rpostet esem 160(oe XV)
  95. Af Sni
  96. fia gf da +Bac + na vY

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 58r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0115?run=74