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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 29r

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: 0.85.

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. 30v); this page is its right half.

The machine reads it as

  1. OD in OE in 3( = 00DDG Esto ax = O D, aX = bb = 09 et aX - cc = DG
  2. erit productum ex his tribus ax, ax- bb, ax- cc aequale quadrato.
  3. Quia ax = OD erit OD - bb = O∞, seu _ = 1B - bb,: O Ergo O0D + bbD = ODD+c
  4. sit O =
  5. et 0D- cC = DG seu D =OD -CC3: D vel + 6OD - CDDa +bbD
  6. 207 + 12a
  7. et 2
  8. = 300 +40Z
  9. a
  10. 602+56a
  11. 602+sba
  12. Aoet +(3O D = 20. 20ZZ + 2. 20, 12 aZ + 12. 12aa, 30v + 40Z, +aa
  13. a
  14. Fiet o= -(9DD = 40. 4072 + 2. 40. 30 Zv 40. tovB, 12a + 20Z,=aa
  15. + bb D = 60. 6027 +2. 60.56aZ +5656aa, 30v + 40Z, + bl
  16. -cc0 = 60.6022 +2, 60.56 a7, + 56.56aa, 124 +20Z7 = cc
  17. in hac equatione destruamus terminos Z3 VZZ et aZZ, ut solum restet Z
  18. fundamentalis
  19. Habebimus tres aequationes destructitias
  20. O= 20. 20. 40 aa = 20. 40.40 aa + 60. 60.40 bb - 60. 60. 20Cc
  21. (1
  22. 0= 20. 20. 30aa - 320. 40. 30 aa + 60,60. 30 bb
  23. 2
  24. 02) 220. 40. 12 aa - 40. 40. 12a a + 2. 40. 56. 60 bb - 12. 60 60cC. 2, 20. 5bboe, aZZ
  25. Ex aequ. 1. fiet 60.60 (40bb -20CC) = 20. 40 aa (40 -20)
  26. 60. 60bb = 20 aa (2. 40 -20)
  27. 2.56.60 (40bb -20cC) = 12, 60 60cC +40. 40 4a - 2. 20.40aa
  28. 2
  29. Aequando binos valores ipsins 60. 60 ex agq. 1 et 2 firt 40 bb (40- 29 = (2. 40-20)b0bb- 20cc)
  30. 3
  31. seu (40. 40bb) (20.40bb) = (2340. 40bb +20. 20cC- 2. 40. 901c (20. 40b6)
  32. unde siet 40. 40 - 2. 40 20 eC + 20. 20Ct = 20. 20c- 20. 20 bbcc
  33. 62
  34. tandemque 40:20 = cc + C Y (cC - bb),: bb. compendi,
  35. causa HCC- bb) vocetur f, et fiet 40, 20 = c (C+): bb
  36. Et licebit facere 40 = c (c+Y) et 20 = bb. Et hos valores
  37. substituendo in aequ. 2, fiet 60. 60 = aa (2cc + 2Cf = bb) vel
  38. 60. 60 = aa, cc _ + ff + 2cf adeoque tandem 60 = + a (c + f)
  39. Superest aequatio tertia, in qua substituedi sunt valores numerorus
  40. Inventorum 20, 40, 60, supersuntque quaerendi 12 et 56. itaque ex eq. 3.
  41. fiee (onsidero autem quia 60 et 40, habent communem divisorem C+ f, posse
  42. inter explicandum aequationem 3, simul fieri hanc depressionem, et fiet
  43. 12. 56a bbc ( + 2. 56abCf ((2. 56 abb C0) = 12, aa C t aacf t ec aac +ccaaf. raalbc
  44. vel + scab 56 bb f = 12 a (a Cc - bb) =) aufs + a ef, et
  45. divisione facta per f, fiet tandem +56 bb = 12a (f+C). Unde fieri
  46. Quod si faceremus
  47. potest 12 = =bb et 56 = a (f + c) = 60.
  48. F esse + fieret ut 56 =60, ita 12 = 20, quod non licet nam fieret
  49. d: a = itaque debet esse = idem quod - et fiet 12 = - bb. Sed
  50. Hlabemas ergo valres intentos, prore nata setise simplices
  51. 20 dbc 122 - bb e se = a Cets) = 44 =C e
  52. sed ita fiet 60 = = a (c+ f) adeoque 60 = - 50
  53. Et ex
  54. sed ita fit e=-
  55. si omissa divulsione consem u ratirem 40: 25 seu fiassemus 40= 20, ce tcf b9
  56. a fint bb Z - bba
  57. ZSolba f)
  58. videamus an itam eadem difficultas occurrat, et ex atr et ex 2 fiet 60. 60b ea
  59. -569 = 5ba
  60. 2.X 20g onoa - 28. 20 A2. 20. 20 (CC + fod:bb) seu 60. 60bb: 20 20ap =
  61. bb - bb + 2cc + 2c. f, seu cA H + 2tf et +60. b, 20 a = c + f et 60 = Za, C+F: bb
  62. CC = 12, aa cccest aacc fstraacces tec ccaace + ccaqet rceaaet
  63. Hos valaes o et 60, substituam in cer. 3. eoanescet in ex 20, et fiet
  64. Se sbt = 12, 2 au C raa aace (a- bb7 =) 2aacff+ Laiff + (2.a a CC= bb) est
  65. 25oabbC
  66. sbacbbi Hets
  67. urau
  68. pato
  69. etragus cs
  70. aees doseets us adt nast in P ti t ena
  71. l constanti
  72. b
  73. Aquod nescio
  74. au liceat.
  75. Quorsi

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 29r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0057?run=74