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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 2r

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: 0.86.

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The machine reads it as

  1. et differentia
  2. Invenire tres numeros tales, ut summa duorum quorumlibet
  3. Siequ aste sit quadratus.
  4. sint numen X, y, Z.
  5. 5s
  6. Xry = aa X+ Z bb ytZ = cC. X. y = U X Z= mm y. Z- n
  7. Ex c et 4 fit 2X = aa + H m bb + um et hy = aa - U = ce + nn et 2Z = bb - mm= cc- n
  8. Ex solis aequationibus 1,2, 3 haberi potent 2X = aa + bb - cc 29 = aa - bb + cc 2Z= - aa + bb +cC
  9. Ex solis aequationibus 4, 5, 6, nullius extribus literis X, y, Z, valor sine interventa alterius ex ipsismet haberi poest
  10. sed loco ultima aequatione tollendo literas x et y, evanescit Z, et fit I1 + nn tum
  11. quem vaborem ipsius rum, substicuendo in aeq. 7 et 9. tunc ex aeq. 7. fit nn aq - bb
  12. et ex aeq. 9. fit U = bb - cC quod si ope aequationum 14 et 15 velis tollere bb, fit I1 + nn aa- cc
  13. quae aequatio coincidit cum aeq. g. quod est signum calculi probi. Itaque sufficinsit ad problema
  14. solvendim sifficiunt aequationes 13, 14, 15.
  15. pro aq. 4. scribamus 3 5G44
  16. 6.5. 6.5 = 4A. 8:5. 8:5 ut calculum in numeris supposititiis comprobure possimus.
  17. pro 5q. 4 fiat Et ta pro a, b, n stabit 574, 3 prob, c, tstibit 4, 815, 6i5
  18. jam pro 14 solvenda generaliter finit: 5+ 4 (16)
  19. (17)
  20. pro solvenda aequatione 14 fiat a + b = dde et a - b = dec fiet
  21. a dde + dec,: L et b = dde- dee: 2
  22. 27
  23. similiter pro solvenda
  24. aequatione 15 fiat b+ c C Hg et b - c = f9g. Ergo b = s9 + f9g,: 2 et c ffg- fgg. 2
  25. (24)C
  26. Et aequando 19, 22 fit: dd e - dec = fg + f99
  27. sit de =hfg
  28. et fiet eutnque valorem ipsius de substituendo in aeg. 24. fit et provenientem
  29. aequationem dividendo, fiet: hd = he = f +g. Ergo ex aeq. 25 et 26
  30. fit d = hfg: C 5+g + he,: h seu hh fg ef + eg+ hee; sive
  31. f = e9 + hee,: hhg - e. Cum ergo ex 14, 16, 17 sit n = de
  32. et ex 15, 20, 21 sit l f9. Hinc jam solutas habemus in numeris
  33. aequatiores 14 et 15, restatque solum solvenda aeq. B. operae pretium autem
  34. erit solutionem aequationum 14 et 15 prius exequi, in venta sunt aequationes
  35. h9g +hhge: hhg- e
  36. substiegendo valorem f in d, ft ex 29 et 27. fit
  37. et n = h egg + hheeg,: thg - e
  38. et l= e99 + heeg,: chihg - e
  39. et 2a = hegg + hhg; hhg - e h gg + hkge: hhg- e,, + e
  40. seura = et2) hgg + hh ge+ hgg + hhge, lihg - e, ee, 1 F. htg-e
  41. Cc hgg + hnge, hhg-c, ee,, X et Shg C
  42. E aC
  43. et 2b = (9 12) e9 + hee, + eg + hee, hhg - e, d9∞. M htig- e,
  44. = a eg + hee, hhg- e, g9, W (2I, hhg-e,
  45. et 2b. - eH Eh03 + hahC.
  46. Et si bonus est calculus debent duo valores ipsius b coincidere, sunt autem nominatores iidem ergo
  47. et 2C = ( d 1 eg+ hee,
  48. coimidere ad huc debent numeratores: et siet C si gt + (eet93(hC Hg’ ee ( )
  49. unol
  50. + he39 + hhgC = (eC9+ (2) h e 9 si et g L etitg + hE9 e (C g e h9)
  51. Jeaque evolvendo omnia, fiet
  52. 16)CCh.9t +3 (2) C hg3 9e n’g e0+ (h g e heg - h’get,: () hhg- e,
  53. quae atque quae duo revera coincidunt.
  54. 35)
  55. 2b = Ch g + ek393 + h0g + h9e,: 1 bhg - e
  56. 2a =
  57. 2CZ 2ee 93 + (3) he g + h Ct g - ek g - h3ge + e gehg: 1) chhg-e,
  58. Habemus ergo aequationes quaesitos valores literarum a, b, C, l, n, pro per aequa
  59. tiones 35,3637, 33, 34. pro solvendis aequationibus 14. 15. idque quasi
  60. semma considerari potest, seu problema subsidiarium in principali
  61. sit h = 2, et g = 1, et c = 1 fiet
  62. 2a = 4 + 24 + 32 - 2 - 4,: 1 4 - 1, seu a = 27:9 = 3. et 2b = 4 +8 + 2+ 4;9 seu b = 1
  63. problemate nostro intercurrens.
  64. n = 5: 3. l= 1
  65. sit h = 2. et g - 1 et C = 1. (per 29) fi et f = 1 et (per 27) 1 = 2
  66. et 2 = 2+6 + 4 - 4 - 8,: 9 seu c = 0
  67. a
  68. 31) 1=1
  69. et (per 19 vel 22) b = 1
  70. et (per 30) n = 2
  71. et (per 23) C20
  72. et (per 18) a = 3 etsar cysibet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0003?run=74