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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 39r

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. videamus an formula generalis secundi gradus uniue indeterminatae quadrato
  2. ut sit
  3. aequari possit. Ver Nempe fxx + agX + aah =, a yy. fiat y= a qu (= h + aa)
  4. 2V
  5. et fie F SXX + agX + aah = ae avvth + a c + Lah, v vel fxX + ag+ = avotih + aa - d aat
  6. qua
  7. quo
  8. vel fxx + agx 3 = a qu (+Dh + a4) fiat X = 4 tr ( vh
  9. 1
  10. v
  11. a
  12. 2a
  13. jaa
  14. quu
  15. 1V
  16. ). Et ex aeg. 3 siet
  17. valores aequando fiet frrvoh frra = aorh - a + 20grv. Hic habetur
  18. 2V
  19. aa+ ia
  20. solutio si h sit quadratus, faciendo frroph - fHa = 0 nam fiet v0 = a h, et
  21. avvh -a: 4 + 2a9v = Y Habetur et solutio si f sit quadratus,
  22. faciendo frrvuh = aveh seu rr = ae: f et frra frra- a;: + 2agr = v
  23. Idem aliter. si fsit quadratus fiat frrae= a et frrvh = aevh + 22gr, seu v
  24. +agr
  25. aE- srrk
  26. vel si hsit quadatue fiat ( avvh - a6 = 0 et Erveh - fra = = 2ag, seu r- + 2ae9v
  27. af. frphi
  28. sed si nenter, fh sit quadratus videndum an non res procedere possit faciendo f quadiatum
  29. quo casu et = Fih eut quadratus (nam = fh: th = - f. h). fut ergo fh = ee et eerr DV = a, seu
  30. ero =ae, suoust R+ fra afrr tahWV = + aega: e, se parr+ aah. f) vv- t dg:
  31. H h. f = - ee: tih ergo fit aarr Qua -(eetiti) WB = + 24g: ef, sed ita explicandoter
  32. fint aa (a: ee) = (ee iht) aa v f 2a6gv0: aef. sed hoc solutu difficilius
  33. XX + a X + aagu = a yy - aah + aa 9). Ergo
  34. 43
  35. 4fau
  36. quadu
  37. 4afyy- 4aath + augg ilet esse
  38. delet ponatur esse 0 et res succedet si 4aa fh- gg,: 4af sit quadratus
  39. sit data formula inZZ + agq + aa anZ + aap aequanda quadhato fiat Z - qx tar,: a
  40. fiet mgqXX + 2mgarX + m aarr ~ fxx + agx + aat. Ergo
  41. da
  42. aa
  43. nqx
  44. a
  45. nar C 4a mguse (merinartaap)- aqu (2onqu + n 4)
  46. aa
  47. + aap Ergo
  48. na
  49. Aamgq
  50. debet esse quadratus e
  51. sid in hoc valore quadrati H, evanescit q et Y, et ila frustra ad hibuta est haec transformatio
  52. quid si facissemus - qu tar,: x
  53. e firiet + in gq XX + Emgarx + maarr) fint
  54. lada
  55. an E Xx aX
  56. + a ap XX
  57. (
  58. 4a maarr (mqus tanguaax) aqu (2mar +a nY)
  59. 4mqq anquaaep
  60. dd. Xx sed et sic destmitur r, et in numeritore
  61. cvanescit etiam 9, sed nominator redit ad
  62. formutam datam
  63. quid ergo si faciamus Z = q + ar, :, X + 5-f huore
  64. ratorem substituamus in mZz + anz + aap seu m00 + an OD + aap DD,: VV
  65. m gq XX + 2 m agr X + aarr
  66. an que + an 95X + anars l: qu (X+5,
  67. an arX
  68. +aa XX + 2 aap sx
  69. aap 1)
  70. Et numerator est
  71. aafxx + agX + ah
  72. aequandus qto
  73. Ergo 4a C mgue tangt aapsma atr Fararst aax ) - a qu (em aqu F angs Fanar + raaps) = L F
  74. 2
  75. 1) Aa
  76. W
  77. Aa (mgus + anq + aap), qu (Lf)
  78. damgumaam + 4amqus anani tamque aapss (t 4a angmaatr) Gnganars qaagnu aaps igap naeistaris su
  79. Aan
  80. a cmmanii ( aqm agran qu at Magragar, aamagrraaps - a aannqu ss 2a anussanar( quanquuapt aanar
  81. et fiet
  82. qu anarar
  83. +am +aempgus) + 2ann qus + aemprr ga impqus aungus aennir = H
  84. 4a (mqq + an 7 + aap)
  85. in numeratore semper simul sunt 95 fcit
  86. sed nondum hinc apparet aupilium
  87. er q) = aK
  88. poteststoni
  89. 920

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 39r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0077?run=73