Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 705 · Overbeck, fol. 123r

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: 0.78.

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The machine reads it as

  1. Ppropositum est resolvere tres Aequationes
  2. ayy Z X + aX
  3. X2 f2+90 + ha
  4. b +cD, + ea
  5. sus Conditionibus a) Ut Valores X d y. non aequentur meris constantibus valoribus
  6. a
  7. sed ut in Aequatione eara maneat unus valor Variabilis Z. vel v. delambo
  8. (2) Ut v. non assurgat ultra unam dimensionem
  9. (3) ut sit b =0 = e ad calculi prolixi tatem contrahendam
  10. (4) Ut sit m = p, d f = h. nam hoc quoque calculo videtur oportunum
  11. Per Condit: 3. scribemus a=f tg0 + ha g-nt + nv + pa
  12. D
  13. Per Condit. 4. Scribemgs: fZ + gn + fa = X
  14. Ha faciendo Z+ a = WV. fit Wf +g2 = X
  15. V
  16. a
  17. Z-xEt nr+ pa
  18. y =Wo tno Ex hus emergit
  19. e
  20. X-q
  21. Conditio quinta ut H. non sit divisibile per v. (qroto emergente invariabilique no
  22. Nam si hoc fieret pone W = qu. fieret lquf + gu - x e qup +nv. v
  23. a
  24. quo Casu tam W. seu Z. quam ipsu v. evanesc et in calculo, contra Conditione
  25. his positis erit ax -Wf+g a. - vnf +C0g 3
  26. ayy= W eo +2Wonvcv +n vcD 3
  27. P - W f + 3N F gu + 3Wfg v+ G u 3 Et resumendo primam aequationem omisso communi Multipsi
  28. cante à e communi Denominatore cy
  29. c3V
  30. 303
  31. fit N f +3Nfgu + 3W fgv +9v + ev f + ergu, = W p on +2Nonver + nv cB
  32. Et destruetis Valor Membris quae v vel v habent propter Conditionem secundan
  33. fiet W. f +3N FgV = W p eV. d totum dividendo per W fit WF = pc0 - fqv.
  34. Sed hoc parto W= p CD f9 contra Conditionem, quintam
  35. S
  36. Sic enim N = p c- f9 quod est invariabile
  37. Desictamus primo a quarta Conditione sic tamen ut maneat m = f quou adssatio iabit
  38. Ab una ergo primarum quatuon Conditionum desistendum est
  39. sit ergo p= dm, e h = lf. Scribemus f2+g0 + lfa = X et Z- PZ Anot o
  40. e
  41. cv.
  42. Veru, si denuo hic ponamus Z + la = H totus calculus redibit in priorem indolem
  43. atque idem incommodum contra conditionem quintam enascetur,
  44. Nihil ergo supere se video nisi ut a Conditione tertia desistendo Valores quoque b. d e.
  45. X
  46. a
  47. PorVicarios
  48. Pro pleno Calculo
  49. qu + (fZ+ ha)
  50. ev + ( ea)
  51. V: a = C: d.
  52. X: a = W: d
  53. y nD + (m2 + pa)
  54. a Co +bZ+ ea.
  55. y= Za x= Fa
  56. Sit pervicarios
  57. nD + (mZ+ pa) G
  58. qu + (fZ + ha) = VI
  59. ev + (bX + ea) =d.
  60. agy = 8 a aar = L a X’ = a
  61. Erit Aequ. . misso comuni Multipl: ae Falis: P: dd = p. d + Y: d.
  62. et Multips. totum per d fit = + 4 sd. Hucusque licari)
  63. 13- g’ v + 39v (f2+ ha) +39u (fZ + ha) + (fZ + ha)3
  64. (4d = d uv +2dnv (mZ + pa) + d(mZ + pa)
  65. seu d- nu cot rvo (Bt ea) + Enven (mtpa) +2 Vno (B2tea) (m E + pa) + CB (m Et pa) Abeted (n Z+ pa)
  66. dd = Ev + 2cV (bR + ea) + bx + ea) 2
  67. Vdd = ergo + Ct (RRtha) + EcV gu (6(tea) + 2 V (Ehad bt ea) +gu (btea) + Aetha) (l tea)
  68. Ergo per Aequ. 8 ita ut Vicarii d. P d. aboleantur
  69. nveo tren (btea) tenveo (mttpa) teno (bst ea) (m Z + pa) + CB (mEta + (atea (n Z + pa) princus Valor aequationis
  70. =gu +39y2 (f2tha)
  71. +2
  72. +39B ((f2 + ha)2
  73. etha).
  74. +evgo. +eo (FEtha) prergs betea) teco (fEtha) betea + gu (62t ea) + f thasxtea).
  75. Pro destruendo v: fit enn g + gc Bec) = g (9 Set a = d
  76. dac m= fi2
  77. pel2
  78. Pro desruendo v ponatur nvbt n vea +EnvenmZ + Enveopa = 3gn fZ + 39V ha +fZ+ d vha +2ogu b pes
  79. Unde seorsim destruendo vr. fit nbc +nea +2ncpa = 39ha + eha + +rcgea A h - . e a
  80. Seorsim destruendo zor fit bun +2 cmn 3 fgg + fec +2cgb.
  81. an L2K
  82. +XCqe
  83. C ad 2C9- I fCc: ro m
  84. Propter Aequ. 5. 6ponendum, enn t2cen = 3hgg + hec +rcge seu = = f = h nda se
  85. Ergo sit e - lb. p- ln, h = lf.
  86. bnntremn
  87. 3fgg +fcc +Ecgo
  88. Et post destructos valores V3 prZ ov. jam sumantur reliqui
  89. m
  90. ne harmonia turbetur
  91. ainv(betea (m Z+ pa) tCn (m Z+ pa) +(be (m E + pa) = ZCD (FZ +ha) (bZ + ea) +3g0 (fZ+ ha) + go (6 ) Af Et had) Hfet hass
  92. sumo e- lb. p. = im. h - lF) fit 2nB. (6E+ lba) (n Hlma) + Cv (nd Alma E,b + 1ba (in Z Alma) - 2CD (fEAIfa) b Etba) 13gu(fE + ( a) L go b alba) eff Ex(fa) At ilfa
  93. Et sumendo Z+ la = W) fit Envirmul + cowrunt birmur. = 2cvb +3gufan +, qu bbrir+ fanir
  94. dividendoque omnia per WV W) fit 2mnust cv + bmW. = 2cbvC+ 3g0f + 9vbb + f31. + fN bb.
  95. Facit W = 2mnob + comm -3grff -2c b0f. - gubb
  96. quod iterum est contra quintam Conditionem.
  97. f3+ fbb + bum
  98. Itaque probasse me puto, ne retentis quidem b. aut e. ullam hypothesin designari posse
  99. be
  100. y ( mZ +no + pa
  101. b2+ cv tea.
  102. Mrobu3
  103. s

Cite

LBr. 705 · Overbeck, fol. 123r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-861255:0245?run=74