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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 14r

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: 0.83.

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The machine reads it as

  1. aequala data 100 + 110y + 101 dy 1120 yy + 111 ydy = 0
  2. Assumatur pP + 9do + r =o faciendo v = myus + ny, et fiet
  3. pv + q. Lo + Y = n r + npy + mpyys
  4. 100t + 110ty + 120 +yy + 149)+
  5. ser y. fit r = 100t. Per ydy fit q = 11t: 2m Et per dy fit q = 101t: n
  6. quos duos valores aequando fit 1IF: 2m = 101 t: n seu 1In = 2. 101m et n = 2. 101M : 111
  7. Ob y fit np + gdn = 10t et quia q= mt 2m fiet 1o1t:n, fiet nnp + 101F dn = 1o tn
  8. seu t = nup:, non = 101 dn et ob yy fit mp + qdm = 120 F _ et quia g = 111 t: 2m, fiet
  9. 2mmp + in tdm = 2 120t m et t = 2mmp:, 2. 120m = W am et duos ipsius t valore,
  10. quem valorem ex priore valore factum aequando posterion, fiet evanescet mn
  11. feliciter et fiet 2. IO(3m - 2. 101 m dβ = 2. 101 βdm = 2. 120 (3β, - 11I ( (3 am,
  12. et fiet 120 ββ + 101 dβ - 110 (3, i, 111 BB = 2. 101 β = d m: 2 m
  13. sit data aequatio no + tordus + regy. Et habetur M
  14. sit aequatio data -aD Xxdx + gydx + bg cydu = aadus = , et fiet
  15. (3= = ∞ Aa ~C et 100 = XX dx et 110 = o et 101 = - aa et 120 = dX et 11 = c
  16. ) Z)C (- dx 10
  17. etfm im) = 4 sC qg (4. 3C) X + f. a ubi omnia puanescunt. Ergo fiat 12O = C1 (cta
  18. sit aequatio data Xx ak +GB 12O gy ax + cydu - aadus = 0 fint B 2aa c ut ante
  19. Geraliter . dB constans, fiest
  20. amt : 2m = 120, A a dx , F 12Oβ( 178. 4, 10L +I d X :, AI. T. 101. 10t = 2. 161. 2. 101. 111
  21. et dm:m = 120. A dx:, C 14 2( aa) (daq 1ED
  22. 120 BB 120 (4. 101 101 : 111. 11) + 101. 2 d (11: 11) = 10. 2 (101: 11), 4. 101 (101 : 111) = 2. 101 (2. 101 : 111)
  23. et fiet Lm: 2m 120. dx: 11. 0, quod non procedit
  24. fit ax dan: 2m = 120 fit sed ita et m et am evanescit, nec
  25. cm: 2m =
  26. obtinetur quaesitum, nisi in casu speciali, quem praestare in arbitr, non est
  27. Ex aeq. vata est dy = 100 + 110y + 1209y ; 101 + 1y = (ex quaesita Y+ n p y+ mpyy qutrquis
  28. fiet 100gn + 110gn y = 120gn yy
  29. qany +gamjus
  30. ~ 101Y + 101 n. py + 1oimp gy t
  31. +1019dn y + 101 gdim gy
  32. FiIr y + 11 n B yy + nc mp y
  33. 11 9dm..
  34. 1119 dn 7y
  35. Rursus ex gy fit P = (101 - 1) gdm = 111gan, :, (1 - 101) M = M1N, et evanescit q quando
  36. ap), 5 = 100 gn: 101. Ex yfit p = 2. 1209m = 111gdm: 1IM
  37. fit
  38. 72
  39. fiat n = (3m, ubi (3 cognita et fiet + = BBmms:, 110 Bm = 101 m d B - 101 Bam
  40. one valore
  41. +2 gutus +290gm yy + . 1204 m y
  42. Ex y sit n ps H0 qu + 2 100 gM +1 n
  43. p = 10gn + 2. 100gm = 101 qan = (100. 11 : 101) qn, : 101n, ubi rursus avanescit q
  44. valores duos ipsius p.
  45. 106 _ _ 10 n7 129y + 11y + 10 =0 differentiando fiet:
  46. 2. H2 yy der + 2. 12 9dg + N +y du _ + 11dy +10 = fit dy = yy d12 + ty d11. y + 10, 2, 2129. + 11
  47. fr
  48. sit data aequatio Xxdx + gydx - aa dy, seu us = xxdx + qydx, : aa
  49. 7y d12 2. 12XX dy - 2. 12 y H y _ - IIXX - 11 yy = 0
  50. Multiplcetur data per +my+n, fiet
  51. 10
  52. + du1 V
  53. CAX
  54. my +n fiet vmy + umyy + 1omys
  55. assumla per
  56. + 12n Gy + 1n y + 10n
  57. mulha licetur et prior per ut m, et sact L um = um 12n seu C - L mdio
  58. n: M = - 1 11. 12 Et 42. 12 8. d1p = 10m - (11: 2. 12) m tandem + Xet 9 = 10n
  59. seu L .tXx + d10 = = (I1: 2. 12) m. fit m = 1XX - d1o,: 10. (11:2. 12) = - 2. 12 + d1, 10. 1
  60. 2
  61. fint =id12m = (= HIm) == () HIm + 12n Et + 12mXX - L dum = 10 m + n
  62. et
  63. tandem + = IL mXX - d10 m = IOn assumantur p +G1E +Y dt2
  64. et 20 + 11. 10 + 32d10 = 0 et 40 + et 1. H 4. 42 dy et 50 + 51 12 + 52 d,2 =0
  65. tollantur ope harum 6 aeqy. primum deo, d du, de2. deinde habebuntur ex tribus
  66. reliquis oplores ipsarum 10, u, 12, qui destuantur, prodibunt minimum 6aeqque. quae dabunt
  67. quaesitum

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 14r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0027?run=74