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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 190v

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: 0.80.

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The machine reads it as

  1. Assumatur h dq + gddz = 0 fiat Z = t. b fiot 12 = d t. b + + dys b
  2. unde fiet
  3. ddze - adt by + de sy b7 + dt dy b + . t dydus b + + days b7, Unde, collectisue
  4. Ed prodet t omnibus et divisis per bi, prodit:
  5. proinde
  6. hdt + t+ dy + gt dydy + 9+ ddy = o quaeaequatio solvi potest
  7. dd+ +29dF dy
  8. videamus an datam aliquam huc reducere possimus
  9. Sit lD + mdo +n ddv = 0, fiat V = W. b7 dv = du b ado = dd1s b + W dydy b + W ddus b7
  10. Unde colligendo in unum, et dividendo per b7, prodibit
  11. Wdy b 2dlodys b
  12. Lu + Budus + nudydus + nioddus = 0 aequem coincidentiamus aeqq0 et
  13. m du pndudu
  14. enwat. F
  15. ft (nW = ot, seu g = nwet, ob dy fiet ht + = m W + 2n du
  16. ob dy dy et dy fet:
  17. A ob y, fiet lio emdu tnddio ( hdt = lu + mdio + nddeo - nu dat: fi = demw: t + 2ndtaa: t - n d itut: H
  18. n dau
  19. seu fiet h = atm 10: F + 2ngduo: t - 2n W dt: Et
  20. vide ams an lice Destmere W, faciendo et m n at d. t = n ddt, seu m - 2nat = n dat
  21. se quod procedit felicter fit enim (m2fat
  22. quae a quatio videndum an possit divelli in duas
  23. quaeaequat
  24. quid si Z= t. 97 f 4= d 87F sie quaeretur log 83 = y logg
  25. de
  26. Ergo d (7) = et y d + logesidus 87 Ergo si Z= +G erit dz = G at + +G’y f+ t loges dy 93
  27. Ergo eZ + fdz -0 dabit et + fdt + ft de y + f+ log8 dy abog9,
  28. lo
  29. ddZ = ddF 87 + d+ 8’ y dlogg + dt loges dy G7 H tdy 97 +y dF G7 + A y yy d hog 5. + Ly loge dys 9)
  30. ddelog 5, ty, gr . iloges
  31. ty ddloges g)
  32. +log Gddus P + t dys dlog e est + loges dy dt 9) + tlog5s ys ydlopge 19 cst + + logg dy dy loge. 8
  33. loge vocetur V, et fiet
  34. eZ+ faZ + g ddZ -0:
  35. fdt + fti a + f + ipdus + tdgd pysus + tdp V ydus
  36. et
  37. e
  38. gdat gdt py tgdt 2 du +gt dudy9 + gt dv Vy dy
  39. 9at
  40. 9depstus +9det dy
  41. g ddi ty
  42. otus cotdidus
  43. si ponamus e = 0 erit aequatio haec solubilis
  44. Quat dy
  45. oteptis ydus +gt ddys Gt lydus
  46. si tam sit e constans, evanescent y, yy, ydy, et fiet fdl + ft ydu + gt p ddus + gt q. P dydy = 0
  47. gddt 29dtre dius
  48. ubn divisis omnibis per G, fit f: g = K, fiet Hi dt + K L qpdus + A 1B ddy tirs Ays dy = 0
  49. ddt +2 Y at dy
  50. ddv- ddy + ddu sit data aequatio 10 + 11 d + 12 del b + 13 dd x, assumatur B = Y + cet, fiet dv = Wodus + ydu + deo
  51. et +dD = Wddus + yddt +2 duodus et dudv = con dycus + gy duodio + a nydydio
  52. 104
  53. 1Ideo + 11 dy
  54. +daco
  55. 13ddco + I 13ddy
  56. 12 deoduo tr2 rcuodus + 12ddus
  57. = p p+: 13 = 4t: 12 fit 2 = 13: 12 n = t. 13: 12. 12
  58. F (id (1 + 2. 1dco) = K H132)+ 2(13) dt
  59. 1.
  60. L. 13 (10 + 11 ded + 13deodeo + 13 ddco) = H dt + ddt
  61. fit H+ at = = H La + = Fdtdo = 2 dt d + = 3 + t + 1. 13 Hdco B Hdcodio + 13. 13+ tddco - tdd F
  62. se
  63. P. 12
  64. 2. 12
  65. .dB Et + GBB dy. + ) C, ddys + V B Clydy
  66. 12. 12
  67. infirdum hinc egitus
  68. ubi 1, (3, conpaates, e, 9,) datae . a 2) a Bdus
  69. 81B
  70. si possemus fdt + ftidus + 9 + Y daus + 9+ 1 B du =0 coincidentiare ipsi et
  71. penendo e constantem
  72. gddt 29d y ay
  73. huc Vb in constrnti ratione ad ot, su b = 9t efici 9BX gt + 2) BA gdt +, tg. 21 (3AfdG = YFF + Ygdt,
  74. et En ot + es t gat + G2 + dq + V a gdat + V A F ddus +.) A dgdt = fat + gddt
  75. et Bnostanti rabe ad I
  76. s fit 5(A YB V F t at = gB1, Fat + 2YBA, Et F 27 B) tgdus - rEsg atat
  77. ex t e AVgtC + gL Y gtat + es 2 Wp H dg +7 ) V gtddt +VAW Hdlus t3) deptytat
  78. 8gt ddt
  79. Fd ftat = e, L + Csp +) da B - gF dat = 8β0at + 2γ Bdt dD. 2 ap g dtat
  80. + ftius tgta + A
  81. = Cha((rZ + SdZ) = rdZ dr Z + t + sddZ, Ergo in s fit igat pty ti e
  82. f
  83. dsdz
  84. giat
  85. (hZ + g dZ) cer
  86. facimus e= dr, d, et 5- 4s tdg soliu etiam potest aequatio
  87. multipticemus aequatione O per m, habebimus ubique em, fm, om loco e, f, 9; et manet in artiham
  88. E debet esse em = dr gm = 5, et fm = r + ds, fit r = df fm = ds = f m = gdm - m dg = Y
  89. et sit fdm + mdf - odam -ram dg - m adque d A gt = em = dr
  90. = v - y +Cd
  91. lco
  92. audv= dgitus tedaetco
  93. hdiodus
  94. e
  95. Lloga
  96. d loydus
  97. alogus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 190v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0380?run=74