Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 8v

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: 0.77.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 9r); this page is its left half.

The machine reads it as

  1. Generaliter video nihiatus inc determinatiorem fre
  2. quaerimus postremo aequationem qua ratura resolvendamus, ubi due: adque habetur per do: dz, unde dco: d2
  3. Qvia ergo nimia determinatio est E5
  4. ob aqui 12 et 16 habebitur deo idzue per dv: dz. sed ita ob aec. C et 6 etiam X: a, et dy: dx habebuntur per du: dz
  5. quo posito habebuntur x: a et dy. dx ex se invicem citra interventum quadraturarum quod est absurdum
  6. ita Nam ita in aequdata 7. tollendo dyidx substituto valere per x. a; haberentur semper ordinarie ex seinvicem
  7. ipsurum rationum
  8. Videamus ergo an alia ratio excogitari possit, ubi initio deo non ingrediatur in valores X. a e
  9. X:a et y:a, nec veniretur ad transcendentes.
  10. X: a et yra assumendos, unde et ejus explicatio nit nocebit. quod fiet adhiberda duplices summas, et postea
  11. cavendo ne descendatur infra in iis tollendis descendatur infra ad, dum nempe ado idioqu multiplicata per aliqua
  12. diffeentialem plimigundus aequatur differentiali primi gradus constanti. Sit ergo X: a =1) (ddZ: d et
  13. y: a = (2) SddZ: dx fit du: dx = Bto) dv: dZ sit jam in data aequatione dy: dx = (4) Xxtyy: aa
  14. fiet dv: dz = (5t0) qu 5a1Z: do + qu. 5 dd Z: dZ et differentiando fiet dZ ddv - d vddZ, :, d2 dz = (610)
  15. (daz: d0) (sddz: dv) + (adZ: dZ) 5 (ddz. dZ) adeoque dZ ddv: ddz = dv, : 2d2 dZ = ()(ddz: dv): dv) H((et 4Z. d Z) : d2)
  16. gaq = dodo ad seu sddz: du dx Cctav. 412 (. 242) = (dvdv. 2424Z) = (d∞: d2) sdlaz: dz =) dudque (dav: ddZ) - dvdv - 2dv dq (a 2.
  17. dx ua siazite) B3: 2 d Z 1Z adeoque quo qu. Sdaz: du 2 dud bdqu dZ (d Avd : ddZ ddZ) = 2 d vEd Z (ddv. dd Z) = 4 dodvilndque (dv. 19) (dl r. d.
  18. dot F q doidqe sddZ. dzue + 4 dvdo dZdZ. qu sadz: d Z = (quo per 5 (9no per 5) (dv: d2) = qu s ad Z: dq a3 4
  19. item aliter ex sto erit sa Z: d= (dv. 4Z) - qu fddxed Z) Quo minus in calculo labamur
  20. per agamus eum ad huc aliter (ddz: dx = (10mo) Y ((dv: dz) - qus daz: az) et et differentiando fiet
  21. aldz: do = (11 m0) (d Z ddv - dvddz: d2 4Z) = 2 (d d Z: dz) 5 ddz: dz 3: 2 (d v: dZ) - qu sdaz: d2)
  22. et dar ddZ: dvdv = d Z dZ ddvsp 2 dz dvado daz + de dv ddz adz - 4 dZ d Z dd Zdaz q u sa d z: dZ - (+ d 2 az la, silv tsedvaq. 1, d1)d
  23. 3: a (4, dv: dy) = 4 qu )dd Z: dZ) du + seu (dr: AZ - qu (aaZ: d Z) 4 d2 = il X dz el Adr (clilvdav: da q dt az) : 2d 2 dv e dv: at 2)
  24. F dB = + 4dZ dz dodo qu fulz: a2 = 4 d 2aZ do dv dd v.: dd z) Sad Z. dq + 4 dx haZ sdd : aZ. ed Fies igitur
  25. e
  26. (daZ 34 d du - aet- dz z aodi e rax + 22q v a
  27. l2 (d dv: dd3) + do
  28. 4dZ (aZ (d2dZ + dodv) dZ
  29. qu fdaz tr d
  30. inde fiet pidaqu dt proitad
  31. 4 dZdZ (dZdZ + dodv)
  32. d Edo- 4 de du a de duuo ve u ala see
  33. compendio faliamus jam constantem aliquam quantitatem, qualis dze ddo: dd do
  34. 4 dZdZ (d E d 3 + dv dv)
  35. per compendium quomodo vocabimus ita enim eam voculimau
  36. et ex aequ. 14 e
  37. fiet ( aaq (15) 2 2dco dodp = 2 dv + dZ 1 (16 d 3 d - 4 dv - 4 deo du dvdlv + 8 deo dv3 + 16 dz d v)
  38. 4d2 (dX Z + dx d0)
  39. seu sa is ita an. Iu a Z S (16 d do Clj A ravar) - ( a - a1
  40. 4dZ (dzdz + dv dv
  41. C = deodlodlps
  42. deo (deo) d 2
  43. pBavagibnr
  44. +diavadq Y (4 dodip aesde
  45. a 1 a ddo + dip avdd-de d da
  46. deo dipdi
  47. + qldaze Hdod +l. serdodds
  48. =dz dd p N. d945
  49. d pall - ae d (( dv al - d9des)
  50. 4 dvad + 4 d p v - 249 dde
  51. dcoulp 2 Y (4 dv dep - d9 dis
  52. ddo per aequ. 15 et 19
  53. add (20
  54. +dipq ub dav
  55. docex. o
  56. +arll Et
  57. Hosteq ( a dv do)
  58. et compendiu faciendistico du) d aco
  59. fiet squr 11 extio ) dvelc (+ av daetu d y - dco uo d9. des)
  60. Uinde differentrando:
  61. de avddips
  62. du dide
  63. dis (4 dudip - d9 d
  64. deodcsta vaex -agag) = 16 du tv + 16d2 dv - q avavdco a d d ud -4d v vidiamus an hanc quantitatem
  65. et 4 4 dv d - d 9t)
  66. liceat reddere extrahibilem sit dz = dv d8: deo et fiet derdr, P 16 +3 d
  67. 3 4dvav: deo
  68. Ergo () d E F (5 d edeo deo duax-(2deo + xdcodvdo dco: s quari debet quadrato daor
  69. seuddo dco d +de
  70. et Bde =
  71. = do + o s C) (dco aleod E dco t a
  72. 2) (4d83d
  73. (2) (4 de - deo)
  74. 2deo deo de dcod5)- d d cot et deo radiols hrtode di pulestimim
  75. 413- deo
  76. B(152 de)
  77. 4 d33- dco
  78. Lndm = icst an d = 4 dco de3, . du dy - deo
  79. XX: 9a = sd : dv
  80. gy: da = 5 dar A2
  81. xdur udd
  82. 2 xax
  83. vuniar ause
  84. 13. pancta super
  85. ignis posita
  86. adicant colla-
  87. tionem calculi
  88. aequationis u
  89. cum calculo
  90. une cao iptur
  91. issem ale
  92. quo dndrirgusade
  93. An+ M =am
  94. nntenterran
  95. n tantir- r
  96. un +2bn _ m
  97. in + 2b n +bb
  98. et n- Snetbb.
  99. Tetat tale vime

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 8v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068072:0016?run=73