Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 20r

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: 0.84.

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

The machine reads it as

  1. Exe
  2. Investigatio Analytica Tangentialium
  3. Tangenetiales voco aequationes adrs differentiales
  4. primi gradus. Assumo aequationem ordinariam quoad unam
  5. indete ordinatam, cujus coefficientes dentur utcunque ex abscissa, et hujus
  6. hanc differentiactore comparo datae. Vel quod eodem redit et syntheticum
  7. est, sed si omnia percurras analysin absoboit or dine assamo aequationes
  8. ordinarias ad crdinatam, et video quae differentiates datae per quamque solvi
  9. 9+ m = 0 hinc dy + dn = 0 quod hinc ducetur, palet per se
  10. possint.
  11. hytam = hdy + ydh + adm =0 sit data aadus + (By dx + a) dx = o
  12. quae multiplicetur per E: aa fiet prodit hdy + βh ydx: aa + h) dx: a = 0 Et
  13. et fit aadm _ aadh = Bt dx se aa logh = (Bdx et aam = (h) dx
  14. adeoque aequatio quaesita est hy+ sh) dx: a =0 posito logh = (βdx: aa
  15. a) hdyt ydhiel + by + m -0 fit hydy eah dy + aydh + aa dl = 0
  16. ral dy + hydm + at dm
  17. +ab dys
  18. hy+ al + ab
  19. + ab dm
  20. Sit data aequalio agdys + a Bdys+ Vydx 1ad ex ∞ e, fiet h- a
  21. Sit data squatio aydys ta βdy + Vydx. + aBdx = 0 quae multiplicetur per h: a
  22. fiet hydy + h(Bdy + hVydx: a + hbdx =c. Et comparanda
  23. fiet ex dy fiet h∞ al+ ab , βua al = h B ee βh - an - ab
  24. et denique ex ex fiet a aBdh + ah d(3 - aa dh H(Bh - ah - ab) V dx: a - adh: h)
  25. et ex ydx fiet dm= m = (Vdx: a sadh: h
  26. = hBdx sit b = 0 et fiet aBdh: h + ad (3- aa dh: h + (3 - a)) dx:a (3 a) adhi. B
  27. -Badh: h + a a dh: h = hAdx. et evanescit h, nihilque agitur
  28. Ergo maneat b, et fet Ca(B- a) dh: h) + a d β + B- a)) dx:a a (B3. a) dh : h)
  29. Lb) dx: A + aabah: hih = Adx quae aequatio solvi potest
  30. ex Canone proxime praecedente nam bdh: hisi est differentia a - b: h
  31. a Adx = ac dβ + (β- a))) dx - ad ax et sit Lsc Z = su Adx: a
  32. 1
  33. 20
  34. Si AdX posito logto = s) axiaa
  35. t
  36. tietque
  37. sit b: h = Z. a et aequatio erit talis
  38. et excanor
  39. posito logW = (Vdx: au seu b =
  40. aleue (hyraltab) + g + m = c. et t = βh. a h b et m= sidxia = dogh
  41. et posito A = aa dβ + (3 - a)) - ab,: a
  42. Data ergo aequatione solvenda aydus + aBdy + Vydx + aD dx = 0. fiet
  43. aloge (hy + al tab) + y +m =0 posito esse - Stonax logro= fdx: aa
  44. U
  45. A = a aadβ + β a) dx abdX,: a dx l+bBh: a - h -b et
  46. henique M - Sydx. a = alogh, et b manet arbitraria toussans
  47. seu f aloge (hy+ Bh - ah) + y + sy dx: a - alogh = 0
  48. posito
  49. posito = 1 fuit et W log W = f) dxea posito h = bW: sondx
  50. et legu = (V dx: aa et A = aa d β + (3- a Vdx- abdx: adx
  51. i
  52. repetamus calculum: ashdys +ydh +a dt +94 m 20 Ergo ta hdy F aydhta d +hidy =
  53. tigdm
  54. im ydx sit
  55. superest x et dabit
  56. t data aequatio Hydus + Baus fVgaX + abi dx nd quae multiplicasa per Ai a dabit hyputhedy+ s ydxia a sd tu) = v. Ergo
  57. (4s p atdB anat (a Bah at a β-aadhe ((3- a) H) dx: a ((β- a) dh = ABaX. Ergo heva nescit
  58. xtaddx =o
  59. Adtro m= Paxia log.t ex du fit an + al + ab = hB sit a l+ ab = hB at Bh- ah.
  60. t hypusdy-
  61. kgys dk
  62. Alter si nsNaq Ry P aaya + RX y ay + altay +
  63. dk raatam Tal ycus quae multiplicerur per rhy +P fictque
  64. indecoparendo ex udus fit hN+ 2aC - n B seu Al = hB . HH. + xphyam ahgus dus + Ehise ge + 2bst ex taBodus + 2hv rylxia + 2kB yex + apB ax =
  65. x
  66. K=Fit
  67. et ex dysit lK Tan = C sO ABK - HKK + apt = a (β3Y et ex yudx sit aK = 2hE dX e seu
  68. et exlude it et ex ax ter aa dl + aldm= sp B ux seu at al aBF a Bah EA ex- = aF d + Bam PK an = siK. HKK tuas
  69. supere s ex yax
  70. sit unde ex se pvicem habentum habetur af (B- K) (t ah + dM) adeoqe habetur asahih +Mper Quadratura
  71. equai aantin n aleat in ente tacia- aptax de atk r uua scy t jusu habesur Sahisi ta e prvinde
  72. caleulus nion succedit
  73. alnil
  74. hunc hac
  75. pagina
  76. aβ est homo-
  77. genea uniteti
  78. ut sax seu
  79. ut loguhuu
  80. ut logX

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 20r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0039?run=74