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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 19r

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.

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. 18v); this page is its right half.

The machine reads it as

  1. sed hanc autem fermam reduci potest omnit aequatio in qua i non
  2. e
  3. pliter sit
  4. Au
  5. assagit ultra ydu et yydx nam semper effici stotes cu aquatione dfferen
  6. tadi, ut tollaram termnus ab ultimus seu obsolatus a quo abest y et du cum
  7. oporteat tantum ponere x hq et panere unde si adesset ddx.
  8. Aliter sic: Cly sdy: y +H fdgru + M my + n = 0. fiet
  9. ponere y v+ tr undem et
  10. Idy + 1fdy: y dy + gy say: y dl F an mdus +yam + dn
  11. fit -5dy: y = l dy + mdy + y dm + dn, : l dy + y dl = my +n,: ly
  12. et liet H U ydy ( Im ydy. + lyyam = lyan = (Im y dyd + In dy + ny dl
  13. lyy +am y +an = 0 firt 2lydyt yydl tamdu Eyam tad = 0
  14. ubi pro gu in aeque 2. substituerdo valorem ex aeq. 1 fiat Ellydus Almdy amy al B aand 20 sit aequalio
  15. sit aequatio assumta
  16. + al yam + aal du
  17. cata Aynus +laβdy + _) y ax + ab dx =0 quae multiplicata per MMl: a, ficut
  18. rlLy dy = 22β dus + (Il: a_ Vy dx +, lB dx = 0 firt per dy, am = Elβ et = 2B( al + al am = 2 (V. a) dx
  19. ser - fa3 dl + fl d B3 + fBdl = se GV. 1X et habetur t nam db: t= J dx ad(37 i
  20. in emceia, ut comparatione, jum aequatione
  21. et sit a dB = ) dx quod non est in potestate
  22. perentiatis cum differentiata, multiplicationem differentialis, imo et differentiatae
  23. trans formationem differentialis H malationem figca differentiatae per explicationem
  24. sed ita destruitur ln hac plagula
  25. (2
  26. Conjunxamus zc varia
  27. differentiatam et differentiandam
  28. Aliter lyga amus + a n = b disterentiando 2lydys+ amdus + yy dl + ayam + a du=
  29. e 1
  30. addeitur prima mulsiplicata adiatur securos fitaalydus tam dus rjydl + ydm + a dn ∞E= 0
  31. conjungendae quationes
  32. sit a aataadl: l = hax et destinetur ju
  33. +sujy ex atimydu +aa hndx
  34. sit et fiet 24lydus+ damdys + Aayam +a dn
  35. et ex aequ. datu ay dys (e dy + J. ydx + at dx--
  36. cetimyd caex
  37. arius al-ah d
  38. quae mulliplicata per 2l dabil 2alydu = 2 al Bdus + 2l)i ydx +2a Dl ax
  39. et fiet m = am = 2 lB av 21 d 3+ 2B al - 2βd1 = 2 1) 4X
  40. (dy Ah+ hdy
  41. y
  42. =0
  43. yy
  44. ldytyali + an =
  45. et prok sdy substituendo valorem = ly+m - n filo - = 17 =ma - n dh + hh dy et ∞ +
  46. y
  47. elgrtiy alosidu
  48. seu -lgydh- mydh - ngus dh + hhydy = alu da- amdus thlus dus + h gy dl + hyam + h yy dn =0
  49. ubi si faciamque m=
  50. -
  51. seu +hh y dy - hm dy
  52. ut hl
  53. = lyy dh - mydh =c
  54. nyu de - hly at
  55. ceton
  56. =hydm
  57. + h yy
  58. fint haydy
  59. thyy dus
  60. ly dh = hldh = 0 sit jam aequatio data h ydys + h β du + kJy dx + hD dx =
  61. +h yy du
  62. ascribi deberet. gnu...
  63. fit jamt fiat jam in = o, et prodibit
  64. d
  65. β ses et ldh - ndh + hdh + h an = hY da et ld
  66. satiahat
  67. seu βdh(+ hat -nah + hd (= hah + hdn = h) dx in hac novisima
  68. et fiet h + l
  69. solutio
  70. pettur
  71. si preter n fuisset n+ fy
  72. aequationis daba nam ficiet Sbax = C3h mihh, unde deinde facile habebitur in
  73. dE
  74. liabe
  75. Ergo habetur solutio hujus equationis ydus +bdus + Vyax+ Bd
  76. lx: β3. - h
  77. est
  78. h y dy + hh dy= ny ahp
  79. hI
  80. aequalis nihilo
  81. st
  82. +. h G dri
  83. a quatio ne substitinuur ipsius db valor fie
  84. Dda +Bdv+ V B x + vav + n dv +e vdx +H dx = c fiat v = y+ _K
  85. Hinc si B sit constans ve
  86. per aequatione, jam solutas
  87. firt au= dy+ dK et prodit y dy + kdy + ydK + k dk
  88. X
  89. pa
  90. sit aequatio data
  91. Eyax Ed
  92. tEs ) ax
  93. + adx
  94. = 0 sit jam k+ n = b, seu k = b-
  95. unde n = nesx WV S)dxio- bluta b sich itto posit ti st logur
  96. seu n logii (i dxilogu b log teate posito log W = _) atri h
  97. copto 10 = si et fit n= hphs pax:h + b:
  98. et denique = bh seu 1= sbb - (Dax et fiit hoc
  99. hsdu + H(= Ddx: dh) + h sdX: h + b: h + y. f = 0 sed
  100. rectum
  101. 7, quod sit Sex +l+n + y, cum l+n componant unum
  102. e sumamus erus. hunc
  103. augeamus addendo p. p y say: y
  104. in soco
  105. et B - - b d n + Eb dx = = n dx L HdX
  106. et (Bax = Bh - e . hh et = bdh - Ma A +
  107. y dy + b dy - y dn t-bden = 0 fit Y = E-
  108. utique ex data aeqvatio ne fiet
  109. +8 ydx
  110. nvax
  111. Cabcne
  112. unde absunti
  113. nM: dx = () a H. n) Lb
  114. log.
  115. 6 f sob
  116. miu
  117. eodo
  118. y) Ay-m ha
  119. et h=

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 19r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0037?run=74