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

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. 18r); this page is its left half.

The machine reads it as

  1. A sdq + lytm + e y + h(dy + Pysdy + l + m +y = 0 fiet
  2. haga +distu + rdys + s rdy sdy+ ydr sdy + d +dm - Ady + ndy + ydn
  3. et quia fdy = l+ m + ny, : , h+ ry = hdy + (Y+N) dus -m dus + _ dn + dm + dl: her.
  4. video optine poni m =0, et fint h lrdus + ly dr + ldh + nrydys + nygar +nd h = mdli + mrdys + mdr
  5. = hhdu +h(rendus - hon dys + hydu + ham- hdl + hrdus _r(rra) ydy- rmdy + rypdu Frdm + 19 dl
  6. Sed vides nimis alte assurgi. Et sane n variabilus est mutilis et m _ frat =0
  7. et fiet h sdly = rysayu +l , 8y = 0 et hidy + ih sdys + xdys + rdys say + ydr say rdl +ly ∞ 0
  8. et sdu V-h dy erdy + dl + dys:, dh+ rdy Fydr = l+ y,, h+ry, unde
  9. hh dy thrdus + rrydus + habe hdy+ rydus F hdl + ry al L.
  10. yydr
  11. =rydus = ldh l at
  12. =0 oporles resse constantem
  13. seu aro
  14. oportet ar dr esse constantem seu dr-0, iter esse atrut as sed ita non potest tolli dyt Ergo calculus
  15. un d
  16. A sic _ _ _ B (yt + fy ny + p = 0
  17. jam d b facile habotur quia si b = W f e bogb = legu. et de logb erori C db: l = dW0 e W seu du = de log b. bC+ C fe. db: B
  18. pricr. malus.
  19. not dh + h (Mdys + ydm + dh) (m9 4
  20. et lipt o
  21. seu qua
  22. logl H (my + k) smvat dl: l + nay + ydn + dso =0
  23. -na dh - pah - hnymau -htiys ydm - khius dh - lis ndus - tisi pam - t s d h - hny at nu -hay th -hpalsuy - h p al t lefi y
  24. inde- nith - pdk dtm hdtnus val
  25. et fint test h loge maynus + hloglmpdus +legl. natydm + nydh +pdh
  26. hndy holngu al +hlogE nyah
  27. hinc ut destraatur dy dx fiat logl dm + m Alil = 0 fen
  28. +hloylsyam
  29. +te ny db
  30. + hlogl pdh
  31. +hhpdt
  32. - hap
  33. sit jan aequa bio data hmtan gaus + Bhimmndys + Y timmn gax + Bhmmnax = o et fiet Hminp = ( )emmn
  34. seu logM = loglogl seu m = logl et ab: l = dm
  35. + Empysal
  36. seu p = fn: p) (n: mm) + Bn et n dh FhmBdh + tmpam Fhmnam + tmpam-hdn = gummnax
  37. et denique pah + mpah + hapam - hdp = Bhmm fit - fit M = pah. + honpa h +hihpdm - hap, : Bhmm HX
  38. F mmji, Bimm + 1 et siet pih +hmpah + hhpdm - hap + Bmmpdh + Bumtimpah + Bmm hhpam - Bmm h d p = Dhrmmm Bi pdX
  39. sed si in assumemus pro constante malim tolli p, nam fiet dp= dnac
  40. =hdn - Y tmmndx dytem dm n (+ B) = 0
  41. sed cum ope duarm
  42. arum aequationum tollantur dt si et A per rationem dh:h id dn:n desinetur in aequatione
  43. ubi evanescat dm, fiet nah + hmncth + i madi
  44. mM
  45. +) - hudB = Aummndx.
  46. quae non est in potestate. itaque praeter calculi prolixitatum
  47. sit -h, 3 + byy tamys + aan = 0 fiet 3yys dy + aly dy + gy dl + a
  48. pet -3syy dy + 2 lydys taamdy +ayy dl tay dm + dn A - h dh
  49. -3hh yydy + 2ahl 1s dy + aahm dy + ahyus dl taahy am + ah d n = 0 sit aequato data aydus + β3 dy +. Vy dx rab aX
  50. et fret
  51. 3tih gydus - 3hh (3y dus L
  52. +aclgy dy +aaβ9 dy
  53. algus dp taanyah + oinah
  54. al yus dh -aamus ah + an dh
  55. 3hihV py dx - 3ht BGylx
  56. ta ) gydx taa fgatx) = 0
  57. qua multiplicetur per , et fiet
  58. habentur
  59. hhA y +aG ifiet
  60. ergo g et M
  61. et m = 2aβl + 3GβB: aa
  62. in ob dx fit a han + andh = 2 a βBdx + 3h(3βF dx. sed quia ad huc duqe reslvendae
  63. et ex dy firt g = hm: β hinc ex ydys fit 2a β3fil + 3h BB= aa fim.
  64. pmpth 4 ny + p =0, fiet: arqualiores, timeo difficultatem
  65. et g = R2 al + 3hh B,: aa seu g = 2ahl + 3hh β, : aa
  66. ob un d fit
  67. my+ A
  68. ny dg2
  69. Redcamus ad priorem:
  70. nyth (mdy tydu + hl) g
  71. = pu-
  72. p
  73. mo (my +h) dl F ndys + ydn + ap = 0
  74. p
  75. Lmnygdlit + Rydu
  76. H, yy dm +leyl. nyat
  77. +llylipyda
  78. +mpls
  79. -dm: nm = dl: 1
  80. .Et frebus foret
  81. sed si lesset constans, et g qu
  82. log. li Mnydys alogl. Mn B dy a loglma ydus + bgl. mab lx
  83. fiet de utrique destuendo gydu, fiet dm: m = - dlologl
  84. + Pdg: g =0
  85. phal:l
  86. si jam y dy st logl. M
  87. seu log m=
  88. logloge. seu log i = log.logl seu = log. l
  89. in milogt = 1. jono unc ex ay
  90. seu p = nB+ et ex dx
  91. poro p
  92. pagig utei g.9+ hatit) - pa B. B
  93. seu log) +hlog l - logs(3+,) = logn = (D(. β341) ex posito h esse onstantem
  94. seu
  95. seu dg: g. = hal: l - dp. p = B( DHi, BF id x
  96. L9: g t d + (3+1) dm: m + h dl: l + (3+1) dl- dn : n =
  97. dg BC: 1 B1) dx +
  98. dn = nBdx
  99. inperest aequatio
  100. Ulil =dn :n = Y dx
  101. seu togM F toy. = Jog. log l. + log. log l + E lX + dB - Vdx
  102. (+ dus= hal: D + (β+ 1)dm: m (+ hal: D + ((3+ 1)
  103. ed cta evanesscunt assumlae ergo mon ticet facere
  104. et ex y iex faciaram hane: Ag: 9 X dh: M A(Bm 1) n.m
  105. si Ddx+dB +da +ri.
  106. qe redecus ix
  107. = Vdx
  108. at: M Lan:M = Yd
  109. Fax+dC
  110. asunsitia
  111. x + B = ex, quod eeciet non
  112. (L Ba) x hat: ) +(.+1M: N Ergus rursus omne
  113. eplupotetale

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 19v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0038?run=74