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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 8r

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: 0.85.

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The machine reads it as

  1. non successit
  2. ut quna smer my dx t andy + aodx -0 summari pt
  3. etra et phydx taqudutardu summari potest, etiam compositum
  4. pg. myaxtandu Py7 1x + agydy + aatdx =0 summari possit
  5. summanda est haec aequatio: mydx + an du + apdx = 0 ubi m, n, p, dantur
  6. per X. Hoc variis modis assecutus sum, sed sequens ob consequentias, in primis placet, qui
  7. fit noltiplicando, Multiplicetur ergo haec aequatio per 9 arbitrariam ex X, cum ergo
  8. apqax futura sit summabiais, quae cunque reperiatur q. ide sufficit ut ms inquax + anqdus
  9. summabilis fiat, quod obtinebitur, quod si comparetur huic aadr +ardus et fiet r = ng: a
  10. unde de = ndg + gdn: a, sed rursus dr = modx: aa. Ergo siet du: q = mdx - adn,: an
  11. seu log q + logn = (im dx: an) et posito b esse quantitatem cujus logarithmus sit uuitas
  12. sret,. nq = b sonax:ant, e q = b A(m x: an) : n.
  13. si proinde fiet
  14. mydx + andy) = D sorqy a =) ay, b. (max: an)
  15. CCI. Sen dx: an)
  16. Loco y jam assumatur gyu + ahus, posito g et h dari ex x, et fiat inde
  17. nCGgy Fahus) x + an (29 ydys F gydg + 4ydh + ahdy), l. sen lx. an). n cussumna est agyy radhus, b
  18. t
  19. sit jam aequatio data ap ydx + aaqdy + ryydx + aa ydy h m multipli. f. Bsemaxiant
  20. Formula
  21. etur per
  22. fiet afpy dx + aa fgdys + frgydx t afcrydus ∞ rahmyax t aahm dus + mgyydxt agnydy
  23. 0b y dys fiet f - 2 gn: pursus ob du fiet f = hn: 9, quos duos valores aequando fit h = 294: 0r
  24. aa n ynh
  25. an yydq
  26. Ob yax sis t hm ax + an dh, seu spdx _ + et qui = hnid x: q et dh: A = anq:,
  27. et dh: h = mq R npaX. _ P - Angdx,: ang. sed ex priori valore est
  28. dhit = 2 (9: N) dg = 2 9d (9: v), : 2g(9. N) = 49 dg + dq: a) = d log9 + d log9: )
  29. superest altinui aequatio ob ydx = n p dx - mgdx: anq
  30. qu~
  31. superest jam
  32. altima coinciventiatio ubi ob gydx et fiet frax = mo dx tan dg, et pro f ponendo
  33. valorem 2gn: V, fiet 2gnYdx = V mo dx + an dg, seu min = 2rdx - a v (dg: 9): adx
  34. t a
  35. -dlog (9: ), : llx : a)
  36. )-ac a logec. v) er
  37. militer reperi rem non posse
  38. 9 velimus multiplicatam ut ibi velimus
  39. sid ita evanescit utrobique dg: 9 vel alog g.
  40. aequare producto ex gy de + afdys, bBd: as) in lytam ubifit aq - p
  41. ootineri, si aequatione pormulam datam in
  43. in sic (a 91 +2 βydys) (. sam a , () + sp yax = 8 19) (C. s. . al : 8), 0
  44. + n 19, + aby) dx + an f 2gy dyt yydus r ay dh F abtus) p. b. sn dx : ant: H
  45. comp coincidentiantum cumdata apudx + aaquus + 19ydx + a v ydy, f. bsucx. an
  46. onax: an): Avanelcet manebunt m m, n, g, h, a: β et 7. 8
  47. et primum quaerentur mi ni et f, restabit demum adhuc una aequatio
  48. ita
  49. am aientrae incognita in ubi quaerentur implicatae differentiis utem
  50. indi indigenus a cet B, reducitur res ad duas a: (3, et 1 Sadx: aβ et
  51. ila et ad (Y: d et s.S pax: ad ast
  52. pro quibus possemus ponere intee lateras
  53. ila vereor
  54. puto necisse fore a ut fet X:
  55. trendentes etores redibit ad f, m: n, g, et sricial
  56. quae evera per ucentur aoduat
  57. C4 myax + an dy fiat ay V v b fint. 12 lvdx et an vir b + b dv, quod
  58. aqrari debet ipsi Vdr +rde, aa fiit b an = aar Rursus aar = mbix +an
  59. sit am ydx + aan dy = mbv dx + an vb dr + anbdu =
  60. +dv
  61. aa, vda
  62. nb =at etaadt = ambdr+ ab dn = mb dx anbdr, sed ita quae situm evanescit
  63. su possumue esfi omittamus compositum u t ubi m et n sufficient
  64. X = b
  65. ne an sp: m) ydx taanch.n)t mVydX + any dy, b
  66. ubi L et (3. et item Vet
  67. sindx: an
  68. aant mgydx + an 2yu + nosq F n (ea guxR taan d (2 y),
  69. se Myyax. + an rydy +am ayax + aan a dy, pnan. an : n
  70. an y den
  71. (Smax: an: n
  72. fit n = g: 2 m= f∞x am: p = an : 9 = an (9. n) fit g= m = L v: qu et m: n = 2p: q
  73. p gydx + aqudus + ar ydx + aa n du, da
  74. restat Am (9: m) dx + m d (9. m) = fr dx seu am (26: 4) dx + an d (20: 9) = a ma: p) rax
  75. unde iterum habetur man, quare resgeneraliter non succcedit
  76. n: m = 24 (.9) (r: P) = 2(V: 1), dx :A (V: 9) = 29: p
  77. nempe. fit
  78. Jyix t.du, na (. snda an Y~ Y L Vdx + ady, s(5 dp. a9)
  79. n
  80. n 5FaX: d9) = b sen dx. 4) 9 = P A PQ b Sindr: an et g -9
  81. e min- a td et n = G. bt ota in b . si s pt ass B

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0015?run=74