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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 94r

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: 0.86.

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. 93v); this page is its right half.

The machine reads it as

  1. 1ea + uy =0 differentiand sit diea + ydu + 11 dy L0. qram dividendo per H. prodibit. co+ y du + du
  2. esta data diferentalis ejusdem formae, quae sit resalienda am dx + nydx + aacy ifiet du.u ndu
  3. etoderc seu Sduiu = Sndxet Rio = StImax et Ga sumax : 1 = yC
  4. M ma + ny =0. ubi pono m et En dari ex x differentiando fiet: adm + dy + yan + ndy-
  5. vel divisis omnibus per n, fiet a dm. +y dn 4 dy =0. sit, jam data differentialis ejusdem formae, qua
  6. netiam bC dantur per
  7. resolvere oporteat: dx +Cy ax + dy =0 (fiet Sdn: n = Sedx: aa et m = Sbaxiaa sbnax: aa
  8. Ascendamus altius, et esto maxtanus + pyy =0. et diffeientiando aaam + aydn rgydp + andys + 2pydy = 0
  9. Esta, differentialis data ejusdem formae aabdx + acyax + eygex fdy + agyay = 0. divis illa
  10. aequationem per 2p, honc per ag, coincidentiemus, et fiet, an: 2p = af: 9 seu n: p = 25: g, et rursus
  11. ap: 2p = e dx: ag. Et datur p. Ergo etiam datur n. sed fieret denud. a dn: 2p = cdx . g. jam p = gn: 2C
  12. et fiet ca afdn: in = cdx: 9 seu dn: n = ccx: af.. Quod non procedi, nisi in casu speciali
  13. ubi ea ost relatio inter data per quam duo ipsius n valores coincidere possint. Sumammus ergo
  14. aliam differentialem resolvendam bax + C vdx + C vvdx + fdo + v do = c. Et esto v = y + F, et
  15. prodibits + bdx +9 7
  16. ex
  17. +et ax Eyd
  18. e Etax 28 Fydx + e yydx
  19. +Fd+
  20. + + dt +ydt
  21. F5dy)
  22. +5dy
  23. + + dy + ydy
  24. audm + a gdn tgy de tandy +ydy 20
  25. 2PS
  26. Ex yydx fit do: p = 2 edx: aa. itaque datur P
  27. Exdus fit an: = =F 2f P + 2pt, et a dn = 2f Ht) p + 2p (a s+ d)
  28. sed exyaxsit adn = 2e px + 4 eptc +rpat. Quos duos ipsius
  29. adn valores aequando fit 2aa fap p raat p fraavater aapatm
  30. = 2a cpdx + 4 eptaxA 2a a pat) seu a
  31. quia autem f habetur per X, ideo possumus facere ads = k ax, et aequando duos valores ipsius ap: p fiet
  32. 2ef + 2et, = ac + 2C+ = ak. Sed ita infeliciter evanescit t.
  33. AAliter tentemus: adm + ydn + ndy. multiplicemus per aq+ py, proditat:
  34. aatam + aty dn + pyyan + agndus +npydys
  35. + ap yam
  36. de dr f. efdx- ad df
  37. hanc dividamus per np, et coincidentiemus
  38. ipsi. aequationi O
  39. a+: p = f+t an: n = eax: ua. Ergo datur n.
  40. Compendio in aeq. C terminus infimus sit Saxet peninfimus Ex fiet am = N np: aaque, et rursus an-
  41. npp se dx = npg 7 dx = aagqudn, adeque fier
  42. dn: n = p4 = dx = ApP SVAX,: aa qq = edx: ad seu p9) - pp5 = 9ge, seu
  43. Inp dx = aagdn,: aap. seu
  44. F Sea 43dx, (od 4. P = 5+ t. Ergo explicatione facta redit difficultas prior, secundum +
  45. Assumamus maa + ang + p + a5 dy: y =0 et differentiando prodit aaam +aydnt andys + dy: 7
  46. eax op nec lucramur
  47. ita frt aayam + agy an t dys anydus dato simili comparanm
  48. mbyax +cdu summ abile reddi pt multiplicando per in, nam fiet
  49. bmydx +emdus comparandim huic dm yan+ ndus nam fiit n = cm et da =t
  50. et du = Cam + mdc = bm. Eigo prodit dm: m = b - dc,: C. adeoque datur m et. n
  51. Ergo summari byax +Cdus, m, posito dm: m = b -dc; c entque summa Cmus
  52. (5
  53. fbys dx + Cclus) compendio vocetuo Si ergo summari potst potest srsi = emus
  54. md N = d scmus) d(sm) = Nam t mds datur (m da = datur Et fiet,
  55. et fit se = fbydx + cdys ,: m) ((d Cemus) am) = sbydx +scdu
  56. msi fdim + emus seu N = SNam + cy
  57. dse = dCemy): m
  58. potitus, am: m = b - dc: c
  59. Sed haec methodus non procedit ad plura simul summanda, ut, si esset
  60. bydx + edus + egydx+ fydy. non licet una eademque multiplicatione efficere, ut
  61. ut ambae partes summabiles reddantur
  62. ad 1042) + Z db + Chy ryde p det fdy tyds
  63. in summabilia plura
  64. sed videndum an non liceat divellere, C
  65. 2, hedb + eydc
  66. + f ydb +f yydc
  67. 37f bde 4bby df
  68. cyde tegydf
  69. + ecdus
  70. -
  71. xase ydx, aam textang ax tpgnax t angulus
  72. uit ia
  73. fiea 4fdc ged5 +4d ef dx
  74. = apec dx apbF Ax
  75. et ase db A = bde + qubeax = Am ec dx tcmbsax
  76. ila habentu
  77. +fc ydy
  78. +bsdy tef ydus
  79. + g besx + gbsyex + gesqycx
  80. si 2 =1 et 32=
  81. ita habitil
  82. std aquatio
  83. sin dan ecdxe an cfdx-q
  84. bfax L qedx
  85. gg = apecax a apb f ex- 4495 dc + uaqc d
  86. tos + et b + Cy
  87. si 3=-E evanescet ydy.
  88. + e + 57d
  89. Habemus ita quinue arbitrariis
  90. b, c, e, f, g. Cum pim initro
  91. adassent solum tres
  92. fa db + cdy +y de + f ydf + fay + gdx = 0
  93. a
  94. Bovius sic
  95. ab +cy
  96. et fiar
  97. 1a db + aa ydc
  98. abydf
  99. ad + egyax +cgy df
  100. faacdu
  101. +abfdys
  102. + ef
  103. sit jam data aequato differenlialis
  104. aax +arydx tpyydx + aagdus + aaydus = 0
  105. .Et datur
  106. firit, df: f = pdx: aa et datur f. Rurtus aa + ab = 4
  107. ab rabgdx: cf = mdx fit g = ncf. dx - a d b,: abdx
  108. 9 = a dc + aabdf - aC fndx,: acdx fiit mecfdx= aecab =
  109. fint abac + aabbas- sbefndx abde t acdb
  110. ir dugbus puosemantbus a et valorilysfit apbcedx. ap bb fax- aaqufbde + aaqbe ds = me fedx- a mbsf ax- aaq esab +aaqu fbde
  111. 13
  112. 49 = mecdx = amb filx- a ag ed b + aaqude
  113. aa, f + t

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 94r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0187?run=74