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

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: 0.76.

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The machine reads it as

  1. Lel
  2. si aequatio vy +hg y +hu et. finita differentiatur, cujus termnus
  3. coeffi ubi ipsius y coefficientes dentur per X, sitque terminus summus sine X, et termnus
  4. infinus sine y, patet aequationem ejus differentialem omnes ejus terminos duplicara
  5. praeter primum et ultimum. Termini autem sunt e+1 itaque termini qui duplicantur
  6. sant C = 1 et fitat 2C - 2 Termini, quibus si addantur duo primu et ut nempe qui fiunt
  7. ex primo et ultimo differentiatis, patet aequationem differentialem habere tetminis 2
  8. Hinc si sit aequ. y F hy + ly + m, Ubi e = 3, habebit ejus L fferentialus
  9. ermnrs sex 2e seu 6. nempe yydy ydy, yyax, dy, yax, dm.
  10. Hinc
  11. aequatio. Itaque ep. ut aequatio alta ejus differentiali comparetur alia epa
  12. identificetur alia ejusiem forma opas et terminis
  13. 2C assumtitius literis
  14. rC, sed ipsa tantum exibt terminos e, Ergo oportet ut aequalio
  15. differentiatis huic comparanda hujus differentiali multiplicetur per
  16. equati
  17. sit aequatio y, ea quae comparari potest erit multiplicanda per y+ p, et
  18. forautam terminorum C. Hinc
  19. cum ex y derivetur ydus etc. erit dyoidm 50 huc dyth xh exlta silvenda
  20. Ex p deriontur gyaus, eritus exult ex altaeda idq exallalio facienda
  21. per yy + py+q sed ita Polvenda rarsus esset dy+hax, et ita porro
  22. sed tatis solvenda nunquam habet opus sobutione
  23. parum praestat
  24. td hE
  25. Ergo hoc methodus
  26. hdx + m dy + _M dx,
  27. yg
  28. Etiyay taldus +Lyycht agal F aado F y+ n = 0 fit AG ylyichir y adtalus a tigus du abs atam
  29. solvi pt haec aequatio
  30. seu nyy de + hydx + m dy
  31. quid Ado pyu raly +aam
  32. + alydus ast dus regusdi
  33. comporandada sit data aydus +Bsga Vytxa abdx mult per s.
  34. apBau + hygdy F hByduy +. hsyy dx: a + tByex rap Bdx
  35. a
  36. + ps dx
  37. (9) +a1) ytr tataus
  38. nou+ a y + aam
  39. aequa
  40. hontantum altormula
  41. aeq
  42. cysitob.duio
  43. ndum simple tretir
  44. p et ana td
  45. en
  46. arya 1am ut Begla v3 au
  47. Fdamydn
  48. rghyyclus + aglydys Faalrdy +gu ah ta guydl fac gram
  49. pulo sic uhilitate rans quaer ut tractetur resvelut
  50. pie sic
  51. g
  52. uyds
  53. tfyau rnttusdus
  54. et
  55. Tarsych + faurydl t aerdm
  56. tal pydk + namenk t a mdn
  57. Axyydy +as ly agnotns hystit regodu aalde
  58. Gytagt (atey naleus ryyda t ayul kacum Ahus tansul
  59. resuma fi am= pB - rl ab ypax fit Asax. a=ddur rash- findrir ob gayfit ap - 2ra t a l- h
  60. Egus ralu+ aam
  61. iquaam = _ 2βrh + aBl - hββ - alY ob ydx fit a Fal+ alda -lnydr: BhB dx + (pVaX =) =7 rhet Vt iss
  62. estat ex ex et inde fit 2rhBdx + albdx.h BBdx Lardm +a m an (s madr. 1E. = prhndi Faslnartt eer ralus
  63. srhun aB Can -hB(5 du -alian
  64. 2Prantar Chartr Erha BAraB l raralaβ C
  65. dne est ad
  66. repreducta est ad agq. O,D, 2
  67. ed verror aplculi prorx later fnciamus m=o res irit simplicur sed credo nondem satis
  68. erit (L B- er BBah- araler- Araral
  69. per laeg. 5 datur
  70. An sic (gytar) Shrayt ydh tadt + an =0 fiet ghydus + ahxalys +gyydh + agydil
  71. an eg, fiet hy yan tadl. Fgyaan ficgyais angdyle +
  72. hus +a
  73. Phay +yan tac x
  74. gytar
  75. hy+ al
  76. rat
  77. hydc
  78. rydus elguss
  79. atgdh taarat
  80. sit 9y tar ∞ hy+al se g-h et Y et fi gyus +2agryt aurr
  81. hiys+ al
  82. hleydus +ahlaus + Ryydhaligal.
  83. ah Gdn +aal du
  84. pandr
  85. aatul = . tollumus yydx et fiet hah + c dh. hde = sen-dhDC dh + hde
  86. + anhdue + cyydh Fal ydh dardu
  87. Hyragui C
  88. + aa ndr
  89. seu2s + = seu c: h = logati
  90. sit aequdala th ydus + tit βdu + hhyydxea xhhbdx
  91. L
  92. +ac Gdr sts hβdh + arth logs F t d(hD +hlogtadr Farah anda-aryde racyar 9
  93. aatal - ar (tB) farat ad r logh) + e ur hB+ adr arcyhxadral= hnb
  94. si + fyEC yy + fyaldysragotyde sgagA + a gaadm )nygap) Afynay tagndus etyaaptagalp
  95. gaag sifet nesent fieret pCoppusiri sp glapdu polysap yalt e gam ax
  96. agregdus fyaada
  97. quiti =Ecgpydy + aglody+ agpydl tanqpam 2cg py dus + 2CG p (dys + 2CGpVy ax: a + ECgpDax =
  98. ande raa ar de
  99. n sent a9 (. 3tali + X aa
  100. Fh
  101. arydc et fint all + anh = arHlogh = h+ EB (a-B + aployt
  102. -arcas =Qyyde a
  103. O ayeat
  104. ytas
  105. e
  106. aq = ahgde
  107. +f
  108. fit ab 2cYa al = XC β aadl = 2C) ax quidsitillam dx et Hodus exhac t
  109. fit apa cydys alaue Fgyydc agay dl rsganam
  110. Am - adp. P
  111. aegulus darta inyae g fiat meento cins aep acpraplm
  112. nygesasenus dal dus
  113. sit jam opodata cniydus + cgnsay, FC gnispaia + cgnbaxuo,
  114. 1-0
  115. e
  116. rget tnygnadnt apadus, et roi dividetur
  117. a
  118. Cgn agnat a sit al- cspax cb dx -9 aa + ad =
  119. dg:9+a apip + a dg: g= a ap. p

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 20v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0040?run=74