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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 147r

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: 0.77.

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. 148v); this page is its right half.

The machine reads it as

  1. assumta
  2. sit equatio ad curvam Generalis Homoeoptota 2, cum sua differentiata 2. vel 3
  3. O= 100 + WWBX + 120X, + III Xy + 130 F, + 121 Xg, + 140 X+ + 1BIXy, + 122 Xy vtsoX, BXy raexy iili p
  4. o2. HolX FIB. ZA L AoXHr +, 121 XydX F 1213 dx + 3 130 X dx +, IXy dex 4, 131 Xy dX + 13 dx + 4140 X dx
  5. ydys
  6. rydy xii ydy xydy
  7. rydus xdy
  8. xyt
  9. Pay B (142 Xg + 123Xg G
  10. 43 132Xyax +Ze ex +4. 141 Xydx L 141y ex +G150X dx +3. 133 X y ax L 4 14C X ytx r2.192 X u dx. + 5. 15VEydx t 151 dx + 6. 160X d et
  11. Xy dy Xyly Ashay xdy
  12. 5
  13. Ndy x xyay grdu nyay xdy y’ay
  14. Hade conjunbrequatio t Hini ex aeq. q 2. quaerendo
  15. valorem ipsius dy: dx fiet dyrdxL m y
  16. (3) io + myL oXLA EIBIXy +12II +3130X L2 M axy + 3. 131 X y 4 B31 V q aoX F 3. exg r2. 32 +412 Xy t 4 1y 5.1X et
  17. x notMIXH oy 42. 121 Xy + 121 X L 3. 130y + 2MXy + 3. 130 Xiy +131 X +4, 140y dy + 3. 132 F j t2. 1 Xy (t. (41Xy +1 41 X +5. 109 etC
  18. se Huic jam aequationi 2 vel 3. conjungatur aequatio differentialis, generalis, homoeo-
  19. ptota data, quae redacta ad simplex, seu in qua dy: ex non ascendat ultra simplicitatel
  20. quae redacta ad valorem sic sabit - e abo + vor vr horyt f ubi notandum in oge dipirqui ubi disse cnliet p b
  21. demntgoXtg + ZIIXG+ Seax qui + 3EXytq12
  22. lequitu partemm sortiorem ut, et xyxadbi inxid
  23. Ly (4) 200 + LVBX + 21y + Zuxy+ 220X + 202y + 2EIKy + 212 Xy + 23OX + 2039 + 222 Xy + 231 Xy + 213Xy + 240 X̀ + 204y et
  24. dx 200 + 201y +210X + 21IXy + 220y + 202X + 221 X 1 + 212 Xy + 230G+ 253X + 222 Xy + 231 Xy + 213 Xyt 290γ 1204X et
  25. Ubi notandum inaequatione F. distingui quoad n ex pressiones coefficientium; nempe
  26. ubi differentialis x vel dy, sequitur partem fortiorem sul in XGdx ) si scilicet oquater 4
  27. dy-
  28. ud nligiem (si scilicet aralogra 4 ad aequationem redureritur) ibi in coefficiente ex
  29. duobus numeris praeponi majorem) hinc coefficiens hujus formae est 221, ubi ex posterioribus duabus
  30. potis inter has tres 2, 2 1 nempe ex 2 et 1. praeponitur 2. major et scribitur 221 X ydx
  31. Xist dyue.
  32. sed si differentralis sequatur debiliorem ut in Xy dx pai praeponi numerum minorem, sundel
  33. lujus coefficiens est 212 et seribitur 212XY ax 7 Quod si aequales sint X et y adeo at discerni
  34. nequeat quam partem sequatur differentiatis tunc etiam numeri sant aequales (ut in 21 xylx
  35. Kydys
  36. Superest jam ut aequentur inter se valores 2et ex ag. 3 et 4. quod al fial
  37. felicius et universalias pro aequatione, 3, prius scribamus aliam generaliorem ad modum
  38. aequationis 4, ne scilicet calculum finstra nobis reduamus difficilem e ac speciulo
  39. dyS) 200 + 3∞X + 3My F3IIXy L 12OX + 302yF G EIXGA912XY 4 330X + 303y 4 3reX Yy 533IXy + 313X9 1340 X + 304 etc
  40. ax 300 + 310Y +301 y +3 11Xy +320y + 302X + 32(XG F3I2Xy +330 y + 303X + 322 Xiy + 331 XY +313Xy + 340 7 4304 X et
  41. ) Horum inferius fit ex superoore mutendo 3 in 1 in antepe
  42. ma
  43. Aequando iptur vol ubi 300 310. 30L 3F
  44. nota, et penultimum
  45. papsat genultio
  46. amim
  47. tequo
  48. eatum
  49. ti
  50. q
  51. Ubi 300. 310. 301. 311. 320. 302. 321. 312. 330. 303. 322, 331. 313. 340. 304 el stu
  52. Valent 110 2.120. 111, 2.121. 3. 130. 121. 3.131. 2127. 4,40. 131. 3. 132 4.81. 2. 137. 5. 150. 141, et. multiplicalun, per rotam s ecto pemin e rus
  53. lus fornis
  54. Aequando igitur valores duos ipsius dy: ax ex 59. 4 et 5. prodibit aeque
  55. duobus invicem ductisnu
  56. indua inersi
  57. 200. 390 + _o 3or X 1 201. 300) t ef 3a Xy + 220 500 X1 202 30y4 22130X y 1 et 2 21039
  58. In aeq. 5. haec lex est,
  59. ut coessicients anus affectus signo t, ulter affectus
  60. 0300 + 210. 300X + 211. 300F) F. (unaaffecta simoplus altera suino minus; in priore pearu enultium aota refert potentiam ipsius x ultima ipsius
  61. 32
  62. =200. 304
  63. D duorum nomeroii posteriore cuufficiense contra sixota posterior unique numeri penultima
  64. addituducatur it alterius anterennetimat et viceversa, et sit prodeunt duorum literaru
  65. N - ZM. 300 Xy
  66. Xret 300
  67. estermina
  68. es. Jiincissine
  69. d
  70. ntum
  71. majorem
  72. totus ed Enteo praevider
  73. prduc
  74. +200.300 + 210. 300X = 211 300Xy F 220. 300X + 221300x y + 230.300X, + 222. 300X y + 231. 300 X y L 240. 2aY. 1231300Xy, + 241300X9 + 250300 8 es
  75. F201. 300y
  76. tr02. 300G. 4212. 300 X i +203. 3009
  77. +213. 300714204. 30 f223300X7 F214. 300 X., t2o5. 300 )1,
  78. E2E 310XIL +213. 3 1 X, t2013 0y,
  79. +200. 30 y +210. 310xy +201. 310 f ,2 1BX 4292. 310y 1221. 31Opy + 212. 310 Xg, 1203. 310 1231. 31. X 1240 310 Xy
  80. 4230. 310 X. 9
  81. =200. 301X L201. 39) Xy 1210. 3015 f 2u. 301 p ( B , 220. 301X +212. 301X 1f + 221. 301 p 4 +230. 301X, -2. 301 X 1 +231. 3015 a2o 30 X
  82. +220. 310X8
  83. +217 301 X. y
  84. F210. 311 Xy
  85. 4201. 3II Xy,
  86. 4203301 7
  87. A211. 311 Xy 4220. 3I1Xy
  88. + 202. 311 x
  89. 1200. 36d x + 201. 3027. p . 1210302D 42I. Vgris = 21. 25 gry. tnarp. 2I22B, tey miptus +uorer
  90. 2 20. 320y, 1 20. 32o X. 12013 20Y3 +220. 320 Xy LN. 320 X, 1or goy 1 2 i1. 3cor C.. 1e12. 2dop. ) tor Mo
  91. In hac jam aequabione tolli
  92. +200. 321Xy H, = 20.321 X +301. 321 81y
  93. possunt omnes formae, sese eodem a200. 312Xy
  94. modo habentes ad X et y, et ut
  95. reliquum ibitipotest per A9
  96. =201. 312X7 1210. 3128 f
  97. +200. 3IXY
  98. =20. 330
  99. 24b0.237
  100. + 260. 322X7
  101. t213. 201 X 9. 1 264. 2t py
  102. +221. 311Xy +230311X
  103. 4+212. 311 X 3 103. 311 Xyt
  104. 1203. 392
  105. 1230. 320X
  106. :21. 321 x +202.321Y4
  107. 2220. 321 X
  108. =211. 312Xy, =220. 312XY
  109. 1202. 312815
  110. 1210. 37 0xi 120121013, = 28. 230 X Fes. Hoxu X 202 30
  111. =cl. 303 (. 2 210. 103F a 3 202. 363 p f. ; 1211. 303 F h 32Eb 233 ,
  112. 2 200. 213
  113. +200. 340a
  114. 1210, 322
  115. ro
  116. 20 3t F. (2di vro. 331 Xyt
  117. L 21. 313 X
  118. 1210. 33 X
  119. 7210.340Xy Y201340y3
  120. +20. 304 25 F2f1 304 Xy 421. 3047
  121. =200. 213 Xy, = 200. 314 X y X180.305
  122. troo. srais
  123. coneisis ircetsod
  124. = 200. 3317 y
  125. xy, ry, xyt, xis etc. et
  126. es prodibit 69. _i 7

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 147r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0291?run=74