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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 197r

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.

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The machine reads it as

  1. in 205 f 1643
  2. 24 2da= raydy + 2 xx dx + yyd
  3. problem
  4. in literis
  5. Sit y = ( x 10 + uX + 12XX + 1X + 14 X + 15X + 16 X 117X ri9 X cu
  6. 2 γy =
  7. Efytus
  8. Kyduy -
  9. +
  10. XX =
  11. - aa
  12. seu 1.
  13. 11010 +ll10 X +, 10 M2 X , H 1on X + 10IE A. 1015 X _ o. 1BX 10. 17 2 L. 0, 8X et
  14. 7, 71. 11 + 11a12 R. V1. 13 2R. 11.14 X. 11.15 + X. 11 1b R. 11 17
  15. .12. 2 B.12. 13 9. 12. 14 f. 12.15 A.tE 1b
  16. 13.B G1514 4 13.15
  17. )4. 14
  18. +2 11. II 3. 11. 12. 4. II. 13. 5. 11. 14. 6. 1. 15 2. 11. 16 B. 11. 17. 9 11.18
  19. FLNX
  20. 4,12. 2, 5. 12. 13. G. 12. 14 3, 12. 15 812. 16. 9. 12. 17
  21. R13. 1 13.14 8.1315. 9. 13.16
  22. assumamus 10 ut datam, quamtaalibe quale in libet
  23. si sit 14 = 1 ecit H= L
  24. Melius sic
  25. Gsi, gy = 20 + 21X +22X + 23 X + 24 X 125 X + 26X + 27X+ 26y
  26. et
  27. + ydy = 1 21 +2. 22X + 3. 23X + 4. 24X + 5 25 X + B. 2bX +7 2y X 1828X + 9. 29X ex
  28. 4 ZXX
  29. = X
  30. sit 2 = - 20 - 1 . F n=
  31. Ergo 2 a 10 B, 1. et 10 24 = -23: 4 25 = + 23:A5
  32. et 26 = 23:94, 5, b 27 = + 23:, 4. 5.6.7, etc.
  33. Ergo fint Lgy = 20 + 21X +22X + 23X - 2 X + (23X- 24
  34. 4
  35. sit 0 = (D ( = X. L X + L X - L X + 1- X - .
  36. Ergo
  37. 1.2
  38. 23 23, 23
  39. superest ut iaveptigemus 20, 21, 22, 23
  40. possumus antem jactie 20∞0
  41. fet: 21 = -20+ 1,: 1
  42. 22 - +201, :2
  43. 23 =13) = 20 (+ L. Ergo si 20 -0 fit
  44. 2.3
  45. 23s
  46. 1.2.3 1.23.4 18 3.815 1.213. 4.5.6, 1.23.45.b.7
  47. Lyy - 20 - 21X - 22X ( X) = 12. 3V - 23X + 3X (=X3)
  48. 2.13
  49. er
  50. G 10. 11 42. 10. 12F +3. 10. 13Y, A1C.14 PY. 1D. 15+ + B. 10.6 +y, 101, X + 818. 5X 9101g et
  51. 1.
  52. 8. 19.14: 9,14. 15
  53. 4.5 4.5.b
  54. 5
  55. ui etiam 23= 0 (do- 1X+ X etc. Ergo do= 1n B. dp 72 1. 23
  56. et si faciamus 23 =0 res redit ad ordinarias
  57. et fit 2gy = X - = X seu yy = 2ax - xx quae est aequatio ad Circulum
  58. Nam ut expediamur: G ydy = adx - x dx visen dy: dx = a -X,: y
  59. ag = - 9y = (E aa) - 2ax
  60. seu fit 2ax = XX = gy, ut ante ergo haec aequatio resolvit, problema
  61. Hugenianum nempe dy: dx = 2aa -XX = yu Idem tamen
  62. i
  63. pote 2 g 30 Cyy 4 +2- 1X - 20-1 X = 20, v. posito 12V ess num.
  64. qe
  65. egus =ogux Aux(x 21. 6V - 23(6X + 13. 3XF BX seu Lry - 10 LL 1X C. ur 2X -20B trox. 2X
  66. seuseus q sit
  67. dy 2.20+2X. X 220
  68. tr umme
  69. +67
  70. ecipitire
  71. Htinc si saciamus y 20 = L firt y9 = 1, + 2X. XX- Eenmlit sd B, 2. 20a = n fiet gy-
  72. 220
  73. a+
  74. et - x esse loga.
  75. mum
  76. Senpotibr sorid 10+
  77. Sin fatiamus 202 1 46 = 0 seu 20 = -5. fiet 2yy + 5 = 5
  78. Hliud problema ejusdem:
  79. e Gu
  80. posite Lex esse Nonmasius loqe est x
  81. uia s
  82. na dy dy: dx = ax - Xy -ay,, aa + Xy
  83. l, aa dy + xydy =_ xy dx + ay dx = ax dx aa dq + du + dx + dx = a dx
  84. sita y a50 + nX + C X + 13X+ 14 X + 15X + 16 X + 17 X + 18 X
  85. E xHds Am +21 1323 1424 +5e 16. 2 1x 17 12 1919.
  86. xydys = , 1. 21 +2. 2 1B. 23 + 434 t5. 25 tb. 26 +7 27. +8.28.
  87. y
  88. sit yy = 20 +21 X + 2L X + 23 X 424X es
  89. 2ydy = 121 + 21X +3 23X +42 4X 152sX e
  90. 222 = f.11 +al2 13f. 13 = -7.1. 12- 2. 19. 1
  91. -13. 23 = 12+ 13 +4. 19 = 8. 10. 13-11. 12
  92. 10 +1 +12 + 13 +14 + _ + 1b +17 -:4. 24 = 13+14 +5. 15 = -1014. 3 11. 13- +12. 1.
  93. aadue = 14 5. 11 2. 12 313 4.14 5.15 646 717 8. 18. 9.19
  94. Xydx =
  95. = axdx
  96. a
  97. 6
  98. 5, 25= 14+15 +6. 16 = -15) 18. 15 - (5) uil 47 1)1219
  99. s et puo ponendr rutorem fiet dea rursus ex aeq est rydus
  100. seu ydy = 5dx 1aD sydy = sax - s v dx, seu
  101. Cr 2ytoa na ampex. ds = sdx = hyyen Gd
  102. idx -Exdx de vii hud e rytus. id rxdi xdx
  103. 5u = 2yy-
  104. d
  105. yy = -10 + 10V. et x = (dv: 1 - Eydy = 10dv. seu ydy = 5dV
  106. yy21.+ 2x - Xx - v iam dxX = 5dB: 1. B. Ergo als dv= dx- vd
  107. 2
  108. 17 Seplemti. 169
  109. 1d 20geF H = H+ 1
  110. Fia = 11
  111. 1 = 2 = 103: 210
  112. 48
  113. 2
  114. si I1 = 0 fit 10 = 1
  115. Ergo peuinde est ac
  116. si fecissemus x+ dZ
  117. Zax + aZ + Lxraf aadx
  118. Z+ x
  119. si 1tn num,
  120. et l log. fil.
  121. fieret Z=yy
  122. = posito 1-H
  123. esse num. et
  124. X esse logs
  125. log. T+X
  126. num. et
  127. 1X LX +L X etc
  128. =-N. posito
  129. l+ P + (3 +
  130. Ergo si con numfils 12 123 723.) eCC
  131. 4. 5. 6.7
  132. 6+ 1 -X
  133. si
  134. CA=
  135. BM=-- (
  136. 1. 2. 7. 23
  137. Ergo 1-n num
  138. et al log. fiet H= l- 12

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 197r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0389?run=74