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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 297r

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: 0.80.

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. 296v); this page is its right half.

The machine reads it as

  1. (8)
  2. et fit D = 2. 61 4050 -20. 60 et O = _61 , -10. 50- 20. 60 + 2. 40. 50 -2. 20. 60
  3. et Pob. aequo. fit (9050 - 20. 60) = - 10. 50C 20. 60) + (2, 40. 50 - 2. 20. 60
  4. seu 60:50= 4+20 40 - 10: 20
  5. Verum in eo jam subesse iideo incommodum quol quod 61.
  6. non inmeditur velores et 6, et ita rursus prva prodit
  7. valor 60: 50, quod non est conveniens; opateret enim ipsam
  8. datam princ praetransformare Ilai sic malim
  9. 65
  10. Sit X = 507Z , et y = b 50ZV, requ et fiet
  11. (16
  12. (4)
  13. fit ed - e et 9- et porro 2. 30. 50.50 5 et 270. 40. 50 + 2. 40. 50. 30 - 20. 30. 9
  14. et debet esse (3ol50. (2. 30. 50. 50 + 2. 40. 50, 90-20. 8080 = (6, 30. 5050 et ita
  15. (1)
  16. habetur quaesitum. Calculum reapse faciamus
  17. dx dx: dy = 10X + 20y + 121:, 30X + 40y + 341. sit X= 502Z y 2 30ZV
  18. . Et ex aeq. 1. per 2, 34,5. fret
  19. ais
  20. fiet dx = 2. 50. Zd. dys 8Z epsim
  21. retsm.
  22. 2.50. Zd9: 807d p
  23. 1050 22 + 20. 80ZV + 121:, 30. 50 27+40. 802V + 34)
  24. et per cintem maltiplicando fiet:
  25. 1t
  26. 2.30. 5050 Z dq + 2. 40. 50. 5ZZdqe + 2.341.59742 C5.
  27. = 10. 502 ete (ut in 2) + 20. 6077 et (ut in 3) + 121 :, 30. 50 ese (ut i 2) + 40. 6027ete (aln.) + 3u 2. 3050.502 d + 16240 50803 vd 1 2 341 50. l 810 50. 802 d
  28. et
  29. Ets
  30. vdx + 2.40. 50. 80 230 dZ +2. 341. 50247 -10. 50. 802y -121. 807du
  31. 52. 30. 50277 + 2.30 50, fret
  32. et
  33. et s.
  34. = 20. 80. 80
  35. . 4
  36. 209080
  37. ceff prodterens
  38. esse e (coefficiens ipsius ZZ0d ) = 36 ( triplo coefficienti ipsius e av.
  39. cerellut
  40. cunue dum con 2. 40- Q. 10 seu 49. - te - 10
  41. etstod esi o exp et , e in g. 44
  42. per X et y sic ut fiat dx: dus = 10X + 20y + 121, : 9 30X - 20 y+ 34)
  43. x ex hoc patet semper posse resolvi problema per communem
  44. geometriam, ce nam oeg. est summabilis, et dabit:
  45. 30 4 230. 50. 507+ 4 10 50. 30
  46. 110)
  47. -20. 80. 80
  48. posito Z = Y ZoX et v = y: 80rFo
  49. atque ita resoluta est aequatio
  50. ex5q tunc ex aq. 8. fiet c. Z
  51. uet
  52. et d fit = 10: 20
  53. et compendo causa ponendo - 1050 -20.80 =0 seu 80 = - 10. 50: 20 fiet aequatio
  54. C
  55. Et poterit summari aequatio 7 si modo ponatur
  56. =1056. 80
  57. quad sn effiteruu
  58. et
  59. et
  60. 22VX e si prique ed et in ory. de: dcba. +.. cd +... 51+. co+. explicuissemus
  61. 60,70, 51, 72, 61,82, = 0 efiet fit O = 0, et D =o ergo BD= C secundaeqto
  62. - yX =
  63. +341X + 341 yy - 121. y =0
  64. 1X
  65. 2. 30 XX + 2. 30y 4 2. 3091
  66. si velium tamen calculam nostrum sufficere sine atra traas formatione, sic
  67. x
  68. 10:20
  69. 10: 20
  70. procedemus: Ex: dy = 10X + 207 + 121,: 30x +497 +341 sit X = 502Z et ot y =60 22+ 802V
  71. 412
  72. o
  73. XX
  74. fiat Ax: dus 2 2. 5eL2. 58Z+Z :, 260 21Z + 8074B= 10. 50 37 + 20. 6027+20. 80225., 30. 52, + 40. 6a971 408
  75. tq
  76. 2.40 10. 6
  77. O= 2. 10.50.60
  78. t 2.40. 1050 22∞dy +2, 4050b02
  79. 1) +240.5060
  80. 2. 20. 60.60
  81. G.3d
  82. -2.20.60807 31- 20. 6080)
  83. (8.
  84. -2. 10.50. 69
  85. 21
  86. 8. 8
  87. 2090. 80
  88. 1. 40. 50. 8672
  89. - 2. 20. 6080
  90. et
  91. seu 2. 40.50 +3, 10.50 + 20.60 =0 adeoque 60:50
  92. oso sa dy ueB
  93. L. 2.400-3.10,:20. Quo posito
  94. summabilis est aequatio 6. Ac proinde generaliter possumus resolvere aequationem
  95. differentialem qualis est . Unde etiam intelligimus alias altiores non
  96. posse semper explicando ad hanc reduci, qua non semper sunt. absolute
  97. resolubiles
  98. 6.51. 60

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 297r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0589?run=74