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Leibniz-Handschriften zur Mathematik LH 35, 4, 1, fol. 8v

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: 0.81.

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. 7r); this page is its left half.

The machine reads it as

  1. 2cox l - 200 l
  2. at-co elay. (1)
  3. sive 2co Xl - col al - co2 13y. a (2)
  4. Consideretur et etequatio D, nempe nempe aI p 4Xy Cd + col ()
  5. ulude rurous A i resolutio;
  6. +n
  7. (4
  8. po at data in g est a f, al n. Cx arvit
  9. um puo ac inseratur ejus va lor inventus ex aeq. 4, fiet:
  10. 260 Xt -col c0 aXyHI, L. y sed hoc male rediret
  11. enim aequatio C
  12. quid ergo: P 0) po ponam
  13. Ponamus 200Xl - 26 5al sco
  14. et ex aeg. 1. vel. 2. fiet:
  15. juugen
  16. 1- v.Aeg. (6)
  17. Acq
  18. (Ex Aeq. (2) ettem aius fieri potest analogi sinus:
  19. 200 XI aty a- al l.y p co yd Mu
  20. fingamus a H fO B olay
  21. oty (5)
  22. et ex aeq. 7. fict: 2x ape yut
  23. 2pX - al p, pp ot
  24. Resumantur aequationes C et D.
  25. ejus valore
  26. et ex iis elidatur primum Co, substituto
  27. 2 t nimirum in aeq. 3. nvel d, fiet:
  28. Satiffactum rari
  29. Aeg. (9)
  30. 2xy Co1 col AXyp = 4Xy e + pl - pyl (Aeq. 10)
  31. Idem fiat in Aeq. 1. quae tenebit lacum Aequationis D. facta scilicet
  32. ex ipsa et D.. Sufficit enim ipsis Aequationi 2. et D. sat vel 1. et 3.
  33. Salisfieri ut fiat Aequationi O et D.
  34. aliquor
  35. At aequationi Est enim Regula
  36. generalis, si satisfiat dubus aequationibus factis ex totidem propositis
  37. etiam ipsis propositis est satisfactum. Satis factum autem est
  38. Aequationi 2. vel 7. per aequationem supposita aequatione 8.
  39. stequation
  40. et fiunt tres aequationes novae, quibus salisfaciendum est, D vel 3. aeq
  41. Aequationi 8, et aequationi 9.
  42. Satisfit autem aequationi
  43. PYHPC+ uoties aliqua alicuus literae ejus ope reperitur valor puag aliqua
  44. indep hitera ejus ope eliditur. In numeris opus est literae illis valorem
  45. +2mpl + purum obtineri
  46. Elidi autem potest litera co, ope aquationis 8.
  47. quod fit facta aequatione 10, ex arq. 3. restant ergo duae
  48. aquationes
  49. incognitas
  50. 9, et 10. quibus est satis faciendum, per tres
  51. pro _ al in aeq (9). substituatur ejus vator
  52. ex Aeq.) 10. fiet: 2pXV
  53. exx
  54. 07F
  55. Ary: lar Py, 2Xy C. L.3
  56. Aq (11)
  57. V. (teg. v et ferex Aeq. a. talis iteu (13, ut, = y p (Exy +l) ary. Ary
  58. Et ex Acq 9. fiet Aey (14)
  59. fui Aeg. (18) 2Y
  60. H1
  61. aprl prt al pl- y
  62. vonamus B, st.
  63. na gl. atey (15) fur ex Aeg. 14. sequens
  64. 1
  65. n
  66. v
  67. e
  68. XP faciamus Aeq. (17) n B pl. vel - a(3 Opl ly:
  69. u
  70. DL P + Y. Hoc ratore ipsius p. Inferto in aequatione 13, fiet
  71. aequationum eyeoter amutu 19 pes B puur, fer. -2rl + βB14 (37 1, β0 et l + βyl ry + aBr
  72. VOP3. H0. excerpantur termini in quicus 8, fiet itegt 21) Byl +)L
  73. fimet palorem ipsius V. et residua erit aequatio (L2) in qua valom Y inventus insert
  74. 6Br
  75. V y1 eync
  76. Bry+VaB310. cujus aquati onis ope invemetur Y
  77. orese equatum
  78. (G -(2, l + et + yl (2Yy) +Dy + y (9ry- ary mellipertum aequatu
  79. +)al +Vop
  80. quatio quae
  81. Pone Xp+
  82. arl
  83. sequitur enim ex Ponamus Lal3
  84. Y posse proavitu
  85. nesi quod est
  86. surdum
  87. Latenmirabile tcys. 9
  88. quiddam in hac.
  89. multiplicatasu
  90. Carci tae
  91. tari calculo sunt Aeq (16) 2rX - n1
  92. ione

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 1, fol. 8v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00067996:0016?run=73