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Leibniz-Handschriften zur Mathematik LH 35, 3 A 14, fol. 2r

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: 0.88.

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. 1v); this page is its right half.

The machine reads it as

  1. eamque dividens
  2. sit ergo formula dividens aequatione data inferior quaecunque h+ K X + lXX + mX + n X + X
  3. ejus altimus terminus x substituatur , ety fiet aliqua formula secundum y
  4. cujus insimus terminus (h erit h+. K et Leetme+ ne + e. cujus maximus termi
  5. nus quicunque e, ut co hoc loco =5, fiat (h) - h - e : e = 310, adeoque erit
  6. positr. C exponente in gradus formulae dividentiss
  7. 90= K+ let mee ne similiter pro e ponendo f, et proch) ponendo (2h) fiat
  8. (2h)h - f. : f = gi D = K + 1f + n Ss + ns3, ZF quarum duarum atquationum
  9. ope tollendo K, et faciendo 910 - g1, :, e- f = 920, fiet 920 = l + m (ets) +n (eet ef. + ff)
  10. pro assumatur 9, cui respondeat (3h), est ita eodem modo sde fiet
  11. (34) -h - 9, :g = 912 = k +l9 + mgg + n 9
  12. et 910 -912, :, -g = 921 prodibit
  13. 121 = l + m (er9) + n (eC + Eg +G9). Et ope aequation valorum 92a, et qut tollendo l
  14. es faciendo 920 - 92+ conjungantur valores 920 et 92 a se invicem subtrahantur
  15. 930 = m =+ m + n (e+ f+9). Sed quia adhuc una super est ita habetur et m
  16. sed quia adhuc superest invenienda litera n, opus est ad huc una minatione. itaque pro
  17. loco ipsius g, assumatur d, et fiat 931 = m + n (C+ S+D), et tollendo m
  18. fiet 930 = 931 = n (9- 8). et sit 930 - 931, :, g. 8 = 9+o et firt n = 940
  19. itaque m = 930 - 440 (et musqe ad 940 (et s+ 1) l = 920 - 930 (et () 4940 (et f, et 519)
  20. seu l = 920 - 930 (e+ 5) +940 (est eg1 59) denique H = 912 - 920
  21. denique K = 910 = quol. + 930e(et f.) = 940 C (ef + 19 + f9)
  22. -930 ee 4+940 ee (et f+9)
  23. 940 (ee + eft A)
  24. 5G10 - 920 C +939 ef- 940 efg
  25. generale ergo pheorema huc redit Quaeritur formula aequatione data
  26. 940 e
  27. xx + mX + nX + et c. Ponamus E esse divisorem
  28. inventam methodo explorandi divijores ultimi termini, reliqui coeficientes X, l, m, n, et
  29. interior exmas dividens, h + F L
  30. feriore
  31. inventum
  32. sic invenientur; posito quantitates assumtas variandae aequationi datae, pro _ X ponendo
  33. ultimi termini aequationis datae
  34. meluti
  35. Et fiet 920 -931 = in (f -9) 4 ne (f.9) + n (ff- 99) sit 920- 921, :, f- g = 930, prodibit
  36. terminum prudmentes) ex hypothisi =
  37. methooo
  38. 4+ C, vel v4 f vel Z+ 9, vel V + B, etc suisse e, 5, 9, D, et c. nempe pro
  39. nempe pro X ponendo Yte vel V+ f vel W +9 vel 2+b, etc, et divisores
  40. ultimi termini cujus variationi convenientes in quavis variatione fuisse
  41. Nempe erit:
  42. gto 92oe + 930 ef 040 efg 45 ef g posito non procedi ultra e, t, g, B, a
  43. esque
  44. N) vel (2h) vel (h) vel (4h) etc
  45. 920 = 930 e. +940 ef - 950 ete
  46. +930 = 940 a 4950 ses
  47. + 940 qo e
  48. + 950
  49. (= 910 = 92oC + 930 ef - 940 efg + 950 efg6
  50. +920 2930 G 4940 es
  51. sg
  52. - 950 efg
  53. 9t
  54. f90
  55. +950 et
  56. eq
  57. 95b e
  58. 910 = (h) = h - eE, il
  59. 920 = 910 - 911, :, e f
  60. 930 = 920-9213 21 fg
  61. et significat omnia omnes ter
  62. biniones, sed in secunda columna
  63. sunt solum vra est, in tertia
  64. sunt tres, nempe trium rerum
  65. in quasta 6 nempe quatuor
  66. rerum, et ita res etiam
  67. in teliquis habet
  68. posito non
  69. procedi attra
  70. variando
  71. ultra e,f, 9, B, A
  72. seu non esse diviforem
  73. plus quam qui
  74. Formulam dividentem
  75. non esse plus quam
  76. quinque dimensionum
  77. Columnae ta et valores tot
  78. ib actui
  79. dent, quot gradus acesent
  80. + 950 audformutae, aut sot decedent quod
  81. postremo gu, g2o, 930, etc sunt integri quorum valores erunt stiprodi
  82. sic prodibunt.
  83. rods dement adjicientur
  84. adementur) quot gradus nut
  85. (decedent) formulae
  86. 9u = feh ) h - 5 ., : f (912 = (oh) -h - 9 , :g (93 - (pli -h - D, 18
  87. 921 = 910-912, 32-9 922 = 910-913, : 9- 0
  88. 931 = 920 -9225:, f. B
  89. continuando
  90. Quedi una aequatis Et quot aequationes accedent unicolumnae horum novissimorum
  91. talvram
  92. 940 = 930-931, 2, 9- D
  93. lit eliam ceternis adiicientur
  94. =
  95. (d =
  96. 440
  97. +94

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 14, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068227:0003?run=74