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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 185r

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: 0.82.

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. 186v); this page is its right half.

The machine reads it as

  1. AB
  2. Sublatio Terminorum ex aequa
  3. tionibus.
  4. X + 21 =(2) = y
  5. XX + 1X + 12 a = (1) = 0 sit Xt b = y fiet x a y b sit X + b () y vel
  6. X = (3) = y - 41. Ergo ex aequ. 1. siet CbGbb yy- 2. 21y + 21. 21 = (4) =0. Ubi ut
  7. + 1. 11 y - 11. 21
  8. tollatur terminus secundus fiet - 2.21 + 1. 11 = 5) =0 seu me =12 a seu 21 = (6) = 1. 11: 2. Sed
  9. idem generalius praestari potest. sit X + 1X + 12 a X ete = (1) = 0 sit X + 21 = (2) = y
  10. seu X = 3) = y = 21. Ergo ex aequ.1. per aeg. 2. fiet y +C, - 21 y + e. . 1. 21. 21. y etc.
  11. +11. V + 11. e- 21 y +11. e. C-1. 21.21. y etc. =4) =0 sufficit autem uos summos aequationis
  12. terminos explicari, et quidem posito tantum explicationis initio, duobus scil. terminis altissimis
  13. in termine explicando s primi explicatione, uno altissimo in termini secundi explication
  14. et fiet: - 21. C: 1 + 1 = (9t out tollatur terminus secundus seu y adeoque eit 21 = (6) = 1.1li e
  15. quae est regula generalis pro tollendo termino secundo
  16. Simili Methodo quaeramus aequationem generalem pro tollendis terminis
  17. secundo et tertio, assumendo aequationem, compendii causa, in qua jam terminus secundus
  18. absit, quia id quomodo fiat jam ostensum est sit ergo aequatio X X + 12 a X r etasto
  19. it sit erL)C Q XX + uX + 2 a = (2) =B. Ergo X F EIX. + aX ) Xv.
  20. Ergo XX t 3X + 21, 2. 4 - (3) - y 22a +21 2t:4 seu X c tury- na +3. 2 4. Ergo
  21. aequ. 4 explicando aequationem + fiet quam multi Jam generalis methodus tollendi
  22. pteram duabus aequationibus communem consiptit in multiplicatione quadam per arbitrarias, nempe
  23. si velimus tollere _ X ope aequationum XX + 11X + 1a = B et X+2 - consistit in eo ut unam
  24. quamque multiplicemus per aequationem arbitrariam altera inferiorem, et fiet 3oxx + 3O HX+ 3oa
  25. 0 et et fint et quidem priorem per X seu 1, posteriorem per X+41. A ex illa fier
  26. et illa man et prior manebit, ex posteriore fiet XX + 21 X + 41. 41 =0 quam subtrahendo
  27. a priore fiet 1 - 21 - 41 =0 _ sen 41 = 11 - 21 et fist 12a - 21. 11 - 21 = 0 seu 12a - 1. 21 + 21. 21 =0
  28. ptro guadibus XX X, et X, ojunctis, fiet: XK0X + 1X + 12aX + 13aB = 0 et 2XX + 2X + 22a = 0 fet
  29. =0 et similiter
  30. po mustiplicetur per X+ 31, fiet X + 1X3+ naxX + BaaX
  31. 31 +11.31.. +12. 31 a0 + 1331aa 9
  32. postercor multiplicetur per XX + 41X + ara A X 21X B a XX
  33. fiet:
  34. 41. =21. 41.. - 22. +1a X
  35. -42a. - 7. 42 a - - 22. 42aa)
  36. ho
  37. t squ
  38. en
  39. 1(P 1+ 31 = 21+41 1331 = 22. 42 12a + 1. 3I = ua +2. 41+ 42a 1a +12. 31 = 22 31 + v. 42
  40. XEC a~ 31 = 21+41 11 = 22. 42: 13 fit XF13. 2(+ 13. 41 = 22 42 + 11. 13
  41. a 31 = 41 + 21 -11 11. 31 = 11. 41 + 11. 21 -11. 11 = 22 a + 21. 41 +92 a = 12 a 13. 31 =13. 41413, 21- 11. 13 = 12. 42
  42. 13af + 12. 31 = 13a+ 12. 41+ 12. 21 - 11. 12 = 22. 41 + 21. 42
  43. 42 - 13. AI = 1. 35. 22 - fn. H 4H 3t, a Ergo 41 =
  44. _I.
  45. cas tres aequationes, in quibus tollendae 41 et +2, ordipemus.
  46. FI. H oraat 2 + o1 2I-0
  47. 103a
  48. u
  49. rII. 1120aA
  50. +10. T2aa. 20
  51. dctI 12 t2 a3. -0
  52. +11. 1.70~
  53. a vel per compendium
  54. 51. HI +50. 22 + 52d =0 61. 41 +6042 +62 =0
  55. 4 14
  56. vis ea
  57. 71. 41 + 3∞ 42 + 724 =
  58. A 42 = - 51. 41 - 52a,: 50 = - 61. 41 - 624.7:60 et + 516+1 +5260 a = 0
  59. -61.50. 650 62
  60. seu fiet 41 = 50. 62- 52. 60, : 51. 60 -80. 61 et 42 = 51, 62 =52. 61, :, 50. 61 - 51. 60
  61. et fit 50. 62. 71 = 52c60. 71 = 51. 63.70 + 52.61. 70 + 51. 60. 72a = 5. 61. 72a = 0
  62. quam aequabionem inter pretando, prodibit.
  63. obes
  64. egH2 - (11 21 122 42 - st
  65. 2
  66. ta
  67. F11. 21 22. 22
  68. 11. 1
  69. +1a
  70. +12 a
  71. J.4 +121 2- 19. 21 +(A (22) M a -(ar 13) . 12
  72. L2GI1. 13
  73. Hia)S
  74. = 1. 2a. 22 1). 21.
  75. + 1. 13a
  76. (= 11. 17. 21
  77. (41. II. IL
  78. - 12. 12a
  79. ∞13. 21 a
  80. etL
  81. +12. 2
  82. 112. 2
  83. duia ld tiga
  84. =0
  85. F11. 12. 21
  86. F11, 13a
  87. Fstih2. 21
  88. quae duo producta
  89. invicem tollendo
  90. prestat pro
  91. ponere pro, 11, 12a, 13aa
  92. porere na. naa, 1a
  93. Et pro
  94. 21
  95. 2
  96. +12. 21aa
  97. + 13 420
  98. a, 23ga
  99. 1230
  100. ta o
  101. calcul
  102. erit ordi
  103. natior
  104. Re sumamus a sigio N

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 185r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0369?run=74