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Leibniz-Handschriften zur Mathematik LH 35, 3 A 37, 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: 0.83.

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. 3v); this page is its right half.

The machine reads it as

  1. epe duarum aequationum ejusdem aterae tollere literam, etlissea per
  2. anonem Generalem res utilissima foret. Cui oanis rationitus jam accessi venit et in mentem
  3. simplex duarum datarum multiplicatio per formuras arbitrarias ad tolledos
  4. omnes terminos suffecturas. Suit ergo Ita enim res omnis reducitur ad solas
  5. Aequationes simplicese multiliteras, quae a me jam sunt ad sanonem perfectum recctae.
  6. Sit _ 1D + 10X = 0 et 21 + 20X = 0. Multiplicetur illa per 31 haec per 41
  7. et C X 1I et producta identificentur, fiat 02 11. 31 + 10. 31X 21. 41 +20. 21X
  8. n ve n urro it 1B + IBX + 10XX = 0
  9. pe. bo
  10. 100 sin _ 2, Huc e
  11. 4131= 10: 2
  12. et 22 + 21 X + 20X+ =0
  13. (31 +30X et per haec per 41440X fiet 12. 31 + 113IX + 10. 3IX X
  14. et 22. 41 + 21. 41X + 20. 41 X
  15. +22. 40X +21.40 20.40 X = 0
  16. aa aequationes 3 et 4 fiet
  17. ia
  18. mult plicentur elap
  19. + 13.30. + 11. 30.. 4 1030X
  20. 20 e 411 et u
  21. sunt tollendi termini tees, et identificando
  22. +ee
  23. 0=
  24. h
  25. 2. H- 2240- 20. 4, - 21 10 20
  26. habemut aequationes quatuor, literas si tossendas quatuor, sed in effecta tres
  27. L10. X. 20 31 + 11 AE. 2030) nomo ron L0
  28. Ex aq. 7. fib - H2. 2020 - 1B. 1. 21 1
  29. et fit
  30. = 1B. NC2 - H. 2020 1. 12. 30 - 12. 20 41
  31. roda
  32. fil: 10rt2 E1 10. 11. X. 2736. 21 - 10. 1. 17. 28. 21. 21 - 1. 1 LN. 20.20 +11. 1I. 15. 20, 30. 21
  33. fit +10. 10. 22
  34. H. 12. 2d
  35. unde denique
  36. 10. 10. 1. 12. 20. 22 = 10. 1X. 12. 28. 20. 22 = 10. 12. 12, 20. 20 + . p. 13, 30. 20. 20
  37. Est error snto nam 10 et 2 A 10, 1, H se debent habere ut 12, 11, 10
  38. 21. 20. 22 31 + 11. 20. 2 30(
  39. 41 12. 31: 42. 40 = 10. 30. 20. 3t ex aeg. 6. fit an. 2B. 2 . 10. M 2. =0
  40. it ex aeq. 7. fit +10. 20. 36 31 + 11. 20, 22 30
  41. -10. 21. 22..
  42. (13) Ex aegus. 1 et n
  43. 11. 26,22 6, 11. 20. 2 (3 4 10. 2V. 2) 312.20.
  44. 0
  45. b= 12.30. 21
  46. seu actu ipso multiplicando C. E 10. 11. 21. 22 + 10. 12. 21. 21 g, i1. 1L. 20. 2 - 11. 12. 20. 2)
  47. = 10. 10. 24,32 4 10. 12.20, 22 + 10. 12. 20, 22 = 1c. 12. 20. 20
  48. - 12. 20.20.
  49. seu A10. 10. 22. 22 (1 5) R10. 11. 21. 22
  50. 612, 12. 20. 20 = l10. 12. 25, 22
  51. 810. 12. 21. 21 a f11. 12. 20.21
  52. 11. 11. 20. 22 A10. 12, 20. 22
  53. H
  54. 10. lo. 22. 22
  55. 10 1 21 22
  56. 12 l2 2020 ag. lo l2 20 27
  57. 10 12 2121
  58. 11 l 20 2
  59. 1, 11 2022 b0 12 20 22
  60. Hinc sc Ubi sequentia notanda occurrunt:
  61. (1) Aequatio ultima seu in qua bin Litera est sublata conate mambtis
  62. ita formata est ejusdem Cllrae coefficientes unius aequationis datae, se
  63. habeant eodem modo, ut coeficientes alterius aequationis datae
  64. (2) item Ex eadem aequatione coefficientes termini primi secundi tertii etc. se habent
  65. eadem modeo ut aequationes coefficientes termini ultimi, penultimi ante penultimi etc.
  66. (9) In omni membro si coefficientes ejusdem aequationis pro Capitalibus assumantur
  67. ascendet Capitale ad tot gradus, quot unitatem est exponens maximi gradus
  68. Et haec quidem praevidentur certa demonstratione, et ex serimento praesenti verificantur
  69. in aequatione altera
  70. (4) Hini etiam judicari potest quot oefficientium sit quadis terminue menorum, nempe
  71. dimensionum
  72. tot quol uitates sunt in summa ex exponentibus maximis ambarum aequationum
  73. (5) Si per notas numerales si coefficientes per notas numerales exprimamus seu
  74. per numerum constantem ex ncta aequationali et graduali et rem Actamust
  75. et dige et ordinemus secundum graduales, patet in omni membro notas gradutles fore
  76. easdem nempe hic 11 2. 2.
  77. et notas sequationsales hrarscloni o,
  78. (6) At notuse o notas aeqationale, hoc loco variantur tum eo quod dum
  79. grad
  80. eo quod aliae atque aliae assumuntur tum quod eadem transponuntur, sunt autem
  81. considera conbinationes ad hibendae quae faciunt summam dimensionum aequale summae exponentium
  82. habemus
  83. Et ex. 0, 1, 2 hoc componendo 4 partes
  84. maximorum, hoc loco 2 +2
  85. 212+ oro s ote 2 +2 seu B+ 9+ 8 + 2 seu 0
  86. 1+1 (10+ 2
  87. v +08 +2+2
  88. Opt (It 2 +0,2 ber2
  89. vel transponendo
  90. 1+2(+0+) 0+2(0+2
  91. 0+2) + 1+1
  92. 2+2 (0t0
  93. Nec pluribus modis variari pt. Et quavis conbinatio unam comblansi patitur
  94. transpositionem. Cam sit bimebe pliores duas notas habens exaeqst posterures
  95. hote
  96. ex eq. data 2. Unde inter priores Un inter ipsas autem quae sunt et ejusdem
  97. laequationis nul fit transpositio, quia cum eadem adsit et nota aeppationalis
  98. a
  99. ninit mutaretur
  100. fine el utue
  101. tom nt eadei a ptta in sunis cenia edet
  102. tionis sunt eodem, nam cmispositio noe srius imenbrum reddit b
  103. 1. 20.21
  104. E.B 2
  105. ane
  106. lo. 21. 2
  107. +12. 20.20
  108. l1. 20. 21)
  109. a+630-
  110. 31C + 30d
  111. bE- ad
  112. Sta + 30

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 37, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068250:0003?run=74