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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 241r

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. 242v); this page is its right half.

The machine reads it as

  1. pars. rdams schedrasimatis. de extractionibus radicum pars 2da septb 1674C
  2. etsi non satis universalia ubiter, s et credam abias praeterea vias superesse:
  3. stonro ante omna
  4. si chimomions aliquod in se multipletur
  5. va
  6. debin
  7. erum radicos
  8. sive a + 3 aYbC + habe + b bc, sive a + habe +3a + bc sbC, qquorum duorum nommum, Quadrata
  9. sunt: ab +bc + 9a b et 9a bc +6 a b c + bc quorum differentiae sunt:
  10. a - 3a bc + 2 ab7 = b C qui esst cubus ab a = bc. Genemliter Clapus
  11. et smpliius res ita euum tiaei potest: d + e cubus pi dd + Bdie + M + C erit d’ +3de, H
  12. 3de + eH rubo ab d - e., suc d + 3C, d, H - 3d + e, C, B, p cubo a d e
  13. vel d Theorema est per elegans, sed qua arte sit moculum, id est quod nosse velim Nisi
  14. id forte per ind inductionem scontiga, observatione in numeris facta, quod sane saepe ad thecrem ata
  15. invenienda commodissimum est. Aeud Theorema: Binomium multiplicatum per differentiam quadcatorum
  16. partium producae aliud binomium: in quo differentia quadratorum partium sie numerus ubus ianultiplicetur
  17. a + soc per (4) a 4) bc fier: (4 a (4Ibca + () a ) bc, bc Quorum partium quadrata a se invicem
  18. subducta relinquunt a- 2ab +bCa - bc 2a bc - b2 sive : a - 3a bc + 3a bc - bE
  19. Elegantissimuta est hoc quoue theorema. Esto jam binomium 2 10+13800SFE ex qua
  20. est cubica; 2249 + sur 53800SI2. , hatius hoc nullum continet fractum, et alterum partem habet
  21. rationalem, secundum artic. 1. et 2. Sed et squadcatum pantis irrationatis, rationale est; cupdum artic. I.
  22. Quadrata partium habent sunt 501 7b0a
  23. -230e0L
  24. 818IV2
  25. vdendm est ergo an ex qe17068 extrta
  26. ex qua extrahenda radiim cubica, fiet:
  27. Obiter annotabo Theorema memirabile:
  28. Omnis numerus cubus Terminatur in numerum,
  29. qui est differentia ultimi numori radicis a denario
  30. sematium
  31. vel idem cum ipso altirmo numtr rudici quinadium
  32. alterminatur in unitatemretiam cubus termi nalitur
  33. si Eosiger
  34. quinarium, septenarium, octonalium, rubus ter-
  35. minabitur in ejus differentiam alimia denario.
  36. Hinc monus cubus terminatur in seplenatium
  37. 1488. 8
  38. et3800512. quolum differentia: 2 121088
  39. 274 + S- 12, nise cubere dabu.
  40. est psolum Juuma
  41. 2744 + 588 s. in +4 - 504 + - 1728. Vem (Y 1728 12S.1
  42. 2240 + 600 s-E, vel 40. f tror 1.3 ex qua quantitate jam radicem
  43. Cubidam exhahemus. sane omnes habet terminos fractis carentes et altrum ex nominib,
  44. srationale, et quadratum utrisque nominis est etiam rationale. Debet ergo radio inbica
  45. (+ ad
  46. 14a + f- 12 bc. in se cubice ducta dant: 2744 a + (588) (3) 196 a f- 12bc - () 168 abe
  47. exhasi posse ex differentia quaddatorum partuim
  48. Et tiet: - 744 a
  49. (4-BLes abc
  50. (2240)
  51. B 196 a s- 12bc
  52. (588)
  53. + 12 bc
  54. (600)
  55. +L 1n8b2
  56. Et quadratorum
  57. unde otrihenda fradio cubice
  58. partium hijus binonius 33760d est cubus, a a differentia quadratorm partum vinbum, quod est
  59. Pone sim datum esse numerum: 2240 af +b0o L- 12 BC
  60. Extralendi binami radix, seu est cubus a 196 a + 12 bc seu es cubus a Nam:
  61. av 6abc rgab, +A9a bc Y, 6 a V5 4b2c3
  62. F9aVc 16a76C - b25
  63. a + +bC cubietoens: a 3 a V+bc ∞+3 abc (bC SZbC, beretesse XbC (+)
  64. cum ilbeat esse a a bc +9ae u
  65. radicem ab
  66. + 2a Y 4 bc. Quadraturi prions: a +6abC +gb posteriors 9ab Fabeq
  67. auferendo unum a sudouaorum padialou ab atterofu: a 3a bC +9 abC +63. Unde pates
  68. sive a+ 3abc
  69. jumsomendi ) + pate regulam supra demonstratam n procederte n binomid quae irratio en injeginatiam stiment
  70. Sed ideogl eo s dissimulanda fucrit. Quasi iinclusum in isa radise. Anpotius uandum am
  71. constat ipsum- in summam 2240 ingrestum) ejusque quadatum esse percnsensuens ab + 6a bc + 9ac, adeoque
  72. quad binomium cmpio aetrum concipendum esse fingendum et 3a- bc, bc, vel 3a +d 1b Aaneltum
  73. Dutique differenta ert quadratorum patium erit cibus, sed quia hac dignosci ex jam facto non potest
  74. moiteile adeatuo tegerus sitonn ad vectansiven ad inignaus apescare
  75. = 2240.
  76. 89600
  77. 4 4 8
  78. 0 760
  79. 64,
  80. a si
  81. i
  82. q
  83. 196- 1
  84. 580
  85. 125)
  86. iret
  87. in 1s
  88. ado extrahend
  89. a 8818112. nempe:
  90. o sit cubica
  91. xquo radio extrat
  92. 4860
  93. 69600
  94. 448
  95. 000c
  96. 3600
  97. differentia
  98. 881 8112
  99. 360000
  100. a b habet
  101. a +6a bc + 9ab
  102. F9a bc -6 a bc +b2:
  103. +3aebb
  104. superest difficultas, quod
  105. a = 3 at

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 241r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0481?run=74