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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 17v

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. 18r); this page is its left half.

The machine reads it as

  1. Remergo ita rassumemus:
  2. Aequatio proposita reassumatur pro , substituendo
  3. hl sulstituende aquationis propositae: In- 15 M
  4. Ventelur diuisio per n3 - 13
  5. pro 1 h substituatur Vn + Vp
  6. fier m
  7. 15l m
  8. set fier co
  9. 2 4 (24 0.
  10. + R1
  11. Inde aequatio inter
  12. An ergo rectous ita:
  13. confeenda cum 4
  14. = 4(2. p0.
  15. -u q
  16. Pone quf ex postenore
  17. Cm co confeaenda cum M -co m + C +2
  18. 1912 (1f- 8, ef - t
  19. (c0) - 2coV- V
  20. Sed restat invenienda T.
  21. nt - 1 tlso + 125A +af astt 1 196
  22. lf.
  23. 49D 19b 7 ayo
  24. + 30(37
  25. +pZ20
  26. .... + p
  27. sideo Determinationum obtinendarum causa, rectius rediri ad aequatio irrationales
  28. Igitur Una determinatio est:
  29. M p 4 ml + - b.
  30. 508
  31. Altera m Y X + 1s P M + 41
  32. Igitur si arbitraria M, talis sumatur
  33. ut quadrat quadratum ejus vel quadrato quadratum, his quibus majus esse debet, sit
  34. aequale, erit valor assumtus omnium possibilium minimus vel maximus
  35. Ex prima aequatione fiat: m - 4l M + al , 6C fict +m +2l p1S6.
  36. sive M p + l 56 + 2l, seu m 1o
  37. es
  38. qu 4 2 5l + 41 10l425 (2
  39. Altera aquatio dabit. M+ - M + 225 lt (225 (1 4 1t2 18) 3372
  40. Ego i m () c
  41. 5337
  42. Ergo- n (4) ( Sor 4 15V et m, la(CH D So +15
  43. Seundum primum requisitum, ponamus M . El fet 25 l 6t.. in integris valor 83 4tor
  44. ipsius m, omnium possibilium minimus affirmatious est 5. ponendo 4 esse +.
  45. Utemm autem nunc quidem affirmativis ne in novas difficultates incidamus:
  46. Altera determinatio dabit hanc Aequationem:
  47. Ergo (F) m (+
  48. ) 15(a
  49. m -15(V + 225 (4 ( 337 17
  50. 12 520E, sive m
  51. 196 195
  52. (3 + 151 Qui ialor est omnium
  53. Et quodratoram possibilium ipsius m, muximus est omnium possibilium maximus, nam
  54. quadrati
  55. si sumatur major tunc valer ipsius m, fiet major quam 15 l m 4(+ Certum
  56. Habemus ergo 15 + 18
  57. 133 12=. Contra ut vulor paulo minorem vero minimo.
  58. +4 +4X eberXa ex 78
  59. Est ergo maximum omnium possibilum 2 L, minimus omnium possibilium 3, quod est absundum 141) e
  60. pondo exs 1. fato a p +X pls mistrore pu x vats ratim propposica a mim. Cxteu Epline prats
  61. = 16 minor quam, 3, ponamus quod maxime, favopabile est, esse 3, ficta 10 - 263 21) E
  62. solutio ergo in numeris ita ut omnes ores fiant affirmativi est impossibilis.
  63. 9 2i
  64. duo nequadralorum quadcuto quadiatus a a +IH, a + a+ 2al + seu 2a p2a l(7
  65. mmeri unitate differcutes ita ut lun
  66. 9 a
  67. Jam ut inveniamus minimum, ex quantitate 10 + 2S5, faciamus: 1a - 250. Est autem 1.B
  68. 14 1 14
  69. enim est, si valor alicujus inde lateris angeatur, augeri etiam valorem potestatis uto maji 269
  70. fit autem maximus, explicando (4) pere pe +, pono 5337 est proxime in in tegris 18.
  71. 225 4301
  72. 51

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 17v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0034?run=74