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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 50v

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: 0.79.

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. 51r); this page is its left half.

The machine reads it as

  1. Rem reduximus ad ff +99 = +2ab
  2. et ffgg = fg = + ab siet ffgg = aabb
  3. et gg- nabb ss = + 2ab - ss, fiet s L rab ff. + aabb = 0. seu f. f ab - o
  4. seu f = + ab e f = 1+ ab et g = (B Hab
  5. et erit 5f +gg 2F ff + gg + 2 ab = 0 = f5 + gg -2fg, erit f = g et
  6. ff = + ab et f = V + ab = g ita erit fg = fabs et f5 + gg - + 2ab, ut oportet.
  7. dy, y B 9+b, y+c
  8. 50y + al34
  9. 1= tad faD ay = a8+ aD + 1OD. B b ytC
  10. yy + by +bc. fint 108 + 4u 8] oD ~ A0 + g4 1OD gC +2810
  11. SaOD, (b+C) 2 VOD
  12. 3 94 fit g= + d + asb +G; + sit et B0+6OD +b+c) (O, D bc ∞
  13. compendio sit b +c = 0 H et c = -b fiot 00+ 31 60
  14. A63 (O+B,
  15. fint = 20n- D at e 60 + 33+ 50D b = 400 + 4 D + 803 seu 300+ 39D + = 0D t bb = 0
  16. bc
  17. Sit D = 100a na firt 3. 00. 000 + 3 110C 0 + 6. 10. 1 a ( + 3 N. H aa f 305 108 + = 001a0 t bb = 0
  18. fiet 300. 60 + 3.10. 10, +2 00 10 = 0 et datur 10 et 3, 11. H, 1 a = 00 ev bb
  19. fiet g = 20+ 2D, a: f ut 49= 400+ 4D + 80D, aa: ff = OD + W +6OD - bc
  20. seu O (ff - 4 au) + DD ( 4aa) + (6f - 8 aa) O D - bc = 0 sit f - 4aa = ag,
  21. fint ag0 (+ agm Abag f 160a) OD - bcff - sit 00D = 100 + n a fieit
  22. 0000. ag00 + ag 10. 1000 + rag. 10. na0 + agnuaa + (bag - 160 a) 10 00 = 00. 110) = b1 (ag + 4aa)
  23. dg 1L. 1aa = bc Cagiq A2) = c
  24. fret 00.00 ag + ag 1010 + 6 ag0ul0 = 16aa 00. 10 = 0
  25. denique rag. 10(ida = lbag - 160a) 00 (11) a Ex OO fit ag g = 16. a. 00. 10- - 8 tc. eva
  26. ay = 20
  27. A
  28. 00.00 + 10. 10 +5, 00. 10 510. = 10
  29. seu (6, 10.00 - 2. 10. 1 = 00. 0ot 10. 10 (+ 5. 00. 10)
  30. et dabitur 10. seu 3. 1 1 seu 3, 10. 10 = - 00. 00
  31. quaeritur gtb, ytc = Cto. sit u quadratus. posito summandum esse it gtb, grd)
  32. Les summari debet dus tay, geb, ytc) sit ay quadralus sad +ta = a C + a D + 2 a 10D
  33. ergo su debet ytb, ytc, seu gy + by+ bc aequari quadrato tentemus casum specialem,
  34. ubi b+C = 0 fiet c = - b et bc = - bb et debet gu - bb aequari quadrato et fiet
  35. ab 00+ + 453) 1OD a (quadrato à Q + f10) =) 94 + 258100 fiat 4 - 2 = (019)
  36. 60), bb
  37. O9 a et 00 +697 =89+0
  38. seu 00 + 37 +6OD-b1 = a a u (015) + OD H. sit D + D = X et = 1X +ua et 00 D - 20X rua
  39. erit 000 + 30D = (10 + 20) X + - (1+ 21) a _ = 00 X fit a + 21 - _ et 1+ 20 = 00 seu 20 = 00- 10 et 21 = - 11
  40. ertque D = (00 - 19) X - 11a et O = 10X - 1a. Et ex ag. N friet XX + 4∞D - bb = +a a xX + Oy sf,
  41. sed OD = (00. 10 - (0. 10) x 10. 20XX + 10 21 RX + 11 2lac = (00 -10) 1 XX - 10. 11 X - 11. 11 = (00 - 1o op X L 00 11 X - 1. 1
  42. et hatemque (4 aa -1) XX = bb = t H, (00 10) 1oXX + cu rio - 11. 11
  43. ubi ut destruamus membra, fiet 00. 1 - 2. 10. 11 =0 seu 10 = 200, et 4 =
  44. bb Aa
  45. seu 1 = ab ab
  46. et - bb = 2 4 - st, - 11. 11 seu 11 = d ana - f
  47. ( s5)
  48. 4 aa - ff = 4 aa= H, fit 4aa = ff seu 4aa -Hf = 0 quod non licet, nam fiecet
  49. 4ua
  50. nam ob valorem I1, sublato 1 fieret ab =0 adde quod
  51. si 11 = 0 fierent O et D invicem in rartione constanti
  52. Ergo faciamus quadudum et fi 0G +9194, et fiat 00r m + 4 4(8+ 0D ~ st Bq + 2598 10V
  53. d
  54. 507 - bb
  55. ff0 + gg
  56. pul = 110D-6f 9= oX F na 3 - (00- 10)x - na
  57. sed video etsi culculu procederet, tamen duci infire ab ita B in 5184 +9 spG, quod on licet
  58. f O+ 99.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 50v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0100?run=74