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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 299r

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: 0.75.

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. 298v); this page is its right half.

The machine reads it as

  1. pay.3.
  2. Itaque altins assurgendam est faciamus q. _ A = ly tm Gs + Ny 4 P yt 4,i, 39 + qys 4 55
  3. Ergo sulfiit g + mur s
  4. aequam quadrato
  5. +E1r. H5155. + 3
  6. ceyy
  7. + n 4 2X1 (+ ZNY qy
  8. y aequa 4 +fy+ 299yy
  9. + f.. + 25997 +g
  10. 3 + by3 + ccgy + dy + e.
  11. 9= e seu g9 = +cc sc f = = b 4b se = d3 2te + + bb = cc
  12. fit set = d ib = 2 ce = bb fit d = 2 b cc - 1 bo
  13. qui imo video, ne hoc. ut tactem ex AX t cx + dd si quaddatis A. ex x - E et
  14. ex X -G sit quadratus, non esse ops ut necesse ut quilibet horum sit quadratus,
  15. sed ut habea du ut sint facti exiquadratis et fuctore communu. Sit
  16. ergu quadratu ab 5y + 99 qu est ges+ 2599y + g ducendus in i yy + hy+
  17. et fit poterit etiam res cedo obtiveri per multiplicationim authmeticam
  18. Nam si sit S + byd + ccGy + 8y +e fint 1by = rcc yy + 38y+4-0
  19. quae cum prioe habet, divisorem communem, inde bllendo y habebitur aequatio
  20. nova sed hanc forte brevius obtine bimus conparatione quam s sublatione
  21. fit ergo yt +9 yst +gyy 4
  22. = V. Ct aa. HK
  23. +sina quy e asgpbys F 9 tek
  24. aa
  25. a
  26. Led saltem sieri potest, ut unus sit factus ex quadrato in simplicem, alter
  27. vero sit simplex. Sieg ut si sit X - =
  28. sed sufficit ut un sut facti ex quadratis et factore communi. Itaque sit
  29. EX-5 = facto ex Hyy +gy +9. in h yy Her y + 1 yy + y+ 13
  30. 9y + y F554.
  31. et (. x. (e) = fado ex Bgy+ hy th illigus t
  32. +55.
  33. itaque factum ex sytgu in exgy etky +C, debet A comparari generali A +b)Engrdis
  34. et fieth, sibi yt + astit y + fth yy
  35. ffyy + 2599y+ g
  36. i gi i KKy + +
  37. .
  38. +1 y + 2fid yy+ Hsey
  39. fsi y (let2fggi y+ gliyy
  40. +Rt yy + 2 fNy + ffH
  41. +5fKK P + sgGKCK yy + g’ XX y
  42. se l’efsemus X = l9 + monx rum s 5, cstip res reducacatur ad prioret mulliplicando ob term. nin et ult. fit, Btdgu fggy +9C
  43. 1-8
  44. het y + 2st 9y + d 7
  45. fit feta
  46. ∞ ay +by régys +doyte
  47. (ff = a: i 8= e: 13 Ex termosecundo fi
  48. Ex terno. 2d0 fit 2599i (= b - ff KK) = b 2 - a KK,: i et 4ff9 i = aaei: t = b - 2R biX K + 915;;
  49. seu 443 = b8; - 2ab iKtt a t
  50. ex termino penultimo 2599t ] = d - g HX) = D _KK ,. F et 4sD F = 4ue:1 = d P- 28 e lt e. R: H
  51. sen que = d2f- 28 e + . 1
  52. Ex termino denique medio dervasa lege aequitatis, tit
  53. 2e13 + a13+ 1 ei: P +aL: 1 + b at. 21 + 81- et : 2t = c
  54. seu 2e1 +3 + 2ait + bKKI F - aK F + d 1’ F - eK 1 = 25;76.
  55. lt
  56. habemus ergo tres aequaliones linea subducta notatas, et tres etiam liferas,, i, t, +3, sed quae
  57. reapse sunt habendae pro duabus adeoque evolutione sacta habebitur
  58. Fortasse tamen ante evolutionem posset. conjungi duplices aequatio
  59. nes lineatae, secundum, E; et secundum (7
  60. Si veremur ne cursus evanescant desiderata? ob similem tractationem, secundum F et
  61. Secundum (Z), video modum hanc similitudinem vel n rumpendi hoc aquilibrium, si s conside
  62. remus ipsius Xd +. X +. X +. X esse tres radices, quae diversimodae X -8, X (E) et X- (E) quae diversimodo
  63. s
  64. ute tecu
  65. Ergo X =G:
  66. Zy9Fry+d
  67. Al. yt + mm y + nyy + pry + q
  68. + 28r.. +285..
  69. P
  70. Yds
  71. aiqu
  72. N y +by + ce9y+8gtC

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 299r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0597?run=74