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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 54r

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. 53v); this page is its right half.

The machine reads it as

  1. et 229C + - rul 42i lepp
  2. u b rige 11 tir 1e9. E4
  3. tiet -e ab facaoreb +44 ac - ro
  4. si Ax+ fad = 19. a fit an
  5. ua
  6. vv- ab +. Ja
  7. Gatac = orv. ab +G8 Hac
  8. =aretaabharue
  9. si desiderassemus
  10. X + mXX et X - mXX
  11. esse quadratos, fuisset similiter
  12. auan t at = grn M
  13. 2 tan ag tan
  14. 94- aa, Van
  15. 1e
  16. vy - 4aa88a
  17. gt+ at-racgss, an
  18. qu (Cs + au)
  19. apem= prgy _ et X= a
  20. qusiversen X- a. votam
  21. it foet vo-gy = 2am
  22. aX + aux
  23. nempe summum
  24. me L ex else poratu
  25. diferentiam ipscrum
  26. fieretraam:, yy aa
  27. r= aam:, vetaa
  28. foret y = vB = 2aa
  29. fierd potest yt D = 2B
  30. et y y - v = aa: C
  31. fieret 2y = 23 + (aa: β3)
  32. et 2V = 2B- (aa: B)
  33. yyt gy vv al
  34. at:, 23+ a qua - a
  35. pera
  36. Efficeere ut datus nunerus an sit differentia
  37. ductum quadratorum se avu- vyanfiat
  38. a y + b = β et y - v = an: β
  39. ldux
  40. Efficere ut datus numenis sit, dfsumma horum
  41. ductum oc non ita facile est:
  42. VY F vv = an
  43. y + v -1 = β y - v1 - 1 = an: β
  44. fieret, y = B + an: β
  45. 2v L-1 = B - an: B
  46. Hica . et CXn. ), se Aones intercurant
  47. Jy an vo
  48. si n esse b
  49. imaginariae. Sed si volumus adhibere irra-
  50. tionales, vel si an sit quadratus his non estr
  51. gy = an = W, sit py = tan + et ayotant
  52. siet 82 + ad = 2dan e unde datur y,
  53. et a san F av: Gian-qv,: a
  54. itaque in numers facile potest quadratus dividi
  55. unde datur.
  56. in duos quadratos.
  57. yu + ex LH. = an fit 3y eo Frbb = an- bb
  58. at2PC + ee + 4+ 245, s = an
  59. dd si numerus datus semel dividi possit in
  60. d duos quadratos, poterit infinitis modis
  61. dioidi in duos quadratos verb. gr.
  62. yy + vB = am sit. an = ee + A
  63. fiat y -1Zae et v = tZaf, fiet
  64. Y3 + vo = aa22 B2aa Ze F eP + 1FZ- 2laftZ + aaff - an
  65. unde fit aZ Z = 2ft + 2ae,:, aa + Ht
  66. yyton +2ry amt2ry
  67. yy o - an 5NV
  68. un numens an sit divisibilis per
  69. vo eevo = an
  70. er) vo
  71. ponamus an in ec+i esse quadratum
  72. nc si efficimus obtianimus quaesitum
  73. an = (ee +) PY vel S+ rr.
  74. dat Numtrum dividae in duos quadratos
  75. 2d ac + un 17 + . an =0
  76. ece rec= an
  77. Z vy = an -v = an voee
  78. sit an duplum quadrati, = 2ec
  79. fit yy - ed = ee - vv, et res facile proredit
  80. si an esset siplum quadrati, 3ee
  81. fierer yy - ee ec vo te
  82. yy an, si an extribus
  83. compuaretur
  84. quad jatas qau ecberet; sit en
  85. B=8+F. exy- e+e, fieret
  86. otasse res
  87. vtieteet 9 28f 1ff -es CetHrgg,
  88. fieret 1 p42 e + + 2F = g9
  89. et na = pV + 20 + 29
  90. se gescoco +29oC + G + 288 = gg -9
  91. fiet 89-8-
  92. siet 8cdco + 2coC +25 = g+G

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 54r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0107?run=74