Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 102r

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: 0.78.

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. 103v); this page is its right half.

The machine reads it as

  1. absolutum non successit
  2. e a +X: A -. gyiaa quaritur Sydx. fiei a FX= y a + aa X = XEyy
  3. en v X= a aa:, ry-aa igitur gy- aa debet aequari quadrato- quadrato
  4. Sit y= 10 + 110 + 12VV,:, 20 + 21V + 22VV. et f= O: D siet gu -aa = OO - aa DD, : 9D
  5. aequetur OD- a4. DD, quadrato quad lalo, ita enim postea etiam ayu-aa facile aequabitur
  6. quaduloqu glo quadrato tantum enim superert, ut D aquetur quadrato, quod facile
  7. P = 30 + 31V+ VP
  8. 30 = 1. 10. 10 + 2. 10. 11V + 2. 1012YV
  9. +1. 11. 1.. + 2. 11. 12B3 + 1. 12, 12V
  10. a qu. 2. 2 1. t2. 21. 2 F 1. 2. 2.
  11. aa W= a, 1. 20. 20 + 2. 20. 2 v + 2. 20 22
  12. yta =menn yea = nnp
  13. y = m nn -a = nnp a. se fel
  14. nn- 20 m- p
  15. n + pp = quado et nm. pp = quadr
  16. 4 10) 36 + 4. 30. 31V + 6303 i vV +4. 30. 31V + 31 p
  17. pro v poratur ex v et Y fit 4.31: 30 = 10. 11 + 20. 21,, 10. 10 + 20. 30 Ex v et B fit 2. 30: 31 = 11. 12 + 21. 22, :, 12. n + 22 22
  18. unde ex 11 et 2 fit 4. 10. 10+20. 20, 12. 12 + 22. 22 = 11. 12 + 21. 22, 10. 11+ 20. 2)
  19. tex v v fit 383 - 10. 10 + 20 20, 1 12 +Z quod et prodit multiplicando V e in v, et v in P
  20. B (13
  21. 30. 314 = Ex v in V fit A30 3 = 10. 11 + 20. 21, 11. 12 + 2121, : 4 Et rursus
  22. Et ex 14 et 15 fit
  23. per V fit 30t 31 = (2) ( n.n + 21 21 + 10. 12 +, 20. 22 : 36
  24. (2) 1. 1 + 21. 21 + 2. 1012 + 2. 20. 22
  25. N (16)
  26. Ces 31.31:, 30. 30 = 11. 12. + 21.2,:, 10. 11 + 20. 21 rividtdo v ser r
  27. H), 11. 12 +21. 22, :, 10. 11 + 20. 21 per 17
  28. en e
  29. 312. 30 12. 12 + 2222, :, 10.10+ 20. 205
  30. Unde ex 19 per 13 fit seu 12. 12 +22. 22, (2 ) 10. 11 +20. 21 = 10. 10 +20. 20, (2l11. 12+21. 2
  31. B (20
  32. enexcteus 10. 10 + 20. 20, 12. 12. +22 22, (2(10. M2O. 2) =410. 10 + 20 287 (2 ( 11 12 + 21. 22
  33. unde per 13 fil 11. 12 + 21. 22, 10. 11+20. 21 10. 11+ 20.2) = 4. 10. 10+ 20. 20, (. 1. 12 + 1. 22
  34. 30 1010 + 102 51 = n. 12+ 22. 22
  35. seu R (3) 1041 + 20. 21 = 4. 1. 12. +21. 22, 10. 10. + 20. 10y
  36. 35= 10r0+ 2O1OFB). ex net 15 fit Ex n est 30 = A: 2. 30. 31 c (per 13) C:, 6. 3131 fit 3. 31. A = 3dC
  37. 2. 38. 3 A +6. 3030. 31. 31 =
  38. 2. 30. 313=B
  39. 1 3A
  40. D
  41. seu 31:30=
  42. Ex 12 est 3l = B:, 2. 30. 31 = C: 6, 30. 30 seu 3. 30B = 31C seu 30: 3= C:, 3B
  43. Ex 11 et 15 fit 2. 31: 30A: D Ex R et 16 fil 2. 30. 31 = B.E
  44. 23 et 2+ fit 4 = BA: DE seu 4DE= AB quod etiontiiberi potera
  45. multi plicanda 1 per 12, et 15 per 16 Ex 20 et 23 fa CD = 6AA, et ex 21, 2 CE= obB
  46. BE
  47. hine sit CC = GAD
  48. sufficiunt 25, 26, 27 nam hinc sequitur 2
  49. Cc = 36DE AB = +DE) His tribus aequationibus adde aeq. 13.
  50. et ex et 11 et 12, 31. 310, 30. 31 = A: B
  51. Ex 13 et 28 habentur 30 et 31. Et ex aeq. 25, 26,27 quaerenda sunt
  52. 10, 11, 12, 20, 21 22
  53. solutio horum in Epistatis mers ad du. Baronem odenhus
  54. Kebretupetac
  55. exa rua
  56. tantu ejus ope, ineniendo quis tunc
  57. vulor y, habeatur y+b, et ytc
  58. qorm cois divisor, rclinquens
  59. itas quotientes dabit P, ipsi
  60. quolientes dabunt m, et n
  61. ad eoque et habebitur m:n seu li
  62. seo modus efficiendi, utrabio sit
  63. quacratus, adeoque et ut se
  64. intota sit quadratus
  65. diseoraso, quod fitri pe
  66. ex _bW. Wib- aa
  67. 9+b- n t- man: aa
  68. fiet fyg. bb= mn et
  69. m= y= m- b = mun + aal
  70. et mui A cando per 3
  71. sit nftco+ infal- a, aa
  72. fit Maa-aab =mnntaob
  73. seu m- 2aab
  74. tiat A~ mfK . b9
  75. N infal a
  76. aabn
  77. non
  78. gab utt e mna
  79. yy - bb = mm: pB
  80. y = ma ba
  81. ga= sk I
  82. titns aa cug inh u influca,
  83. hh. aa = nsl3 1
  84. D th anfia + 2C+ a
  85. adfancot aal
  86. hih - nesll- 25
  87. maeum
  88. ergopoet aa
  89. Efla+a
  90. Instat Ergo mu
  91. Restat austat 2gah = 2fsiK + faK
  92. Staa: na e
  93. rahe 2Fb4 at. son t=
  94. fit m. 1bppn
  95. Bsbraa, un
  96. mmetrame
  97. sed h. autento 2htt aem 2s imeraea ser.
  98. app-ann
  99. y-bb
  100. aequand
  101. seu 28= - 61
  102. qoquaad
  103. i 5
  104. appr an
  105. ap- ad
  106. -2uslm rin
  107. anumm
  108. e
  109. 32= 1. 7to
  110. 16 422-
  111. uet
  112. Aaua
  113. sit a
  114. ga + 2 ahb
  115. 99c0co +2900 ak + antiti- a
  116. nan sit 10 = + si, fia
  117. ad lt inth ragir in fKk = in flg - 29 3= mna + bp
  118. sit v- CB KV+ B
  119. sfkKCOCo +ZB alteco n haat
  120. naeram portesale
  121. 102. 103

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 102r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0203?run=73