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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 51r

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: 0.80.

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. 50v); this page is its right half.

The machine reads it as

  1. y +b + taz in y+ C+ taZ, = gy + by + bc. H (2y+ b) taZ videndum un possit
  2. identificari aaequari (quadrato a v +taZ =) v0 + ft Z + 2 vt taZ; fiet v = (yt6) a -27 + abt c)
  3. et gy + by +bc = (00 + AZ =) aggyy + ad B + a ab HZ, fist aa -ss
  4. a
  5. fiet Z = seu affgu + affby + abcff + aaffZ = agy t a by + a bb + f Z
  6. inde Z = a (f5-aa) yy + a (ff- pa) b y + abCH,: fs (ff - aa)
  7. sit C = - b seu b +c = 0 fiet Z = a yy D - abB
  8. et
  9. 1, b6
  10. EEbd
  11. 28c
  12. Nempe 9 + b + saq in y - b + sac = yg - bb +aZ + 2y saz = vv + 1Z + 2t utaz fit v - a y
  13. ft- aa
  14. Et vy - bb taz = ac gy + ffZ, vel affyy - affbb + aa HZ = a gy t f Z, fit atfradius - ap 1
  15. seu q = 4 9y - a bb. Comprobemus actu ipso
  16. ft (. aa)
  17. yt b + at (e s ma) in gub + at (3 . 3t aa) dat yy. bb + navus - aabb + 2ya . . . . . )
  18. st
  19. H-aa
  20. quod debet esse quadratum a 2, 2 + f1 (23 - b) = au gu + Hyy - Et 1b + 2y a 1(. . . . )
  21. quod consentit priori. Haec ergo res succedit nam yy - bb L aagus - aubb = yy + aagus -ff bb
  22. f
  23. st-aa
  24. +t aa
  25. F Hua
  26. Esto t _ C0 = 104 + 1DQ fit coco = 09 + D8 + 2 1OD. Debet coco + b in coco- ab,
  27. aqua iden reddi extrahibile, fit D et idenlificari quadrato a v + f 1OD, fint ay = OG + D8
  28. et l = 4(09 + D9) et tandem 00D = E4 qu (O+ D) abb
  29. ff- aa
  30. quod ut praestetur identificatorie, e considerandum est C) non ascendere nisi ad secundum potet gravum
  31. sed valorem ejus nisi coerceatur ascendere ad quartum. evercitio suplex, est, una ut e fiat constans verb. g. =f
  32. baa seu C = h(C + D)+ L
  33. a Yes. aa) ut = 4 (O+D) -
  34. a
  35. unde () +D = (h. + 4) (() + 5) Ergo h + a = 1 et hh + aa = ah seu bt. +
  36. 1fmaa
  37. et fiet CD = qu (0+)
  38. Cd = 1+0 + 1FD sit coco = 50+ fD + lo t ab in pt c0+ = ff C fqu (O+B) + afs∞D + aff (O+V) YOD
  39. seu hih =ah + L aa = L aa - a. seu h = = + Y - 3
  40. et coco + ab in 1oco - ab = cot - nabb = ff qu (D1) +afOD- aabb
  41. +4f (0+ 5) 107
  42. formula identificanda quadrato a aB. + gYB D, quod est aavv + g90D. + 2agv 11OD, fit V = 2H (O +3)
  43. () - 4
  44. ) qu (O+ D) aabl
  45. 99 - 4 f
  46. qu (3+D) +990D, adeoque tandem
  47. Eo
  48. = OD. seu fF Qu (O+ D) - aabb
  49. = OD
  50. gg- Hss.
  51. ilH. da)
  52. ab -)
  53. sit _ h L (e13) + L cab = et a ((0+ 5) = n Hegg. 2H)
  54. a gg, a)
  55. tiet hF + sed ita addendo duos vulores, ut misus prodeat O+ D, deb. L esse hf + af = 1
  56. na
  57. ta
  58. et h - = = 0. Ergo hh = aa et f et hhf + aaf = aan, seu fR- aah
  59. Y(g9- 275) compendo A Zaa
  60. utque adeo f = F D isi h = a et f= g et ab
  61. Fiet. L. O. + D 2O+ ZD + m = O seu O+D + m = 20 seu C = D + 2M
  62. et = C + = D - m = D sen 0+ D - 2m = 42) et D = C -2m quae
  63. consentiunt. Seo inritur abjurdum, quia I(gg - 4f) -0.
  64. res ergo hac via non sucedit.
  65. Alter Redeundum ad OD = sf 44 qu (0 +8) - aabe
  66. H-aa
  67. si retineamus Q inconsta variantem, sed faciamus ut qu (0+ O +) sit constans = n
  68. ea _ et sit O = h sM C + h ab et B - a
  69. a aa t
  70. a 1 (. aa)
  71. = n = -2a
  72. sit cd = 10Q + (DG et cocd = 02+ 3Q 28 son et ponendo C+ D = n fint coco = n8 + 29(0D.
  73. 5t0)
  74. a a
  75. tr rtf. aa)
  76. 9G(4, +) 1. (O+ 3) + (98 4 - 4)03 - bb
  77. = 2 1
  78. (: aa)
  79. ubi in (4 + aa) qu (0 D) + = OD destrui debent altiora, ut fint has haec quantitas aequalis
  80. ac au
  81. fit v = 42Q, O+ D,: af et
  82. ab
  83. h(. an)
  84. Ergo ut O + D sit = constanti M, fiet p, fiet 2 + 4 = 0. seu hh = =aa seu h = a f- 1, et
  85. ab
  86. et _c in gg + 940B + et Cot - nabb = 4Q, 8+8 + 4816D ~ xv aa + 2av . 1OD
  87. Constantiu quod fiat explicando C) et D per 8. restabit EG = A C) = bb 2 0 explicando 0 et 3 per 84
  88. quod; a praetentari pt
  89. D = 20X + 21 a firt habe
  90. A-4aa = ag
  91. e
  92. e
  93. acy
  94. seu (5+- 4 aa) qu (O+ D) + 4 OD sit 9 = X et O = 10X + 11a, et
  95. erit (C+) HaC ,. 10Xit 2. 10
  96. 4Op =
  97. 20. 20X + 2. 20. 2 aX + 21. 2 ca
  98. et erit (11. 11 + 21 21 + 2. 11. 21) aq = am
  99. (ap.) F.A 0. 20, ta. 20. 2) ax + 2. 11. 2100
  100. quod ut
  101. oustru
  102. erut
  103. 4 10.20
  104. aa
  105. aa Y 10. 20XX + 10. 2 ax L H. 2aa
  106. seu 1010+ 2020+2 120+4H
  107. +3( +2H) 10. 2020 ad
  108. et ob ex m - H ( (io. conpar 1 , A p. 1 4 20. 21 + o. 21 + 11 2) (1+ 25) =0
  109. 20 ax
  110. Batur 1121. datur et B pr ha
  111. fiet . ut ua Funa tas 4. 10 20 01
  112. et 1021 + 11. 20 =0 et -11. 21 act. b)
  113. eu 1o - - 24 seu 1e =- 1
  114. ergo datur et H per fia
  115. ex 2 fit B. 11+20 21 20 eu =-
  116. Ergo 10 = - 2
  117. Ergo . 1i daFf Ag. 5 dut 11 et 21
  118. aeq. 3 dat 10 vel 20
  119. Ergo fit 11 = 21. Ergo 11= bY

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 51r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0101?run=74