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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 340v

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. 341r); this page is its left half.

The machine reads it as

  1. ses A irrationalit partem, et ea v fit 1on1o a 303I8 = 1. 70. 190. 240 + 2. 20b0
  2. propterb V fit 10. 140 + 50. 340 = - 2. 38140. 343. + 2. 20 B0) po d, (P fit n. 140 +31. 390 2 - 2. 31. 1403 40 + 2. 2. b0
  3. in lesimali prute prosic. V fit 1e 1o 130. 70 = - 2 . 190. 340 + bB. 2 1013 4 At V fit 1, 43+ BI. 3 45. 3 -2. 1 H CC Mo. sH + bo2l. 1r 31 + ba
  4. proper v fet - 2. 704. 140. 3 40. + 2. 20. 71 b0 - 270 31 140. 340 + 2 2t 10i be (, 0. 217
  5. ex aq tetr fit + 2.10 31 . . . . ( era + =. 1 3 50. . . .
  6. Ex 1013 fit (. 2. 10. 3050 - 2. 78, 190.340 = 20 b0 ror3a - 2. 20.ib
  7. Ex 2 et 4 fit
  8. x 6 et qe lit
  9. 190370
  10. d5
  11. 2. 11. 31. 50 - 2.71, 140. 340 = 64 + 2169, 1131 - 2. 21. b0
  12. 20.50. 10130 b0 = 20. 70. b0 = 2. 10. 30 5050 2. 70. 70
  13. 20. 50. b 10+30 bo . 2 20. 70. bo 17 21. 50. 114 31 bo = 2. 21. 71b0
  14. f. 10. 30.50. 50 - 7. 70.70
  15. C fei
  16. 7. 11. 31.50, 50- f. 71. 71
  17. e
  18. 20 ((B50. B = 2. 20. 71 - 2. 21. 30b, b0
  19. 10) Y 20. 31
  20. 140340=
  21. per aeq. 5
  22. 21.30
  23. 2. 10. 31.50.50 + 2. 11. 30.50.50 - 4. 70. 71
  24. Htabemus ergo tres valores lipsius 140. 340, adeoque dua aequationes, a quibus abest absunt
  25. 140, et quibus si dertia adhuc accedat, ab his independens, habetimus quae sitam
  26. sufficientes aequationes sine 140, et 340. Et quia ope aequ. 1 et 2 invenimus valorem
  27. ipsarum 1 140 et 340 pagina praecedente. jamque per s
  28. 83 et 4 conjunctas cum 1 et2 ad huc novam aequationem obtinuimus et novam stidem
  29. per aeq. 5. Superest jam ut novam adhuc obtineamus per aeg9. 3 et 4
  30. inter se conjunctas
  31. +byl C rhc
  32. Cx +
  33. XyaB) p
  34. e compendum pro 12, 307 ag. 3. et 4. sembamus ax + by = 3 (e rmy =n
  35. pro 140, 34
  36. talX+ bly = et
  37. alXX- amyL N’a
  38. argep+ bryy = er+ n5 su bt an
  39. l5.. +45..
  40. ar+lS = br + 15 d a - br = m - 15
  41. fit r: 5 = M = l, :, a - b
  42. it yy = 10- a1
  43. fit tarXX + bY yy + ar xy = er +ns + par
  44. ar + l5
  45. p sun
  46. y etva.
  47. Hoc suopone nocanda
  48. (TY = mC -b
  49. b
  50. seu a Xx = gy + 2 xy = Cr + n S+ ar+ (sBpp
  51. sit s-1 et Y = ma l 5
  52. et fici XX + 9y + 2xy =
  53. ry -
  54. seo
  55. X = S me-(C + an - bn + rp an. Bl Hm C le + a - bu - 2p am bl
  56. y = Ime - lC + an -bn + 2p amabl = Lme. le an -b 2 - 2 p an bl
  57. et X jignifiell 140. et y fignificet 340. patel
  58. sed quia in C3 et n rursus labet 140.340 et fit 21= 20, 10+ 30. 10. 31F11. 50 = 10. 3a. 1+31 3: 10. 20, 10430- Quos duos valores ptru 21 exegg. 11. et 13.
  59. itam el fit xy = LCn amcbl - m - n ab - 40340
  60. i vel 8, vel 9, ve
  61. hic iterum haberi 140 vel 340
  62. =2. 9 70. 1131 50 Xy ( f 10.70, 2, F 3, b0
  63. Un rkab - Cn anebt
  64. l
  65. na - 31 q F ffser 10. 540 =
  66. inubrru o sepliolle. nve t 2
  67. initio hujus paginae,
  68. _ NGC ep. fit C3 = - 2, 10. 30 50Xy F bo. 2 10 430
  69. X= se nt) Fugo vdia
  70. ser
  71. seu XX+ ryfrpus = em - cl f an -bn 4 a nc a l + a b1 s
  72. sit eX + 9y + 2Xy = hq et xx tyy -2xy= ht
  73. fet x = 1h9+ iht et y = thq- sht. Ergo
  74. finc si (1.). et ((2
  75. bltam10. 31. v. )
  76. n’a etfiest
  77. bI - am
  78. XL9 = XX +yy + Exy = em -c + an-bn 4 am- bC 2p
  79. am = bl
  80. n3 = - 2. 11. 31. 50xy + b0. 2t. 11431 C71
  81. Ny- B sC l.na fibpanXu, = + 2 l. 7 1 1090. 5CXy - 1.31. 20. 101 5 a b0
  82. bt am
  83. C. tuil t n. a. b + a nil l. a. tB tip
  84. a. m- l + l. a- b
  85. am= al) + C+ ad - bl
  86. Sam- bl
  87. tam- bl
  88. 5.7
  89. am - bl
  90. X. ideo
  91. non sufficit, sed pretius omissa
  92. extractione scribendum
  93. Ax = 1n umebt- sim - nab
  94. av. 34
  95. (2) am - 6l~ Bet
  96. et hoc explicato, tandem nova extra.
  97. chore habebitur X G, pova
  98. recg demum erit aequatio ab B et
  99. Vage liberata qui novus
  100. valor cetsi irrationalis, si cum
  101. aliqui ex ipsis 8, 9, 10, conjunga
  102. tur, habebitur aequatio nova.
  103. Nempe ex valore 10 et 8 fil aeg.
  104. prima, ex valore 10 et y aequ. 2da
  105. ex valore et nova inationali
  106. et valore 8 ag. 3tia. Et per
  107. has tres aequades liberas ab, 40
  108. et 340, psa habet praestabitur
  109. oparatio ratabsolvetur.
  110. in ag. XXyy seu 140. 340 =
  111. explicita pro xxjus potent substitur valqu
  112. psius ortus exvaloribus desu invicem ductis
  113. ita habebitur x9 rationaliter nova aq
  114. quae esse qui eut varot 1) qui junjendus ipsi
  115. o dite t a e ete a ea tut lee
  116. Hab

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 340v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0676?run=74