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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 41v

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: 0.85.

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. 42r); this page is its left half.

The machine reads it as

  1. +40. s2VV +41. 52 aWV(+2. 52aa2
  2. =5. 42 4 4 = 31. 42 a 15. 4 aa
  3. sed si velingreunquer d seu 20 et 21, serimamus compendio 4o2B Y + 41 a V + 4raa
  4. et 0= 50 1 + 51 a V +52 aa, Et componendo duas aequatirenes fiet
  5. 4+40. 50 21() + 40. 51 a W + 40. 52 aa = v fint 40. 51 = 41. 50 et 4052 =4)
  6. - 40. 50
  7. = 41. 50
  8. compendio (1: 2) nabb=aec vocetur af
  9. = +7. 50
  10. quod applicando aequationibus duabus
  11. mo vierroumer quae ssunt initio paginae praecedentis, fiet
  12. 3, 10. 20. 30.. 2. 10. 11 aequ. 2. 10.20. 317 (10. 10
  13. 20.2
  14. 30.3)
  15. 10. 30, 21 (310. 20
  16. 20.30. 11. 430.30
  17. O 3. 10203011. 1 4 1t bia +f. a=
  18. et 3. 10.20. 30, 11. 11 + 1yb: a + f: a aequ. 11. 21. 30 75 10. 10
  19. 11. X. 20 5
  20. 21.31. 10 ) 30.30
  21. ubi neglectis 10, 20, 30,
  22. quiqe altius assurgunt quaeramus
  23. solum 11 et 31
  24. ID si compendii gratia 10,20, 30, essent 1. haberentur pro non ascriptis
  25. 31. 31
  26. et fieret ex priore aequatione 6. (11 +21 + 31) = 6 (31 + 21 + 11) quod est divinasse
  27. Exposseriore 3. 11. 11 + 117 +
  28. 29. 21
  29. 31. 31
  30. 8II. 21
  31. 7II. 31
  32. (21. 31
  33. et fiet tandem 11+ 2 + 3t = - f: b
  34. unda jam quaeramus 21
  35. fietque ordinando
  36. = 1I. 31 - (11 +31) Za
  37. + (b B - (11 + 31)) 2
  38. si essent 11 +31 = 0 fieret 21. 21 + b 21 + bb = 4. gaa - 3. 11. 11 = ha
  39. 21. 21
  40. qua sit mipor quam
  41. 4. 9aa
  42. sed si non sit major, alia opus est hypothesi, et fe possumus facere
  43. se = 11 + 31 seu 31 = b -11
  44. et fiet 21.21 = H. 11 6 - 11. 11 = bb - 11. 11 - 11. 11 - b +
  45. praestabit videri an omnia liceat
  46. fiat
  47. ( H absolutus terminus en
  48. I aequalis nihilo, V
  49. secundum 31, fiet 31. 31 + b 31
  50. za
  51. + bb = +-
  52. 4. gaa
  53. = 2. b 1 = a. b. 11
  54. + 11. 11
  55. 2b. 11 = a
  56. quod etiam non semper inrealibus
  57. revocare ad
  58. rationalitatem, ideo
  59. succedet.
  60. 11. 11 + b _(1 = 11. 31 +d
  61. 31.31
  62. 4. 3a
  63. 2o et ordinando
  64. P
  65. a
  66. = a6aa - 6. 1b - 3. 1111 - 5a
  67. 4.3. a c = bb - 18. 1 ab 2711. 11 12 fa
  68. + 11. 11
  69. l 3) et Il ita explicemus
  70. javicem, at in 11. II + 31. 31 - 11. 31 evanescat quadralum, sit 31 = _11 g: a,
  71. unde
  72. fiet 11. 11 F 11. 11. 99: aa = 11. 11. g: a =0 seu aa + g9 - ag =0
  73. Ergo faciamus
  74. +aa - aa, quod non licet.
  75. 21 = 1t g + a, _ nh 1 = 514 et 31 = 61h. et fiet
  76. et fiet
  77. aa gg - ag + =aa =
  78. C 1 = S19 +Y1 h vet 31 = 61g +814,
  79. +51. 5199 + 2. 51. 71gk + 71. 71hk quod debet esse = 0
  80. +61. 61 98 + 2. 61. 81 gh + 81 81 hhr
  81. 516149 - 1. 51. 81 gh, 4 71. 71 hh
  82. d - 1. 61. 71 gh
  83. faciamus 11. H + 31. 31 = 2. H3 + 2. 11. 31
  84. faciamus 2._. 3HII. 1 + 31. 31 B (G: a) (11+31) = 0 et
  85. + 29. (11 431) + 11. 31 X f = 0
  86. b+ 39g + Q11- 11. (5 +
  87. 3a la
  88. fiet 11+ 31 = g: a et 31 = (9: a) - 11 et fict
  89. seu 11. 11 - 4 11 + 88 = 39 + bg +94 + F=
  90. 2a
  91. qua 3aa.
  92. 99 + bg + f
  93. raa 3aa 3a
  94. quod aequandum quadrato ab 9 Aequatio 1 divellatur in duas
  95. 1. 11 + 31. 31 + 2. 11. 31 ∞ = 4 (11+31) =0 et b (11431) + Q (11131) = Z. 11. 31 - 11. 31 +a
  96. 11+ 31 = g: a seu 21-9.a
  97. seu
  98. seu b+ 29 (1+31) = 3. 11. 31. + F: 3a. Ex priore fit
  99. quem valorem substituendo in posteriore fit b+74 9 - 3118 + 3. 11. 11 + 3
  100. = b+ 39 g = F = raa gua ga
  101. qqu
  102. gua d
  103. 3
  104. 4
  105. Aliter redeundo ad aequ. A fiRt. 11. 11 + 31. 31 -2. 71. 31 (+ 2. 11.31 = 11.31 Y B (11131)+
  106. = de
  107. gaa
  108. I1. 1) = da 11 +Deaqe
  109. =11. 31= Za= a aequanda quadrato seu copendio - H. 31 - m: 3a = quadratio.
  110. sit 31 = -11 + 41 et firt er. 1 - 1. 41 m. 3a = quadcuto H H - 2. H E + 51. 5I
  111. Erjo
  112. a
  113. vidamus an 11. 11. + 31. 31 - 11. 31 + se 31f. 1M + in F possint reddi divisibiles
  114. adeoque A Auadrabo H. H. - 1. 4Y + Z 41. 4+ 4 2, 1, 51 - 2. 45I + 51. 51
  115. per f aq + 31F hocdu r+ 31L + p divid sit 1tHgq L9 n eq +31. 31 Th +(Gh + CG, + p. 119+ P31)
  116. eit eq = 1 et lA = 1 et gh + et = - 1 sit p = 0 et m = 0 et n -
  117. a die t eihs 1su te
  118. ert 4- 1. e t= 1. quod hon licet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 41v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0082?run=74