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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 89r

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: 0.77.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 88v); this page is its right half.

The machine reads it as

  1. Calculus paginae precedentis viam nobis offerre videtur ad huc
  2. faciliorem, edm scilicet in aeq. 31 efficiendo, ut fractionis nominator vel numerator
  3. sit extrahibilis, quod praestat vel sola aeq. 35 quae dat bat = + Crr Quod adlo sufficit
  4. Hia
  5. quod si similiter ob nominatorem faciamus bb- B. bbrr- aaH = (2) bbr- pat, ubipro e
  6. at substituamus ejus valorem + Brr: b siet WB - BB. bbrr -Br: bb = 4 (2) bbr AB Crr.: b
  7. seu (bor3- bb BY- β ber (+ p, b Er 81 Ept, et divisis
  8. A
  9. 44
  10. omnibus per 1X, sit 3b + 5 (r = B seu b f- b Pr - Bb + B1 = 4br. b 5 ab p (7
  11. VY. Br -p + seu 48bBr - b (βY - Bb+ = 3b + 3B= Y. Hanc aequationem utiliter
  12. resolvere in duas, faciendo bB p = n B3Cr. seu r= b_ et 8B3 a - pibβ- βb = 3b +3(72
  13. b 3. 9p - p -1 = 3b L 3β2 bB). eu 3b 43 2b46 (2b ( - b (5 1an - p - 1. adeoque)
  14. bβ N4 - e- 1
  15. = b + β Sed haec aequatio producit aliquid impossibile
  16. nam fit bB. 2(B - ( 2- 1 = 3 b + 3 ( n - 63 nb
  17. seu bβ11 = 13. = β. quod evitandum qua licet
  18. 3β+a bbB: Y = = B b - 3b
  19. Ergo omissa divulsione aequationis () in duas nodo acto fciamus er = 8B
  20. seu Y - 4b = (16b 37 - 3β - 3β b - p 1 368 β
  21. 3β41
  22. 3B+ b(
  23. s
  24. 3β + b2B
  25. seu r = + 4b3Bb 8bB. 3(L, B
  26. 3B3+ b B
  27. 2bbβB non minor quam 3 bt + 3β - 6bb (3β. sin bBt2 non minuerquam (+)67+) B2 13
  28. faciamus aequales, ut calculus sit, tanto brevior, fiet: β (4) F2. 3bβ = ( bb: 13. adeoque
  29. B _ = (4) 2 (4) b: 56 p. (3 + E seu B = B (+) 11 +r 3 b
  30. et Y =
  31. +4b
  32. 3β2+6
  33. 4b
  34. + 4b
  35. 143G +2. 13 + , 17 -
  36. seu β = (4) 1b1f 312
  37. 45
  38. x
  39. B+r = 3(+ -
  40. () 2 (+) 1216 +136V2(D1812
  41. et =
  42. (414)
  43. s
  44. 3
  45. s Hetds
  46. 3
  47. bbrr= (+ 1(4) (4)613
  48. V6
  49. et at = bb (4) 16(+ 116 13
  50. b Ad =.-
  51. 16 _12+) f)613
  52. bb = at = (+ 5 16(1 912 bb
  53. L) 1816
  54. B3 = 1b 241213 = 2+1B3 bb et bb = βB =
  55. 36
  56. 4(+)(+)213(4.
  57. bb
  58. 1+ H.3.
  59. 8 312(4 (+1 18013
  60. aat
  61. 8
  62. 104 + (+ 60 8
  63. 27
  64. bbrr- a a H = 36 = _ 104 (+ (4) 18 s3 (4) (4160d34-- 63(+) (4) 42 13 s
  65. jam multiplicentur invicem bb = AB, et bbrr aate, fiet: ( -19+ (+ ( +) 110 Y3
  66. oportet ergo esse (+) = (+) et sed tam quia productum hoc de set esse affirma-
  67. tivum quispue quale quadrato 4 (2) bor= Bat. sed video hoc non
  68. succedere, quia 194 major est quam 110 13
  69. 1)
  70. Calculus ergo resumendus duae sunt aequationes una: bat = + Brr
  71. (3)
  72. altera bb - BB. bbrr- aau = (2) bbr = Bat. seu bb est btr bat -t Br - Bbat
  73. seu B B: (p p2, (e per B2 quominus error surre pat, adhibeamus
  74. ubique numeros sit b = 5 et at, 184 et BA C et Y, C; 3142 fit 314 () =b266
  75. ubi in rei veritate est (61, hic vero numeros supplet G 6b. 3322- 1144
  76. porro 33 =22. 3366 -1144 =(2) 336-214 - (576) Hac arte ubique
  77. instituere licebet probationem per abjectionem novenarii, aequationem 2, utrobique multipli–
  78. 162
  79. Cabimus per 33, et tum pro 34 substituemus valorem ex aeq. s. fit 53. 22. 33336b - 331144 = (2) 3336- 2314 h F iiq ng4
  80. seu (3666- 39 635+26.6)- 22566(+ 267: (6) 566) 13626) (26: 63 308
  81. st deprimendo pit 3322bb fit - 66 : 67 - 33 = 4 136. (6) -576) 4 6 17033 (1548 4b
  82. omissis jam fictitiis (6) et (576) fiet 66 +33 4 1) 36 =0 seu fit 6 = 8_ +3
  83. seu fit i ergo at - r = + b et at = +βb (quod si Br = at esse debeat
  84. fint +BV = + Bb, et r = +b, hoc ergo succedit in casu Hyperbolae) substimamus iam
  85. valores inventos sit numeroter exhuohendos fractionis: b
  86. X 2bSXX + 16 1a
  87. num b +C NB Minatornit +bb XX + 2b X + b4 + 2eC B. +ee BBBE
  88. eB
  89. et fict
  90. (B
  91. ssm
  92. a
  93. Eao = ex (+et
  94. Ae(b. = Bbb Aubi rursus surcedit extram hio) 1B +ee b
  95. st teced bHC
  96. Xr + 2bX +bb astr. B +) Hoc mido quod mirum est tota fractio (F
  97. 2
  98. IX
  99. 3
  100. dit50
  101. 16L 575b4(1b
  102. estconstans. deu de integro exteriatuur.
  103. fiecet ∞s, 3. 2 quod absudum hoti
  104. 17
  105. seu
  106. +ioqe
  107. e
  108. reo
  109. 162
  110. 12
  111. 60
  112. 60 42
  113. 6470
  114. 120
  115. 92
  116. id
  117. 308
  118. 8 194
  119. Ab for
  120. 184, 40ode
  121. 2(16 194
  122. 40. 194
  123. 776
  124. 1746
  125. 194 5

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 89r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0179?run=73