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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 27r

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: 0.76.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 28v); this page is its right half.

The machine reads it as

  1. entemualiter equationem 60. 6a (20c - 46l) 20. 40a (:0 - 40) = 0 et fingagus esse 20 - 40, a = 4, 20c- 40
  2. fiet 20, a 4 C = 40, a t b, f. et 40 = 20, a 4 c, :, a 4 b et 60 660 = 12040 = 20 H(a + C, : a +b)
  3. sit 4C + et 20 = a - b, et 40a == a = c enit 460 (a - b, a -c), et cum in Coniccus curva, cui
  4. haec destinamus sunt b et c quantitates rigativa hinc. a a - b, a-c est quantitas affrrmatioa
  5. ademue 60 est possibilis
  6. Est ergo 20- 40, a =. 20c- 40b
  7. 20- E. 47a = 40 c - b = 20c- 40l
  8. Aitera aequatio resolvenda est 20. 30 (20 - 2. 40) a + 2.50. 60 (20c - 40b) - 30. 60. 806+
  9. a (a - b, 30 (2C- a - b) L50a (a - b, a -) (c:- b) _30H (a - b, a - c)
  10. L2.30- 40,
  11. 0 seu ana
  12. et
  13. 30, 2ac = aa adrb t ab t lb + a t 30, aa 2C - aaa C a ab ab2c + aba fabl + aba- abc Cbba tb
  14. 30 (f(a - b, 2ac- aa ba + 50 ad (a - b, a - C) (cub). fit 30 = dec- b Cr aa -): a
  15. et 50 = +2ac -aa bce raa = ab): aa
  16. Certia Aequalio resolvenda est
  17. 12. 40 (2 40) dat 2. 56. 60 a (20c- 40b) +1 260. 60l = 0
  18. seu 12 (a = cg 2 2b + a + C) +rpa ab - ac +b) 12 (a -C, a - b) C + 2.56+ (a- b, a - c) (c - b)
  19. seu 1F 12 (a -c) (2 ab taa + aC + ac - b C) + 2.56 (c - b) H(a b, a - c)
  20. fiat: 12 = 21b-c) Naa- ab): a et est t
  21. 204 +b 1 et
  22. et 40 - 20 = 20) Eca +b = 1 = 20, E= 20a - b s. F C = E0a - b p = A, srol -t0- 20 - 20 s
  23. 0a+
  24. 20a +b
  25. fiet c = 20a - b = anac e 20a F bcd fiit 20 = AC - b + bcA, 1, 4) +4
  26. i 60 fingereter = 20 = 40 fieret 20 - 40, 20c = 4ob = 20. ~ a
  27. seu 20. 20c + 40. 40b 220.40 b. = 0 sit C = VY et b = - β3β, et fuast
  28. =20.4u c 1+
  29. aoVY 20. 40 aa = 0, fiat ββ + V7 - aa = PB)
  30. a LC + y sin aa = CCFYY + 2B) et a B et B 2ost +).
  31. A po
  32. potest suma 20B et (40 - Y
  33. et 20 + 40 β3 a X 1.) 7.
  34. et fect 6o β- V esse g+
  35. Ex aequa pet d . 30 (+B 30 +B (+ B- 3) p B +)y) + (3(3 2B) + YY) eB
  36. fiet a = + (8 4)
  37. +
  38. et 60 et (+) + 20) (+) f 20β = 0 et fit.
  39. 20 = Et fier potest 20- (4) + B et F
  40. 20 = (+) 6 + 40 -(1)) et 60 -() B(+)
  41. seu 60 = (+) a.
  42. Ex aeg. 2 siel fe (o A 2. 4) t (p.) -(4) 2u 5a (20
  43. 30F20 (20- 2. 40) a ∞ a Bβ) (+) 2. 50 (20) 1 + 40 (B)
  44. P. e a -) B F (1+)
  45. seu BB- 2β)8+ B 1 (4. ) 2. 3( (+) eY) (4 0)BP) = quae aequitio d di ptest per β3-)
  46. et fit 30 a 2β (+) (4, 2.50(), =d seu fieripotest 30 = +4) et 50 = a
  47. 30a.
  48. Resumamus in aequ. 1. sumsimu 60 = 3 (20 -40). firt 60 20c et aC = -yy et ab = = ββ, et ex aeq. 1. fis
  49. 22to-40) (. 20y + 40 (3β) +20. 40 aa =0 p 1 seu, 20. 2014 4. 40 338 20. 40 (3= 20. 40 a a: N
  50. F20.40
  51. Ergo fiat β(+7 3 + aal.s = + 2β5 (+) q al. D +B +7) + ux
  52. et ficret ex huraequrtine + β +7 fjaled) = et ex pusic rd avito ( C = (( 20 4, + p) a t 2)
  53. Naplical facire
  54. An sis 2au 20.207 140 403 4 ) = 12 40 ) +. 20 20. 40 (Y + 20. 4ol B 1F p) + 20 +0 a4
  55. 3
  56. 2. 20. 41
  57. si admiteremus imginacta posset, poin 60 = 1 (20 40). et ex aequ.d. f. Eet A (20. 40) C o s
  58. seu aa: A A = 20. 207)+ 40. 40 33 = 20. 40 B(3 - 20.90)Y. qu et peret 4120 )40β = 0
  59. s poneremus 20. 40 (3(+.). 1. t aa =. (+1) 2. L9. 4 (. BV. sed ita finit aa: ad quan
  60. tX
  61. Faciumque re 50 = R. 20. 40 fiet A L. 20. 90 ( - 20)) + to (() 0 - 10 = 40 - 20, ab
  62. re titus negativa, quod non licet
  63. Si fiit 6060 = X 20. qua, fiet. A (ao C qu1) t Eo - 4) a u = 2017 + 40 β( = (40- 20) aq: X
  64. sed non video aliquid commodi inc nasci
  65. siet 4u 40 (3B - a4) = 20 (V7 - a4)
  66. fiet 4 W)Y = = 20 βB
  67. et qup
  68. set hoc ut prus. Finganm aa: = c BB+VY
  69. et potest esse 40 = β3B et 20 =VY sit A = 1 fiet
  70. ob - 20)1 +4o(d B = (10 - 20) aa, fit p 7 = ( - y, (B 3 + V7
  71. 20c - 4cb = ((3 - p+ + (+ = aa (2- y7)
  72. 60. 60 = β31) Ergo 60 = = β)
  73. Itis positis in aq. 2. siit 30 fad (-s ( )B 30(e ( ) ( - ( p e 1 ) ((3) qu. 50. st ( y
  74. it ut patet
  75. fiat 30 = + . 2βa a (BB )7) et 50 = aa B3) - y5
  76. Et in aeg. 3 tint 12(2YBC Bna BPIY WVH) + 2. 563) (C X - y47 = 0
  77. 37
  78. seu 12(2 Bp y + (5) aB - p6- (Y BB p ) + 2.56 (B
  79. fit 12 = + 2 7 (pa pa5 et 56 = fBY) (BC+ 7Y) - β 4 seu 12 4 2ffer
  80. 12 = 4 2aa) (1). () et 56 = (i) Vaa = β
  81. os a iactun ti adet iot is e u 10. 60.
  82. 30no, gdiditer. im eaius li tandeus avenduu lduitum et ne siet v 20. b0 i a
  83. ac
  84. X
  85. h.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 27r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0053?run=74