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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 202r

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: 0.74.

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The machine reads it as

  1. RyX+a
  2. X, X+ a, X+2a. El
  3. XPXFa3 X+2a5X+sa
  4. g. 4 5..
  5. Al
  6. t
  7. (n 41
  8. 1. 3 2 5 3Z 4. d, 5
  9. 1. 2. 3. 4.5 6 7 89 10 11 12 13. 14. 15, 16.
  10. + 2n 1
  11. st 2
  12. X) XIXTa) X, XFa, XtLa) X, XFa, X+ 2a, x+ 3 a (∞ X +a, Xt 2a, X+3a, Xt +a
  13. X, Xta X+2a
  14. (XI Xta, XF2a, Xt3a, X + 4a
  15. X, Xta, X+2a, X+ha, XF 4a
  16. Numeri A, sunt numeri producentium in termino quovis seriei A, B, c.
  17. BC, et
  18. ubi:
  19. sed pro serie interponenda producentes sunt numero 3: 2, 5: 2, Ctc. set (non apparet
  20. quomodo numerus ipse terminorum possit esse fractus
  21. in serde A, sint termini m, fiet, (M): m = x+ha (mD: (m) = X + h+i)a
  22. fit na = (M) :m =X et ha = (m): (m) -x -a unde fit
  23. (m) : m X) = (mB: M) (= X = a seu (mD: (m) - (m): M = a seu S= a
  24. inserie B sint termini, C, et fiet (n): n = X+ ha, xtihtda seu fit
  25. ninseu
  26. (2) n = Xtha + a (X+ho sit X+h = Z fiet (ZZ + aZ + L aa = Cn) + L aa
  27. (n)): (n) = Xthatra, Xtha +3a = Z+ 2a, Z+3a, seu fiet
  28. 32 + 5aZ +6aa = ((n) et fiet en - (n) = +ZZ + sa Z + baa = 4 aZ+ 6aa
  29. 2
  30. = aZ
  31. = en) = (5) = 4aZ + 6aa fit 16 a41 2Z + 4 8aZ + 36 = 6 (5) (5). u unde
  32. Es
  33. 16 Z 16ac (2) = 16Z + 36 et fil Y32a3 = 13) (3) - 36 a -1 6ac )
  34. a
  35. n +484Z -(5)18)
  36. et fit a (5)15) = 815) = 16(1) - 12 aa. seu
  37. (n) (n)
  38. (1) (1)
  39. ( (n) (n
  40. nn
  41. = 2()
  42. (2)
  43. n
  44. L= 8 aa 6) - 48a
  45. inter BL, eN, med. prop. D. medio loco collocata, das
  46. eqao samicam media harmonica Hyperbicam, media arithmetis
  47. eat rectam. Quo si nar et si bc = dd m est med. geom
  48. si b + C, : 2 = d est med. aritem. sit L + L, : 2 = d med. har
  49. cC (
  50. 2b 4 ZC =d
  51. quitan
  52. d ved. aritem. +
  53. 2∞= + Z = =)b 0bsc =
  54. 2 b
  55. e
  56. quid si B L fab +L fac = d seu
  57. ac aabb + L (60 CC) =dC
  58. bb + dd = ae seu apbb + b + C + 2bbcC
  59. bb + ee = af se bb F seu a bb + a’ éc +a = af. undem
  60. quid si bb + cC = ad
  61. abb + (aa b b. + (Ib + cC)) = a)
  62. libt _ = 49 seu a bb. + (2((a. bb + (2) saabb + 13 (bb + CC))) = a a
  63. Y sy yy _ + (y) 1y) = ay) se y ag si e
  64. 60C sit (y) = 3+ du et (7D = y + dy + (dy)s et ficf.
  65. gy + gy + 29dy + dydy + 2y(dy) + dy(dys) + dy (di) = a y + ady 117a
  66. Hic dubitati potest, an tali ratione desinatur un quam in veram curvam
  67. id si sit CC 2y + = Ry) = (y) fiet 2y + L. y + L dy 4+ L (dy) = y + e dus
  68. ubi nemp
  69. differentiqu tosur sut
  70. ubi evanescente y fit tandem L(dy) = dy seu dy est coustans.
  71. et reducendo
  72. (2yy ( 29 dd 5y lly
  73. L
  74. L
  75. + 2 y+dy +(dy) = y+ dy
  76. posita dx constante.
  77. Edus ay-rtyatus (it y rus (9yAt 2ydys + dy dys (+ y Hy s dius ay) t 7y
  78. lydes
  79. tyd et sit dydys + dyldbys trodus = y dy) quod seu d9: dy)= y2 y +dy +ldy)
  80. us
  81. s
  82. +∞
  83. an liceret Ent invenire curvam
  84. y: (9) = (dy): dy fiet (y) = yy + (7)(7V, :, y + (yD quae
  85. Et
  86. ut desiderabatur.
  87. foret progressio auti harmonica de qua ad curvam redigenda laborai
  88. si
  89. ZaX = yy
  90. ago curvis valgaribus possunt duci tates prosrietates sit
  91. non vapat
  92. fit 2aX + 2a dx = (y) (y) et 2a X +4ad x = (y)()
  93. follendo
  94. Baec gearqsi a
  95. rax ex duabus prioribus fit 2adx = -yy+ (y7(y) seu 2adx = 2ydy + dy dus E
  96. et tartus 2adX = 2(7) (dy) +(dy) (dy 1X sea Ergo 2y dus F dydue = 2(7) (dys) +(dys) (dy)
  97. seu Eydus 4dy dy = 29id9) +2dy dy) +(ay) lay J. nen 2y ddu = 2dy(dy) = d9) dy) = dydy
  98. ubi in infinite parvis patet esse ganududunam A dyu sunt
  99. intrartisixfte pava
  100. fit
  101. e
  102. yddu Lte ininfinide anai
  103. C
  104. onlicis
  105. i infims bb
  106. et
  107. ad, quia in epsa
  108. terminationis
  109. Etoce
  110. alles
  111. boree lit
  112. c
  113. =d2C, 10
  114. sd - b1
  115. si
  116. d=
  117. -b
  118. cb
  119. = cd -c
  120. bbac
  121. bC
  122. in
  123. s
  124. d
  125. gdy
  126. Fddyddus
  127. agdus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 202r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0403?run=74