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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 124r

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: 0.83.

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The machine reads it as

  1. Concipiendo abscissas x procedere in progressione Geometrica; eo ipso
  2. omnes auae figurarum simplicium fiunt quadrabiles. sit enim
  3. V = X e quaeritur sydx = X dx. sit dx = x deo posito ed esse progressionis
  4. Arithmeticae, fiet sydx = X da. Et reri sunt progressionis Geometricae
  5. ideo summari possunt aecrescant in infinitum Ce q
  6. b bb B3 1
  7. cob _. b, b lob,sbb 1.bs3
  8. =s. 1+b +bb M.. et s, xete
  9. 1
  10. AX, X XY, SA XX Xxdx = A Xdeo
  11. 1- pert
  12. 8
  13. deo sR = W X + X f X + X et = X, 1+ X + x + X et c, du
  14. = XZ d quid est rectam FA:, a X duci in rectam co
  15. 7 x3d an = X
  16. AB unilas est major quam X ultima nam X debet
  17. esse minor unitule, ut potentiae ejus decrescant
  18. hr logarthmica, ubi ACd est co, et covse
  19. est AX seu X. et coY suit X. ita Y in du
  20. ae quantur ipsis areolis ad curvam Y Y. 2 laque
  21. omnis quadratura signit simplicis recncitur ad quada–
  22. turam igo areae Logarithmicae qualis est V4. sed omnes loga-
  23. rithii co sunt similes. Ergo res omnis reducta ad unam quadratura
  24. Et reperietur logarithmicas inter se, ut numeros respectice
  25. sed a si esset ns(it) x ponamus itx esse progressionis Gcornehrilae
  26. nec
  27. Nonidem erunt et d (1+ X) progressionis Geometricae. Ergo et
  28. ) Ergo net dx
  29. 1+ B 1+ 2b + bb 1+ 3b + 3bb + b3, 1+ ab + bb + 4b3+ bt, etc sseddemto b 2b + bb 3b. + 3bb. + (3
  30. 1+ b
  31. 1. sunt
  32. b, 1+b
  33. 1+4 2b + bb
  34. 1+ 3b + 3bb + 63
  35. b, 44 2b. 1.
  36. 1 2+b 3+36 + bb
  37. sint X progressionis Geometurcae eo et ax et A X progressom G00
  38. et d (1t X) sunt progressionis Geometri cae d (1+ X3) est (- 2) A (1+ X (1GX)
  39. sint 1+ X, progr. Geom. erit et (14X) progi. Geom
  40. sed qui e quaerend cujus progressionis X, sit _ B = 1 =+ X erunt
  41. d
  42. 1+ X numeri, et cd logarithmi. Ergo si deo constant erunt 1+ X progress. Geo
  43. 2
  44. a
  45. o = deo b
  46. dx = de (1 = X.): n. X
  47. si esset = = - 1 faect m - - 1
  48. dx
  49. -1
  50. Et 7 (1 + X) ax = ( +1) 1t X2:n
  51. - (de
  52. n. X
  53. si esset B=X fierent X et X progess Geor. puosita dD contante et fiet
  54. et erit s
  55. 1 =XH
  56. d n, Y
  57. deb= nxax et B do = n
  58. sit
  59. = Y
  60. fit do = de.
  61. nm
  62. I: m I (X
  63. m+2) de.
  64. du
  65. (9 +r. + 5) etc =Y
  66. (19.. MY + n5) = F
  67. SyAx (vax = Co fit tySvdx + dx V sydx = deo
  68. (l. + m +n, et) = C
  69. (yvax = Y fii yu du dp
  70. C D = flq. +
  71. ( yy qu (Suax + vn qu (Sydx) + 2 vy (su du) syex
  72. fam deoded data = es, fiet = yy que sude -voqul sydx dx = ge vyax
  73. Axax
  74. deodeo: dxd
  75. gy soix ve sylx dx = vydx sit y = ((1 + X). fint 4X- L
  76. 2svdx sydx
  77. 2sydx 2sotx fiet sydx =
  78. L. e aZ= L.+ = +A F. R23:2
  79. incipiendo a Z = 1 sit V = Ex fiit sd 2 incipiendo aat
  80. seu.
  81. sudx sydx
  82. vel Sydx = Z (I +X) 3.2 et f sit v - sx sit sudx = L X
  83. anpo (et L(X 1 X) d = Cd = = (X X +X) 3. 2 et deo = 4 (XX + X) : 2 3 sexcx t H

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 124r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0245?run=74