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Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 17v

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: 0.75.

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. 16r); this page is its left half.

The machine reads it as

  1. imo non
  2. ye p puto haberi posse. Nam. ejus momentum ex xpest.1
  3. ex 7+B, est
  4. Eurgo
  5. r, Y.B
  6. y, y-e
  7. y, 7+β
  8. y, r. B
  9. Ejus monentum ex y-β, est
  10. Y, rrB I y, y 2
  11. Ergo f 01
  12. eodem modo.
  13. Enui
  14. 3, y. B
  15. 7, 7B
  16. 72 1I
  17. Y, rip quama differentia est
  18. Tam: ex N. Bdat , exZ ut
  19. Y7 Y. (
  20. Y77,C per 3+B dat , per y dat 1
  21. Habemus ergo
  22. y, 7+B T) y, y2 B sive.
  23. y, Y1β)
  24. Hinc illud altem ducinus.
  25. bTI b+ B, b+2β)
  26. 4yC. 2y, + 2y, y - β
  27. Y- se
  28. superest, ut quae d Circulo et Hyperbola dicca sunt perficiamus.
  29. scries: A 3.
  30. e y, yiβ
  31. 3, n
  32. VireB ( y 94. Ergo in aeq. 1. substitulis vatoribus ex aeq. 2. et 3, fiet.
  33. va +
  34. B+ B, b+ 2 yt I Y y .
  35. 55.
  36. sive 2
  37. V Y.
  38. + 2,y- V
  39. 5, =
  40. Beognit.
  41. +
  42. bas bB
  43. cognitae...
  44. rationigadnents Diametrum
  45. Ea sic cmnacrobitur amalytie: E y yoB. Ponendo, y. esse ardhmetice crescentes; et . esse inremen
  46. tum. Poimam autem V esse 1. et ipsam β. in erementum constans esse 4. Habuta, autem summa
  47. Unius
  48. 1
  49. 1,7 + β secundum hanc quam dixi explicationem, habebitur, et summa cujus libest, quomodocunque
  50. prima seu minima y. , et intervallum constans ipsarum 8. explicentur.
  51. Quod ita ostendo: Primam y a quaecunque sit vocemus Unitatem appellemus V. Retucamus
  52. ad unitatem, quim von serieus ex quadratura circuli pendens ita erit in numeris.
  53. 7,0+2 1+2, 144+Z 118, 1+81
  54. Quae a sere
  55. erc Haec series quadmplicata redibit ad hanc.
  56. 4, 47 :
  57. que B
  58. 41 4 +1+ = 4+2, =+2+2
  59. 2,2+
  60. in eo tantum differt, quod prima y. sumta est non 1. sed. cuferantur a se invicem, sane:
  61. e pando Z pro y et proB quando non significant 1, fiet.
  62. 3, 7+ = β
  63. E y+2, y12
  64. sive fei: Y+ y + 2 r E,
  65. unde. + sic 2y, + 3
  66. fier 712
  67. 3+
  68. = y, Y+ 1B (3, n. 1 = v 1e3)
  69. Y, V + = β, Y +3+
  70. 2v +3 + B
  71. V, x+ ZB, Y 12 + =B.
  72. v, y+ 2B, y + 2 + B I yr : B, Y12 3, yrE BY) 3 v2, vi
  73. Habenda est Ergo series ista:
  74. 2t 213 2 hioc = v. 16 . 5, + 2. Eer 1 1 t, 1r, 2. Bn 33 seu 27.
  75. 5+5 5015
  76. . sed haec progressio parum tratabilis.
  77. + 3 4 + - i set eErculo = + L - ex Hyprtula. Hum dlaptum, L - + 3 - + etc
  78. ex qua auferatur praecedeas ad circilum, fiet : + = L + 3 = H - + 2 - + + erc. 8i contranddatur
  79. frer:
  80. Rer.
  81. 122
  82. =2 X = + 2 = L ∞ - = erc si ab 1 - = + + - 2 etc. auferas = - + - 1 erc.
  83. 50 -
  84. 4M pom 2 13 in 2o 30 2 16 etc habentur
  85. 10 eli estun l. V. En rst a.
  86. e
  87. habetur ex quad. Hyp
  88. vid sec plagulam VIII

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 17v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068022:0034?run=73