Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 1, 17, fol. 7v

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.

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. 4r); this page is its left half.

The machine reads it as

  1. linea restat ex perrunda Methodus, prindivisibilium, seu Fermatiana
  2. ca culum egrego contrahit. Pone scibret circulum secare sectionem Conicam, in punctis
  3. Ergo erit sits
  4. aa
  5. en
  6. sed e i ea coinicidere, seu X (X) esse infinitae parvitatis.
  7. Dui
  8. A5 esse 1 GY + DG, et GZ , jam GY_ seu F4
  9. ave (a co co a)f + (acacO) X F GY. et
  10. PGH +DF-
  11. +DF -
  12. -DF +
  13. + DF +
  14. γ, sive (aa04) d +(00a) y. compendiiantem
  15. quae
  16. V(Y)
  17. AFL AX
  18. I AF+ AX
  19. +AF - AX.
  20. inscribendo causa pro (acocoaf ponemus simpliciter f
  21. pro (aaca) a, ponemus simpliciter d, quia non aliter occurrum
  22. ry
  23. a
  24. 1
  25. d et f. at plo et pro (a60) X poremt pifa co
  26. ponemus V. quia eaedem literae non aliter in calculi
  27. occurrunt.
  28. Erit ergo GL, P+ X. et DG
  29. d + Y.
  30. fX + X + d + 2dy + s, et pro y substituto ejus nalire e aX + a X fiet
  31. (B) af X + X + d+ ( (3) id Traxtax + 2aX + a N, et contrahendo βp aX AbJ) los, fiet:
  32. (1 S + d2) + bX (ponendo bp B2f + 2a) + d X (ponendo DB+ + a) + (3) id raxta
  33. atidem Si) h + bx + be +d X + 2d CX + 83 e + ( sid Srax trae +a X fa ex + a et xdeletis
  34. communibus fier: +(V) id Srax + aX bC + d Cx + . . . . . . . . . . . . . . . . . . . . . . . . Aquadrandontrotio
  35. abjectisque
  36. fet: 4d
  37. gd aX + 4d a X ( b C + 45be X + 45
  38. om
  39. +9d a ex + +da e, et Q rursus deletis communibus, abjectisque ea fiet: (2DC + 4
  40. ab 2bg + 168 be
  41. e multiplicatis,
  42. 1N da C 4 0d’a CX, et quadrando utrobique fiet:
  43. ex, Gd....
  44. X + 16524 4d rax + a X (abjectis silicet omnibus in radice contentis per
  45. divisis omnibus per e,
  46. 4at2e
  47. vel X
  48. ax
  49. 4 1 e 16d a 2(+ AD) 1+ 2X +
  50. aut a
  51. ordinataque aequatione habebimus:
  52. dbu X3 +oqfisob Xa 2
  53. 184 2 84 an.
  54. AsX + ubgsa
  55. +214
  56. M
  57. xd a
  58. da..
  59. L 495
  60. = d’a
  61. n
  62. 252
  63. v
  64. X f d a39
  65. 8
  66. in circulo
  67. unde nisi erroo in calculo insit erit XF, 2g. quod
  68. X
  69. Est autem d in parabola pa, in circula p0.
  70. utique absurdum, necesse est ergo in calculo ermtum esse. Unde in circulo ( XX + XaX +d a 4 0
  71. fieretue:F X _ + LaX + N Y, - 2aq + a, sive fiere X + S - a -a
  72. sive X + 2aX + a 570, sie X ⊓ -a quod est absurdum, calet ergo enor in calculo
  73. Egitur pro constructione Ellipseos redeamus ad calculum a nobis ab iitio indentum exploratae
  74. veritasis resumtaque analogia, et ponendi:
  75. F(+F) 4(+F) f B_ h,, et d p, (1 +d tet 1+27
  76. et stabit analogia gnero ds: d +2ddy +8. v2.
  77. a
  78. a + 5XV
  79. 1
  80. a. Ergo si d ro. problema erit planum, item si h0.
  81. poncudo aq + y Z Reret
  82. q + qua
  83. 7, et sotoe pot. st problema mollo et dua habebimus aequationes: dz - 5y Z A y.
  84. Le potius a9 + y 5, 4 Z quae est ad circulum; aquatio
  85. :7a modo silice signe in caelers pore nata
  86. 3 s9
  87. autem ila est ad circulum aq + y
  88. untemu ut res postulat. Caeterua ex his atet in paribola problerun esse planum; mo genercliter
  89. ponendo aZ 1 pro aq + dea tiet: altra aequatio: d + S V
  90. a
  91. 1 3 14. Hui patet oame
  92. constun problema ope axirculi et cugusdam Hyperbore lari rectum Z transver sumque aequalia habentis
  93. a
  94. Y 19
  95. ayr
  96. pone. V
  97. vagt
  98. 7 3
  99. a + y_a eit 47
  100. 127 12d Sagt st + Saitus et act
  101. aequatio ( ordinata eri. +a V frodV + daY
  102. 1 +
  103. ye
  104. atC
  105. A Va, ma aequatio k alta.
  106. et ga erit = A2.
  107. et.
  108. sue Y e + 22
  109. inzaque Atque ita
  110. + 15d9a) +d a 4 10
  111. nunc quidem modum ostendemus, quo constuctio
  112. set. ii Ellip si quoque 3 Hypebula sic satis dorevis
  113. ceddi possit Tantum ergo ponemus gp r. et 0 idque univers aliter adeoque in ipsa quoque parabola observari potest
  114. dimo male, .d non pucedit, nisi in parabola. Ex aequalione
  115. Ebrr 2s
  116. quod si jam (extra pacabolam.) ponatur 1. 6br + EOY, huc 8p(.6b7F 2( +Zg. entu
  117. + 2t bg - 1 4
  118. selur
  119. qu
  120. e.5
  121. valor
  122. inde
  123. Atabela 9 ex supposita b. sed non podenda bps r2B. possumgetiam faceae D V4+0. ptque ita sumere 9 talem hut fiat j0
  124. quid mea sententia ontarum coutumt est, quia universalis d sit ostrnctio, excepta partctu
  125. satet autem
  126. AF+ AX

Cite

Leibniz-Handschriften zur Mathematik LH 35, 1, 17, fol. 7v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067979:0014?run=39