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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 60v

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: 0.82.

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. 61r); this page is its left half.

The machine reads it as

  1. et habebitur: aa
  2. 2a4
  3. aa
  4. zax + axa
  5. aa + 2cx + = XX
  6. 2aX + a XX
  7. (s. jam X sit quadratus)
  8. aa F2CX F C Xx habebitur
  9. quaesitum, priau habebuntur
  10. Naqu. 4aaq - 4a vvq+v
  11. + Vva
  12. posterius habebitur sposito
  13. quod e affinmation)
  14. sed sic melius:
  15. sit xaqu yycode et
  16. sive ZZ eq aa
  17. perii
  18. et 2a 4 a X et denque
  19. si fairamus:
  20. faciludo:
  21. +c. fat
  22. bb rax + a xr a siat aequ. Xx
  23. aequ
  24. eote +a
  25. Haec aequatio mutanta est in aliam rationalem,
  26. sic ut assumta nova indeterminata v, secundum eam
  27. vel Z dx=
  28. quantitus X aZu fat rationalis; ita enim figura
  29. reducta erit, ad aliam homometram rationalem,
  30. Itaque ponamus: E aeque
  31. X lugu.
  32. F ago. X + X, fiet:
  33. va X qx
  34. a (+
  35. E KC aequ.
  36. paxtax
  37. seu vo troxie aequ e mo dan. 29b0
  38. 97
  39. ratax
  40. at
  41. aqu h+Z. s sit (2+ +8 qu V. fiet:
  42. ago Z+ s _ -c aequ Z - 2 sC Ergo
  43. a. per rationales
  44. Ex his manifestum est, haberi s2zdx item
  45. 2a 7 a x aequ yy co eC
  46. aequ
  47. quia: bb a
  48. 2Z- ca
  49. 2AX + a XX
  50. aa
  51. habebitur:sad
  52. seu quadratura figurae, ex dato XX (per rationales)
  53. et aa + 2CX + = xxoq Vcorvee ex data (XX du qseu moment momento figurae
  54. (41
  55. Ergo 2a + a yy cowe aequyy1 ee
  56. el. aa + 2C yyco coe+
  57. +Cyco ee aequ’yyco ée
  58. et pro a in aequ. 6.
  59. ponendo valorem ex aequ. 4
  60. fiet.
  61. lac yycovex += ayyco eg
  62. 4 +
  63. + 2Cyycoco +Cyco e
  64. aequ. yy loex. sive fiet
  65. eaequ. habebitur e. sed
  66. quoniam ista prolixiora,
  67. satius redire statim ad X
  68. ex tangente verticis Habetur autem (Xxxdque si
  69. modo habeatur: S. XY dx.: Ergo habebitur quadratura
  70. figurae, si modo habeatur: (X3dx.. sed
  71. XZ aequ X quaabb
  72. 2a X + 4aC XX f 2a cX
  73. dx + fXX + gX + hiX
  74. loco X scubatur ey. et fier:
  75. dey + fecyyt gey Mhey
  76. quantitas quanda quadrato
  77. ab lx + Cy + hCyy. quod
  78. sub finem hujus plagulae fiet:
  79. 2a + ax, Z H nf a77
  80. ergo tantum opus ut inveniatur aabb dq
  81. 24Z + a XZ
  82. Habetur autem (xZ dqu, exdatasZ ax
  83. aa FZCX + E XX raxtA XX
  84. debet esse quadratus fiat multi
  85. plicatio actu ipso:
  86. +a XX +2a CX +
  87. compendio
  88. n7 Ax p
  89. a ia 4
  90. 2Z43
  91. aequ caa aa 2a dx 4 aa a x dx
  92. rax F L XE (IIA F2) Lba
  93. 2Z ca
  94. datur ergo 7+t 27- da xY sed haer
  95. pendet ex tribus: (7)X dqueZX. et (Xdx
  96. datur autem suexx per aqnationem primitivam
  97. datur et
  98. sa dx semper ergo datur
  99. Ergo X_gus dque aequ aa d77 x 4 a xZ ax
  100. seu DaZ
  101. Ergo 232 (2) bba dq aqu. 2aZ ax + x Z x
  102. - bbL
  103. 27 ca
  104. aa X + L. dx
  105. d + dxy et AZZAX p
  106. est autem 1Z Z aequ. _ Mx iZ + a Ya. et Xxt bb a
  107. ergo fier: 6G aeq.
  108. C +a
  109. x + dy Y -bb c3
  110. Z2. la
  111. A
  112. E Ca
  113. _ faxx
  114. +2, 14 49
  115. sed inte habelus cantus a dx + xta qudalinide possi
  116. quq 29743
  117. C aequ

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 60v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0122?run=74