Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 943 · Tschirnhaus, fol. 95r

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: 0.78.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. alam
  2. a
  3. tilineum
  4. cieneem
  5. ponamus a Adc ete quadran-
  6. tem en culi et AFsit X,.
  7. F
  8. E)
  9. ad E
  10. fa secare in duas
  11. parbes
  12. CdA in ratione data 1 ad n
  13. FE v.
  14. X. A D, y
  15. e
  16. cujuscunque modo sit talis
  17. ut in eo casu quo X est AB fiat 7= 0 verbi gralia si ponamus
  18. AB, esse b. ( et y e
  19. vel Xx- bb,: a, vel simile
  20. Quod s praeterea, velimus in eo
  21. e X - b
  22. genecaliter b= 12br. in Quiddam divisibile per X- b..
  23. et FEseu et dy: de:. b-X :y ita in eo ca su fiet, (vdx = n ydX.
  24. ergo (et V - yy+ n-1 X. b p: 1Y
  25. FdA f sydx
  26. AE C tali
  27. AFEA suax
  28. vdx C + Bfa aZ= Hsy dx. Et differentiando utrobique
  29. sed Leu relationis ad X assumi potest
  30. fiet YX se et radius ABLb. ese
  31. fiet X- b in AB =0 eV
  32. l A
  33. artiamopbitione ad Z = budx. y est datae relationis ad X.
  34. unuuisit
  35. pB, ocurrate
  36. AEHC, i N et 1
  37. seu vib(Xx inxaubxn
  38. seu
  39. quo
  40. et ut numerus ad numerum, vel linea ad lineam seu in raivo data
  41. se
  42. adatur DEqua sit et
  43. ex cuplo:
  44. s
  45. verb. qi. sit Trilineum ABCd, quaeritur linea ceA
  46. Ccirculs
  47. al
  48. s
  49. eu
  50. unde orferentiando aeg. 2
  51. unsde e
  52. evanescente ax habetur V. quaesita
  53. a
  54. bill
  55. bb. nbx. trbp x Led
  56. e nempe vdx + adE
  57. Sed si
  58. nut n’ydx
  59. datur
  60. autem
  61. Hobax-bax tnal b gerum si velimus praeterea, ut v eo casu, sit aequale y
  62. E
  63. e
  64. debet esse
  65. C 7 per X ergo _ et dZ per. X et dx,
  66. GNxs Xb. ydx +og majore arte est opque. sit ergo
  67. t
  68. et de= liX,
  69. X - b = C
  70. 1 . b.fiet Svax + h Z nsyax et differentiando
  71. ya. Ero differentianto;
  72. pagux et fet
  73. e
  74. I vax + de hdx + Xdh - bdh
  75. du quo fucto satisfiebe
  76. aqualion. . Nam
  77. ys
  78. X
  79. b
  80. et
  81. 1)
  82. . fiet Y +h
  83. fiet (ydx + sn - 1 X. b aX: y , n. 1. XY. BC
  84. itaque fiet
  85. (7
  86. 11)
  87. et
  88. et - en: a
  89. fiet
  90. = n ydx.
  91. ni
  92. p + X b Y: a Tanc
  93. 2
  94. ubi in casu
  95. 12)
  96. ny
  97. ubi in casu
  98. 9
  99. XLb fiet
  100. Ergo assumq
  101. y et fiet ch = n - 1 y.
  102. fit y + n-1. XB_: y -n. 1. X. b. 9 (potest h pro arbitrio, hoc tantum observato, ut in casu speciali saltem
  103. A 9 m+ v
  104. s
  105. seu SVax)3 (CE ) perS
  106. n(yAX. Et differentianto
  107. (4)
  108. 1t1
  109. itaque er quadrante firrculi cum X = b, fiat h ut cn ∞eg. I1.
  110. semper,
  111. de esse pn. x2: y. seu M semper esse = n - 1 1s erit etiam verum in casa speciali. ITaque
  112. + n. 1. y.= ny. quod succedits
  113. 2
  114. in X DE. loco ag. 7 scrbemus:
  115. VdX + n - 1 y. x- b, e n sydx. scet
  116. na yax aNdx +n- 1. X- b dyn n 19 dx
  117. ais safq eotn e fet v nay detxb tox ny y- n- 1. X- bdy. d. ubi pono dari lyids
  118. 1
  119. ese continue proportionates, Generaliter arax
  120. red n
  121. rocy nberi pet inde lineae natura
  122. ACH
  123. AB, ut R ad 1.
  124. det
  125. et por D prratlelar
  126. duc ips
  127. e

Cite

LBr. 943 · Tschirnhaus, fol. 95r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 79). https://leibnizlegible.com/page/DE-611-HS-867509:0191?run=79