Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. -

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: 0.86.

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The machine reads it as

  1. the Distance C D, lettine one Foôr oF che Corripal-
  2. ses in C, cross ineLxis ac N and NV; L0 Mall MHCK
  3. Wheretore And a mean Proxorrional becween
  4. oE DF = MtO and L. M, ihich ler bem l
  5. Poines be the Foci required.
  6. LhIS FIBUIE.)
  7. And rhen make ML C = C E oE itie Hyperbola.
  8. For chen ail che LIyporhenuse N C, bc che Di-
  9. Aance trom the Centre C, t0 the Focus H, se
  10. quired.
  11. GOROLLARN IL
  12. Since che Rectanele DN F ]- Squate CF-
  13. Square CN: Theretore theSquare CHI == Square
  14. C. F = Rectansle D N F. Duc cheretore FOr BrC
  15. vicies lake m == C N, andchen ivill che Rectangle
  16. DNE =mm. - in chis Noration, or wvtich
  17. more belon.
  18. P R OP. III.
  19. En che Fyperbola (Sec Fis. of ProP. L.) ehe LatuS
  20. Rectum is eo the Latus Fransversum:: A5 tBC
  21. Square os any Ordinate IK, is to the Rectanst
  22. BIF, contained under the Lines intercepted be
  23. emeen it and the Vertexes of the Latus Franl
  24. versum, and the Ablcisa.
  25. Forhere (as abore) = Latus Rectum, 0b
  26. =Latus Fransversum, ando e c d e ec d, vilt
  27. bc = K ISquare, and the RectangleDIF, i5
  28. 0b b + co b b. Wheretore place chose Terms
  29. accordins ro che Condirion oF he Propolicion
  30. 6,
  31. COROLLARY I.
  32. (bY Cor. L. Prop. 2.) ihe RectansICD N F.
  33. : Cohich Ouanrier - = -, is also (BY
  34. Cor. T. OF this Propoposition) proved equal 1O A C
  35. Square: Jis plain che Rectansle D N P = AC
  36. Square, ot 10 a fourth part of the Fisure, 25 Apol
  37. COROLLAEY MI.
  38. Elence cis plain, That rhe Sgnare OF (C F) tiale
  39. che Fransverse Diameter, is Forhe Square OF (AC
  40. OF P F) HalF che second Diameter, 25 tis called: :
  41. ASche Latus Fransversum ro chie Latus Rectum.
  42. For 0bb 00cd
  43. cd: : 0b:
  44. t
  45. :: 00bb: 005 d: : 0bb:
  46. COROLLARY I.
  47. Axain, Since C F Square: A C Square: : ob:
  48. B (by Cor. 3.) chac is, :: AS he Rectangle
  49. DTE: TK Square (bY chis Proposition) elie Square
  50. OF halF che Transverse Diameter, is ro chie Square ot
  51. talE che Second Diameter; (Ox by Cor. 2.) 10 the
  52. Rectansle DNE = A C Square):: AB che Rect
  53. ansle DLE, 10 EC Square oF chc Ordinare
  54. E
  55. COROLLARY V
  56. Fence che Square oE che Ordinare FE L, (Prop. 3.)
  57. Which hicherro in che LIyperbola hach been deno:
  58. ced by 0ecd eecd, (lec Prop. 1.) may receire
  59. a netr and asetul NToration, etus: SincC C F =
  60. : 0b : : 0ccd = cccd: cobb F ccbb. ies Square will be o . Sax cheretore, aS C F
  61. Squate: 10 etie Rectatigle D NF:: Rectonele
  62. And ervins by mulciplication oF che ExereamS DLB: e02 Fourrh Pertm, ertrich will be etie Square
  63. and Means, vou will sind che Came Ouanciey
  64. 00cb d -1- e0b0c d arise trom bocti. And
  65. cheretore che Terms are cruls Proportional.
  66. P. F. D.
  67. COROLLARY I
  68. Inche Hyperbola (Sec Fiz. L. OE Cor. r. OF Prop. 2.)
  69. IsAC Square, Or its equal F F. Square (- 0oc d
  70. extrichis = OF D P mulciplied inEO L NI) bC Fatret
  71. OnE OF CF Square, or ies equal C H Square, (1. c.
  72. OnE OF 0OCd1 00bb
  73. bY Cor. T. ProP. 2.) chere
  74. willremain uotiole Square Rodt is
  75. C D = hale ihe Lacus Fransversum DF.
  76. Wheretore here, it che AXes be giren, che FOci
  77. arC (O 10O: FOr draw thro the V erTCZ L, R F per.
  78. oF ehie Ordinate LR: and in chis Nocation ic vil
  79. Aand chus.
  80. 45d0b
  81. b
  82. :: 50150cbb F. ecbB
  83. cotemm, deomm = 0cbb = cc bb. 50
  84. hat ehie Squate L K, is equal E0 + c m m,
  85. 4eemm =o c bb = c cbb. The V (e oP vtiete
  86. pendicutas 10 L. D, and egual 10 C A, and wieh
  87. vill Follon in che nent Propohaion.
  88. Sine
  89. 00c
  90. eRC
  91. lonius callS ic.

Cite

Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. - . Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/806933011:0427?run=74