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: 0.82.

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The machine reads it as

  1. E
  2. chetormot PropostonalS, viz.
  3. And mulriplyins che Fxcreams and MeanS; You
  4. Produced boch ays; which hens hes alc. cus
  5. proponrional. P. E. D.
  6. WVHCrCTOre iE IC LaLAS RECrUM, AIII. LHC AIS
  7. Transversus be giren in the EIlipsis, tis casie 1O AnC
  8. cd
  9. ehe second AXC. BY mating a5 ob:=
  10. 00l
  11. (= Rectanele DC E) E0 20C d = Square AC. )
  12. Wheretore A C is Hnomn, and consequentir its
  13. double AB.
  14. :
  15. sum, Latus Rectum.
  16. L
  17. 2 a 2. docL L. 10
  18. AIsO sinCC C F. Square: A C Square : : ob:
  19. 0cd
  20. 5 chac is by chis Prop. AS Rectang C D LF:
  21. SquareTK. ThereFOre SGNArE C R: Sgnare A C
  22. :: Rectangle DI P: Square LR. ThariS alIO (b7
  23. Cor. 3.) 25 Square C F: R ectangle DN F:: Rect.
  24. ansle DTF: Square IK.
  25. COROLLARY VI.
  26. Wheretore chere wilt beFound a neu and uletul
  27. way oE exprestins che Square oF che Ordinare LR
  28. (wrhich we tound abore in Prop. T. W 25 00c d
  29. cecd.) HYou mate aS C F Square (= 0 0bb
  30. : Rectanele D N K = (o0bb. = m m, By Cor. 4
  31. Prop. 2.):: 50 Rectangle D L F EO L FOUKTH, PFO-
  32. porrional; Which orkins Algebraically by che
  33. Rule of Threc, will be found co be oc bb -- e c bb
  34. temm ammec
  35. The Adramtase ot which Norarion will suffici-
  36. EVhose Square must be 0oc d = Rectane le OP cheenuly axpear in thC next Proposion.
  37. Larus Rectum into rhe Transversum; i. c. theFigure,
  38. a5 Apollonius calls ir. WVheretore che axis secundus
  39. and any Second Diameter, is a Mean Proporriona
  40. becween the Latus Rectum and Transversum; OrrO
  41. speale wich apollonius, is equal in Pomer eo the Fi-
  42. Fure.
  43. COROLLRKE 1.
  44. voed
  45. Since the Square OL A C = , and che Squ
  46. OF C N (che Distance oF the Focus trom the Cen-
  47. C) = 0 0 bb = 00C d v7 Corol. 1. 0f ProB. 2.
  48. Pur them into one sum, and ches will matre
  49. 00bb
  50. : wohich cheretore must De equal 10 Square
  51. AN: And consequently che Line AN = Z, 1. c.
  52. E0 haleche Larus Transversum.
  53. Wheretore it rou hare che Axes in an ElliplIS,
  54. eis eale ro find the Foci; For rou need only open
  55. the Compasses to the Distance DC, and setrine one
  56. Fioot in a, crossthe Transverse Diameter in the Point
  57. N and N.
  58. COROLLREE M.
  59. Since bY Cor. F. ProP. 2. THC RectanelC DN F.
  60. Ca
  61. was prored equal to =, Wvtrich by Cor. Prece-
  62. CT-) CN = =0b = eb. m. BUL Ln wil
  63. dine = A Cq. iis plain RectanssC D NF = AC sBC = Cn = Ct = m
  64. SquarC.
  65. 2 0b + cb.
  66. eec d: and che Rectanele DY F is cobB-
  67. ee b, IH isb; as hach been evn in chie forme
  68. Proposirions: Place cheretore chele 4 Ouanriries it
  69. c
  70. CDROLLARY IV.
  71. The Square _ C F (- hallche Trantrerse Dia
  72. meter) is to rhe Square oF A C halF che DiameTeF
  73. snt. d5 Latus Lb sa C0 Latus Rectum.
  74. ::0d00. 8dd: : 0 bb : 0c 4
  75. oc d
  76. 300c
  77. tCt
  78. obb ocd
  79. 15 : ob: : 0cc d = cccd: 0cbb-
  80. Wwill End che same Ouantier 00 cbc d =- occbca
  81. COROLLRRY
  82. . 60
  83. .t. b. Latuo Lrars oe
  84. PRO P. V
  85. In che xllipsis, ehe Aerexate, or Sum os che Rishra
  86. Lines VN and Pn, drann from the same Point
  87. R, in the Curve of the Ellipsis to boththe Foci Y
  88. and n, is alvays equal to the Transverse Diameter
  89. or AxiS D F.
  90. THCPrOOFoF Which depende on che Contiderari.
  91. on ot the Rectangled Friansles II NI and TR n
  92. Where che Sides beins piven, che Hyporhenules
  93. are easily tact
  94. For il (25 in Cor. 4. Prop. 2. You callC N = m,
  95. cher Will m BeV:
  96. 100a
  97. AndLN =
  98. Whetetcte

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/806933011:0289?run=74