Leibniz Legible

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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: 0.85.

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The machine reads it as

  1. dietes are a0 che, Squares ot he Oidinates
  2. The Larus Rectum may allo here, 25 vvell 25 in
  3. he Pgrabola, be Ceomerrically foundo
  4. LDKOELARE
  5. N BC ThC FOcuS; ihen will L. N = 2 b ane its
  6. HE che L atus Rectum L. MI, be applied (0 as rhar
  7. EE vou sind srst EI F, a chird Proporrional 1d L
  8. thie Abscissa, and 10 R I (OF F F) che Ordinare
  9. (Sec Fraxis 2. in che Parabola.) Atcet Wnentind a
  10. Fourch Proportional LL. ro DI, cheSun C Lan
  11. Transversum and Abscissa, 20 TIF, and toD P, etie
  12. Catus Transversum. FOr supposins LS = II F (2
  13. it misut casili hare been made by drawing ic a lit.
  14. dle lorver) ac che end ot wrhich place S, and dran
  15. D5; 25 2I(0 I E parallel EOFIF: TNeN MMAN L.S
  16. beche emus ca. 2ct dd 1. 1d.. (6.
  17. AE.) (oDF: L. F.
  18. COROLLARY IV.
  19. Erom wohich eis plain, chat tavinae EHC Latu
  20. Rectum and Transversum, the Ordinares in any PTy.
  21. perbolamas de HC CC CuIr
  22. casly described.
  23. For cakins any pare ot the AXIS (a5 L I) Forthe
  24. Abscissa, ana aking as D L: 10 L L :: 5001:
  25. Square
  26. 4
  27. .Bursby chis Proposicion) a
  28. che Square R l: Square L NI :: Sois ihe ReCtan.
  29. Se DLE: Rectanole D N P. That 16, 25 e 0C d
  30. 10ccd: 0ccda
  31. 00cd
  32. 4bb :: 0cbb + c cbb: 10
  33. Wohich will be found eo bethe Fourch Perm
  34. bp chis way oE Noration. Also chis Rectanele
  35. DNE (bcins made out oF che Whole Line D P
  36. wich rhe part added P. NV, mulciplied by chac pare
  37. added F N) cogerher wichche Square of C P, che
  38. haltos D E, (= = O(00b b, 1. C. = OE0b 5quare) i5
  39. equat 10 d = 00b
  40. = C N Square, the taH
  41. Line wichche parr added. Wheresore C. N is che
  42. co a Tourch Proportional LS; and chen sindins a lDistance Trom che Pocus = 1. .0c d = 00bb
  43. mean Proposctonal Berween IS and the Ablcista
  44. F I (suxpote LK:) That Line PR righely applicd
  45. Mall De the Ordinate soughe, chro Whole POint B
  46. ehe yperbola W Pa(5.
  47. OE lohick MC FOrmex Par dC, is che Court ac
  48. Or he Rectansle ander e Lacus Rectum (20 d.
  49. and Fransversum (0b): Or a5 Apollonius calIs it, the
  50. tourch part ot che Fipure; and che orher parr Dob
  51. der the Fines lyine betmeen the Ordinates and the chat from hence we may have a Canon co deter-
  52. mine che Focus ot any Fyperbola, thus:
  53. Add thC FOUTH ParE OF the Fisure (Or OF che
  54. Rectangle under the Latus Rectum and Transver-
  55. Lecthe Axis OF theSection E B bC called i b, 25 Sum) r0 che Square OF hals che Latus Transverlum:
  56. and extract chie Square Roor oF che Sum, chai
  57. Roor all be che Distance of the Focus from che
  58. Centre, = CN. And iE trom C N vou tate
  59. halt he Larus Transversum, C. F, ehie Remain-
  60. der, F. Wd is che Distance ot che Focus trom che
  61. Vertex.
  62. Wrnicn Rule is vers eatie in Practice: FOr
  63. 90bb
  64. +
  65. is nochins bur ihe Squace Ot C F; anet
  66. is onis L os D F mulripied ineo L. HI.
  67. OP. II
  68. In tne xyperbola che Squares os ehe Ordinates K Y ana
  69. Vertices or Extreams of the Latus Tranlversum
  70. and cheir respective Ablcista. Sec Fiβ. PrOp. 1.
  71. belore L. L ivas called e b: Then by considerine
  72. Prop. 1. eis plain, thac the Square of C F wilt BC
  73. 0i cd - ii c d; and che Rectangle DF F
  74. Wviii (by Mulciplvins D F - = 0b -) i bby F F =
  75. i b) be tound r0 bcoi b b. - ; i bb.
  76. ABaI the Square oF FL I, will BC EO the Square
  77. OFGF: : 25 0e0d -) = c cc d (By Prop. L. equal 10
  78. 11) i5 10 Di c d 1i i c d (nO proved = E0 thC
  79. Square ( F.) Tharis, caleing awvay c d, which is
  80. COIMMON, 25 0C-= 0 c, 151001-l i i. Bur in such
  81. very Proportion are the Rectangles D L F and
  82. Fior DI F =- e0 b b - 1 = e e bb (because
  83. DF == ob and EI = c b) andD F L = 0i b b -
  84. 2Dd, a5 Was proved just abore. Nou there is
  85. no dondt DuE e0bb 1 = e c b b: 0i bb - ii b
  86. ec: 01-Y 1i. Whecctore chesc Rect.
  87. GF, are as the Rectangles D IF and DF F, un- iS = OE che Square oF che Latus Transversum. S0
  88. EL
  89. Wheretore

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/806933011:0426?run=74