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. 3 6 b : 66 0 6d0
  2. 14 0d.
  3. and cd.
  4. For il y0
  5. che ( a e d (I 0b.
  6. 1
  7. (Decaule the Radius IS =r) and conHo L 25 ehe
  8. Aris ot a Conick Section, che Part a c in che Fi
  9. eure will be che Abscissa Or incer ceplC AX pOPer
  10. co che Ordinare be; Wheretore call8, a5 is ulu-
  11. alu che Abscissa x and che Ordinace y, chis gene
  12. ral Properey oF che Cirole will be chus expressed
  13. 2. yX- X X=y y; FOr a e Deins X, a d n
  14. 2r-x, and chac mulciplied by x SH 2r X XX
  15. extrich must bc equal 10 D b a= y y
  16. e be
  17. It ervo Lines (25 a f and a c) trom a Poine (a)
  18. Wvithour a Cirole be dravn ro ies Circumferende
  19. wichin (a5 e0 C and f,) the Rectangles made by
  20. hose Lines and cheir Fxternal Parrs Malt Be equali
  21. Thac iS, II cab== If a c. Or thole Lines are
  22. to each orher in a Reciprocal Proporrion ot their
  23. Exrermal Pacto, i. c. ac: a5: a0: ab.
  24. Demonstration.
  25. E. Fhe Frianples a eb and ced are similar;
  26. Becaule the Anples ac e are equal, and ac, bc-
  27. cause in che lame Segmene; cheretore che sides
  28. about che equal Hnsles are Proporrional, ul lon
  29. 4C: cb: : e0: cd. D. F D.
  30. Sorol. 1. Fencer i ruo Chords eut each ocher,
  31. the Produet made by che mulciplicarion ot lu
  32. Paris ot one Chord, is alvars equalro che
  33. Produe ot rhe Parrs ostheocher:
  34. Phac is, che lP ot chefxireans a
  35. mean Lerms b cc.
  36. Corolt. II. IF one Chord (a d) be a Diameter,
  37. and the orher (b0) cur ic perpendicularty;
  38. then is be or irs equal ec, a mean Proporii-
  39. onal bermeen che Parrs of rhe Diamerer ae
  40. magine che Lines a b and b d 10
  41. bc drawn, he Triangles x end y will be similar.
  42. and theretore a e: cb:: 0b: c d. And cher
  43. Dravo bs and eo: Then are che Trianples eac
  44. and abf equiangulat, or rhe (f = Lc, being in
  45. ehe lame Scxmene, and a is common
  46. Lheresele a e: ac:: a f: a b, and then al
  47. retharely. a c . af:: ac: ab
  48. Mereto e X ab (=e ab)) d C
  49. fac.) R. F. D.
  50. Problem I.
  51. Fo divide he Circumterence oF a Circle inro a.
  52. Ay RAMBeF OE PAFES ROE abOVC 1O.
  53. Suppose che Cirele, A B C D WerE 10 bC di-
  54. The Diamerer AC divides che Circle, inTB
  55. 20 L Radius AF being made the Chord.
  56. AB, is the side oF rhe Isexacon inseribed by 15 e4.
  57. Lhe Line B D is the side ot an Equilarerat
  58. Prianple.
  59. ad.
  60. And A F the side oF a Square interi
  61. vided
  62. tvo equal PaPES.
  63. Euclo Theretore
  64. 80 ob atao d A dd AA d C A L AEC
  65. Xo 2 33. L. Heto 1152C
  66. and chis mar be called ihe Generat Propertu et) P. L:, ihc Rietr Line F L, 15 che side ot a Pentai.
  67. he Circle, arisine fron he ate o) the lurve
  68. edl it you cate a hoiarnert tat Crecte 3t Glndt ad vis uti

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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/806933011:0160?run=74