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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. and vet are OY CHIS LFODOIITIOM aS ThC AD-
  2. fessa LL ai L, WetetOC LL 10IF
  3. Ihe DF M ONSFR AFION os mhict
  4. Practice depends upon ihis.
  5. THac EN Beins = ~E COF F. F put ib.
  6. 0cC
  7. ehen Mast. NF = ib-
  8. 5. iotiose Square is
  9. 2ibB - 0CCi 00CCCC
  10. 1660. Fo Wtich il Vou
  11. add che Squate os G F, twhich in ehis Way oE
  12. Oc L. ML, and lL. aec iA Collat
  13. Proporrion. 8. E. D.
  14. PROPOSFFZON VI.
  15. Nocacion ras abore seed ro be oi cc, then in ehe Parabola the Parameter is ro the Sum os
  16. the Square OF N C Will be i ibb -= di
  17. 1
  18. DOCCCC
  19. any o Ordinates, as their Difference is to the
  20. Difference of the Abscista.
  21. 160B. Whole RooE in chis Nocarion will L CaY, PL. che Parameter, is 10 TH F= F C.
  22. Be ib + . 50 chac a Line drann trom
  23. he Focus rO the End oF the Ordinare will al.
  24. Ways bc equal eo the Abscissa F F - R Y
  25. Thac is, (supposins F. O rakien equat 10 F. W
  26. roche Linc FO.
  27. PR OPOSLT FON I
  28. ::(Sec the last Fieure) ThatiS, tOFIO:: OC
  29. cheix Difference, is 1OI F (OFR O) ehie Difte-
  30. rerce ot hC Abscissae.
  31. Let P F the Ereater Abscissa be called i b,
  32. and che lesset P L, cb. Then, Dy Prop. L. the
  33. Square ot che Ordinate R L will be occc,
  34. axid consequeney cheOrdinate ir (etF= V: 0ec0;
  35. (02(0 purtins i instead ot en V: oicc will be
  36. che Ordinate P6.
  37. Flarins thus noced them, IE YOU PeE TMC LATUS
  38. In ehe Parabola FR CTI, the Squares os the Rectum, the Sum and Disterence oF the Ordi-
  39. Ordinares are as the Abscis.
  40. TLY HKFDCF: : EL. EF.
  41. rhC Square ot LC tHC Ctdiate, WIH DC eqUa
  42. 0 che Paramerer mulriplied by i b che AbIcisa:
  43. Ahat 15 = 0i cc: as hefore, ihe Square OF R
  44. Wa5 == 0c60. But Rectangles harins the lame
  45. Bases, are as their Alticudes; Wheretore chele
  46. Rectangles vilt be as che sscsa: And chese
  47. Rectanoles aee = TO InC SGuares OF the OF
  48. dinares; Wwheretore the Squares ot che Ordi
  49. mares are 25 C Abscissa. 8. E. D.
  50. nates, and che Ditterence ot che Abscissae, alier
  51. the manner ot tour Terms, in disjunet Geome.
  52. trical Proporrion (25 belon) rou will sind the
  53. Rectansles of the Exrreams and Means equal,
  54. and consequently che tour Termsro be cruls Pro-
  55. porrional. 2: li. D. AS,
  56. Param.
  57. Dcc. Sum oe ne Orc. . . DiR. OF chieOrd.. D. ABP.
  58. Y: 0ice V: Deco V: Orcc = Y: occc. ib - eb.
  59. Arid 10 avoid che Frouble os Mlulciplication
  60. in Surds, wtich isthe Cale of the rwo Midale
  61. Terms, vou need only consider chis Theorem:
  62. Thac ehe Sum of any. Tuo Ouantities multipliea
  63. hy their Disserence, is equal to the Disference es
  64. their Squares. For (o vou vill casily find that
  65. che Product in boch Cales ill be the same
  66. Quarrirs 0106 = 0eC6.
  67. 15 in a duplisate RatiO OI L. F IB F HV
  68. by che Construction ol chelsue, Il Wi
  69. be che lame in l. O, wrtrick is parallel W0
  70. chac is, EF. P N:: F N. F T. ANC
  71. FOxIEE E F Be called ib, as F L was vet
  72. called eb: Then che Parameter beine
  73. LC. LAaC1d, L. 1s L... 1 l. 1a la
  74. On Which our Famous Mr. Bater Founded
  75. his Clavis Geomerrica Catholica, Which wras
  76. untenown ro the Ancients, and communi-
  77. cared cohim by Nr. Tho. Strode OE Maper-
  78. con in Dorsetstire: And by wtrich he Chewe
  79. how ro find che Value oF che Onknown
  80. ROOt in all Eguations, noc exceedins Bi-
  81. guadratiots.
  82. Dec Construction and Centrat Rule-
  83. N. B. This is ThaE PrOPerEy OE the Parabola
  84. COROLL AR Y
  85. IF a Line, 25 L O, be dravn parallet eoche
  86. Diamerex or Aris ot the Section, aud be
  87. cuc by che Transrerte Linc P C in B,
  88. and By che Curre ot the Parabola in K;
  89. hen all O L, ML, and R L, be in con
  90. cinual Proportion
  91. FOr the Triangles F FC and F NTM BC-
  92. ne similar, and NM parallet 10 F C
  93. Pec D BC che ParaMeteE OE any Parabola
  94. 2. C. TR.) BHE ChC SGNAEeS OF C F and sDectire Absoissae A and a. THeN T AIM EO prOVC
  95. Lhis Properr ot che larabola, L ull DACI.
  96. demonstrare in my Alsebra, Pas. 78.
  97. E muse BC EO FNF : : a5 F G. PY MI Wtose ro Ordinates are O and o, and their re
  98. H are in a duplicato Rasio t L F 10 F. WV, seac P. 0 + 0.: O = 0. A = a. Wtiici

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/806933011:0596?run=74