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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. a
  2. Whecetore C +]- 2 a2 t22 and E F =D H-
  3. 2aC + ZE b. BNI EEg; t FCq. = CFg. -CY. g
  4. =CDgi + F D9;. 1hat i5, 4 a a 2 2. + 4 a 2 + 2.
  5. 4ba2- 2b 22 + bb + 22 + 22d + d a = Bb. + dd
  6. Expunioe bB F d d and chere will remain
  7. aa2 Eraax ta 40a 2022 +22t 2 d 2
  8. 0. nr
  9. Then it vou ArA mulcipIy aIl ehat Equarion b3
  10. PP. and divide ic alcerards by 2 you willbrine
  11. ix c0 chiis, 4a a2 f 4a 22+ 2- 4∞b a 2pb27
  12. DZ + 2 p p a =0.
  13. Or to reduce it ro a more Regular Form,
  14. Z = 4a ZZ + D P Z 4 p b a
  15. + 4aaZ + 2 P p
  16. 2
  17. Or il von hac called che whole Line C a by che
  18. Name ot a (25 Baker calIS ic p) che Equarior
  19. evould cand thus,
  20. X +2a22 + P p Z 2bP a -0
  21. F a a Z + 2 pb a
  22. -2b
  23. Nou compare ihis Equation Member by Mem.
  24. ber wich one siren eo be solved in che ulual form;
  25. a5 suppolC, Z + m Z Z +r 2 +5-0.
  26. Drawins any Parabola tatee DC-m Decaule
  27. 2 a=m) and apply ic inco che Parabola at rixir
  28. Anoles EO ThC AX AO. Nexe comparine the Co.
  29. efficients in the rvo next correspondent Perme
  30. Vou havep p +aa 2 p b =r Or p P + = mm 2pC
  31. =r: And consequeny, 1 - PP + nm-
  32. BY
  33. Ertich is che Rule 10 Aind C D, Or 10 deter.
  34. mine che Poine D, nearty the Came (chansins on-
  35. Iy The L EEterS) Wich Bater S first Rule.
  36. Then again, compare the nexE ro correspon-
  37. dine Terms in Boch Rquations roserher and vou
  38. have 2pp8 2b p a = 53 Wheretore d F 2bpa
  39. Wrhich beins all a Hnovon Ouanrier, che L ine FD
  40. is knoun, and consequener che Cenrral Poine L
  41. ot the Cirele ro be described, Whole Radius ill
  42. BC F C. Or FO, and which will cur che Parabola
  43. 50 25 ro sire you che Poines C, T and N; from
  44. extience lertine FaII Perpendiculars eo che Diame
  45. rer C FF, chey MaII bC the 3 real RoOrs oF chis
  46. Cubick Equarion, ZZ Z L m Z Z Fr ZF5 --O.
  47. And ertich are Nesacire, and wrhich AMrma
  48. rive vou will sind in the Constrution ot chese F
  49. quations by che Parabola: Which lec.
  50. IF rhe Liquarion had been 2 Biquadrarick,
  51. suppole,
  52. (1 + m Z - n ZZ + r Z 5--0:
  53. Then che Circle vould nor have passed chrouetr
  54. the Verrex oF che Diamerer, bur chrouxh anocher
  55. Point eo be tound accordins ro che Rules menci-
  56. Polirion et aet
  57. rected more calie, simple, or universal; secine
  58. any Parabola beins once tor ale acleliou, l
  59. sire au che Loors true or talle, ot any e quation
  60. vichone Reduetion, oe ans Alleratton unalio.
  61. ever.
  62. ened in Des Cartess Construction of Fiquarions; rilt be pataes lo che Scyle, and t0 one ano.
  63. ewtich is, 10 let V: sit s reprelenr che absolure
  64. Number ox siteh Perm in luch an Eiquarion, and
  65. have a Negacive Sign) ac righe Aneles 1O PC
  66. on che Verrex oF the Diamerer; buc it ic be L. 5,
  67. chenthat Line V: must De inscribed in another
  68. ther.
  69. Semicirele made on che Line EC; Whict beins cowards rhe Aphelion, as che sun is trom che len-
  70. et trom che Vercex ot che Diameres C, Will Bive ere os che Liccentrique cowardo rhe Poribelion.
  71. CENTHI
  72. in the PeripherY Ot CMaL SCMMCL OH LC,
  73. Poine chrouph which che Incerlectins Circle re-
  74. quired Mall PaIS. Sec the manner ho the cen
  75. erat Rule is investisared in che last Term ot a BI
  76. quadrarick according eo this Merhod OF MF. Ba-
  77. Per, under che Word Construction.
  78. Erom which appears.
  79. The Analticte Mertod by wohrich NI. Batiet
  80. ddeo a Lde; Tor a Parabora ven atetDea
  81. and a Point in is plain siven in Position, ne ex-
  82. Prestes ln ays, the Radius ot a Cirole pastine
  83. chronge Verrex ot any Diameter, chac is, by
  84. ehis neu Property, (That the Rectanele made of the
  85. Parameter and Difference ol us scssu, is equat
  86. to the Rectansle made ot the summ of the ro Ordi
  87. aates into their Differences,) ro express rhe Ratio
  88. oF the Radius co che siven Line ot che Parabola
  89. lo hat aEquation oE tour Dimensions, and re-
  90. jectins lc Liquals on boch lides, he depresses ic to
  91. a Cubict. de adjoinins c il a quatsels set inC
  92. Fsomosum Comparationis, chereby makins the
  93. utsble equal co nochins. che equation lubsilts in
  94. a Biquatraticse, havins all irs Terms: IE the Circle
  95. be supposca ro pals noc chroueh the Vertex ot che
  96. Crametes, Vol Chrouph d Lo WICA BeMB OIM
  97. ed vich che Vertex and center, may terminate a
  98. Risbt Ansled Triansi
  99. L Lquation he compares with anocher lke
  100. Ic, and equal l chen by equatine che C0-eff-
  101. cients ot chele cu Equations he prelencly disco.
  102. vers che Central Rule; Whole univertal Exrent
  103. appears in andraticte Equations, adtected under
  104. al Parodicte Decrees; Tor al che orher Cases
  105. wrhere any ocher Perms are mancins are bucCo-
  106. rollaries, or more compendious Constructions de-
  107. rived trom rhe generalRule. S0 char che Inven-
  108. tion ot che ue scems as much due rothe last F
  109. quation ot che C0- efficient 25 ro the atorelaid PrO-
  110. perries, whicl is demonstraced by archimedes in
  111. the Section oF a Parabolicke Conoid by a Planc p2.
  112. rallet corhe Axis, and es particas uleu oy siu
  113. sius in his Anyticts, wrho chereby constructs a
  114. Biquadraek Equation, Keepins aIl ies TermS.
  115. Buc chen the Analysis oF Slusius by breakins che
  116. quation into no orters ro sind cvo Places is ve-
  117. ey disterene trom char whereby our Aurhor tound
  118. his Centrat Rule ) CAAA HESLCLE BOLHLLM CAL NL CX
  119. CFNI of a Cirole, or oF a Sphere, iS chat
  120. Poine From Whece all Rignes ctan l ine
  121. Circumtelence or Surtace are equal. T0 tind che
  122. ntre of a Circle, sec Chord.
  123. CEATRE os a Dyal, is chat Point where thC
  124. Axis eF che World incerlects che Plane oFtheDyal;
  125. and rom chence in chose Dyals charhave Centres
  126. all che Four Lines are dravn. YF che Plane ot
  127. che Dyal Be parallel ro che Axis ot the World, ir
  128. can bare no Cenere ac all, bur alt che LTour Lines
  129. CENTRE os an Eltipsis or Oval, iS chaE POInE
  130. wohere the cvo Diamerers, the Transverse and the
  131. Conjurare intersect each other.
  132. CENTRE of ihe Equant, in actronoms, is a
  133. Poine in che Line of che aphelion, beins exactly
  134. distant (0 Par From che Centre of the Rccentrique

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/806933011:0146?run=74