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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: 0.83.

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The machine reads it as

  1. the midale FOInE OL THAL LIHC LL, LoCateU M
  2. Centre os ihe dection, oc rdeher ot ihe opposic
  3. Sections.
  4. let
  5. 1
  6. Square oF IK: Wheretore etie Rectansle F E
  7. =PK Square; Wtrich in Ehis Nocation Will BC
  8. oc cd= eeca
  9. Or Conracteals,
  10. This done, procecd (as directed in Cor. Y. Prop. 1.
  11. Ot the Parabola, eo firid che LatUS Rectum) by C2y-
  12. in8, 25b: c: : 0d: , in Words, as che ParaI.
  13. let tothe Section is IO ThC PaFE OE the Diameter et
  14. the Base intercepred:: So is che Latus Primarium.
  15. toa toureh Proportional; ris plain, che Courrti P exm
  16. vill BC OonC ParE OF the Line TS, or in ehis HIOca-
  17. tion = = Lavus Rectum R L (oT L. F.) snd hC
  18. Ortrer will be Coune chus: AS b: c: : 8 d: E
  19. Or accordins c0 Apolloniuss ay of Exprestion in
  20. chis Provosrion: AS ob: : :) cb: : 502
  21. thac Will be Tound io De ehc Fourih Proporrional as
  22. besore: Whien is non found oue according c0 chc
  23. Fermis ot ihe Proposuion, becweenitié Lacus Trans-
  24. versum (0 b) andche Ladus Rectum =, arie THC
  25. Abicista eb.
  26. Wheresore decd cecd, the Square ot Htie
  27. Ordinate LR, is manilestly equalto the Rectanole
  28. uneer che Latus Rectum and che Abscisse; ayd al(0
  29. to anorher under ihe Abscissa, and rhe tourrti Pro.
  30. porcional. 8. F, D.
  31. res EOROL L AR Z si dor ecor
  32. Hence ihe. Realon ot. itie Name Hoverbola-
  33. Wrhich Apollonius sare i0 ihis Section,, is apparent,
  34. viz. Becaule che Square ot che Ordinare exceeds
  35. che Rectanele under the Parameter and Ab-
  36. scissa. ait 11
  37. MEDROLBARY H.
  38. IE vor mulciplys che Lacus Rectumlo c d, (wtieti
  39. is nored here as in the Parabola) bort. abore and be
  40. lo che Line by b, che Parallet r0 che Section;
  41. chere will arise ehiis Ouantity
  42. b
  43. Which beins reselred inco Proporionals chus:
  44. A5bV: Cd: :b0: ; eires exactiY Apol-
  45. loniuss Canon For fincirs he Lacits Rectum, (in
  46. Prop. 12. Lib. 1.) viz.
  47. ASthe Square oc ihe Bide os ehe Cone in whictu
  48. che Section is made, is to the Rectansle berveen
  49. the Scoments oF cheBase made by a Parallel co che
  50. Section, and deaun etiro ehie Verrex of the Cone
  51. ii dois che Latusi Transversum 10 che L acus Re
  52. dum.
  53. Thus in ehe anmexed FiBure, che Curi L17L
  54. it
  55. qi
  56. is an Hyperbola
  57. :acts ct cit B3i
  58. Wherc The Line P. D, Beins che Conrinuation
  59. OFthe Axis rilI ie meer with the opposire Conc, or
  60. opposice lide oF the former Conc C B produced, i
  61. called by che Name oF che Latus Fransversum; ane
  62. ek D
  63. En an Hyperbola GP FL F, ibe Square of. Ie Or
  64. nate LK, is equal botheothe Rectans le L. L mac
  65. andor ihe Parametes L. B, and tho Abscilla L
  66. and also 10 the Rectanele LS, made unuer +h
  67. Ascissa P L (Or L. R) and anoiher Lin BR
  68. ste is a fourth Proportionat eo D) F the L atu
  69. Tralretsum, P. P ihe P arartierer (or LAtus RC.
  70. clams ada ts t ehs Absetta.
  71. blos gicique sde stius sti
  72. Tet the Bde OF the Core AB, in Whick chie Se
  73. ction is, becalled à; andctiro B che Verlex oFche
  74. Conc, deaW B MI parallet co the AXis ot iE Secti
  75. on, and which call b. Pet The inTETCCPECE ParF Ot
  76. che Diamerer oF che Ba(C A M, bC calledc. Let
  77. LL = cb. Then by comparino chesimilat Prian-
  78. sles A B AP and P IN, IN, in this was oF Nor2
  79. tion, will BC = ec. And il vOU PuE MC =
  80. and che Transverse Diamerer D L = ob; CHeB
  81. ob -) e b. ANd BY TCRION OF THC M.
  82. milarier oF che Trianeles B MIC, DE P alc
  83. DIO, rou will sind thac P P must be exprelles
  84. Oy odq atid IO, by 0d-) ed; and consequeney
  85. DO == od. (The Ceneral Reason of all whas Wa)
  86. es Potation, and the may of morteins to obtainu, sou
  87. vill sec in ihe Parabola.
  88. This done, tis plain chat I L Square must be =
  89. 10 che Rectansle NIO; chatis, in this Nocati.
  90. On = occd -) = e ec d, 25 7 ou ill sind by MuIE
  91. plicacion. Wheretore iF occ d - ecc d, tll
  92. Square oF LK, bC dirided by che Abscissa P. L = ed
  93. ehe Duoriene must be such a Linc, wtich loBecer
  94. il D.
  95. Wvick F I, cam mie a Rectansie equal 10 he

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/806933011:0425?run=74