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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: 0.89.

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The machine reads it as

  1. F L
  2. Here also, as in che Parabola and Fyverbola,
  3. the Square L HE = Righr angle NVFO, prhich jou
  4. ill sind in the Fllipss, must be noced by o cc d.
  5. cec dus 25 in che Hyperbola (pou may (ec) ris
  6. 0ec d = eCcc
  7. IF theretore vou divideocc d = eec d == the
  8. Square OF the AbScisa Ordinate TF, by FF thC
  9. AbsCissa in this Nocation =e b, ic Wwill Aand thus,
  10. 0c0 d - 00Cd, or utichis equal
  11. Eo che Line TS; and wtich wichr che ABScissa
  12. E I = eb, will make P S, a Rectanele =- 10 LK
  13. Square.
  14. and it von ork here 10 tind the Larus Rectum,
  15. accordins to the Canon siren in tlie Parabola, by
  16. (apine a5b: c. : 0d: , vou will have
  17. FOr chC LatuS Rectum; Wtich vou sec is plaints
  18. one parr of che Line LS; and che orher, viz.
  19. =is a Fourch Proxorrional eob, 0 and e d. That sind 2 l Proporrional (F FI) rO F L and R L
  20. 15, in Apolloninss way, eo ob che Larus Transver-
  21. sum, = he Larus Rectum, and e b che Abscissa,
  22. (For the Pame Ouancirr -,. comes out bort ays
  23. Wheretore the Square ot the Applicate F L, i5 c-
  24. qual co che Remainder of the Rectansle IL, con-
  25. Fained under the Latus Rectum and Abscilsa, wvten
  26. Out oF chat Rectansle anocher is catren wtich is
  27. made by the same Abscissa, and a Fourth Proporrio-
  28. nal R S coche Larus Transversum, Latus Rectum,
  29. andthe AbsCiNa. Q. F. D.
  30. COROLLARLES.
  31. 1. Hence che Reason ihe Name Fllipsis giren co
  32. chis Section, is evidene; because the Square of rhe
  33. end K, When rixtuls applicd, will alvars be inthe
  34. Ordiriate is lels chan, or defectire oF the Rectangle Curre o che Fllipsis.
  35. under rhe Latus Rectum, and rhe Abscisa.
  36. COROLLARY H.
  37. ThC Latus Rectam LCLC, as ad s La
  38. bola and (Iyperbola, is here found by malcins 25
  39. b: Parallet ro the Section: is t00, the produced
  40. Diameter oC che Base oF che Cone:: 50 is o d, the
  41. Larus Primarium: E0 =, che Latus Rectum F. L.
  42. And hereil che Ouantiir abore and belon ehe Line
  43. be mulcixlied by b, rou will have = a guan.
  44. rity equal to the Former, bur more agrecable to
  45. apolloniuss way ot Exprestion; Who gireschis Ca-
  46. non FOr the Latus Rectum, 25 bb == che Square ot
  47. che Parallel eo the Section, is 10 cd == to a Rishe
  48. anele under the whole Base and che pare produced
  49. :: C0 is ob = Latus Fransversum, 20, (Or
  50. P.) che Lacus Rectum.
  51. DLLARY III.
  52. Wrtich Lacus Rectum max be had C eometrically
  53. truo.
  54. Ftavins che Ordinare R L, and che ABSCINA F I.
  55. li L.) And ihen tind a tourch Proporcional 10
  56. ID, (che Difference beteen che Latus Transver-
  57. sum and che AbIcissa) eo the chird Proporrional
  58. E FI, betore found, and roche Larus Transversum
  59. and chen char Fourch Proxorrional Malto cu Latus
  60. Roctum Couptc, L F.
  61. COROLLARY N.
  62. Flence may as many Points as rou please, Be
  63. Found e0 dram an EllipsiS, Whose Latus Rectum and
  64. Transversum are siven, by sindins Ordinares, and
  65. applrins chem co che Axis chus.
  66. Take any Abscissa, a5 F. I, and then make 25
  67. DE, FL:: S0 DI: IS. Then And a mean
  68. Proporrional bermeen this Fourth, IS and E I
  69. erhich ill be PK, che Ordinare Coughe; Whose
  70. P R O P. HI
  71. In the Ellipsis the Square of the Ordinatos R I, GF.
  72. are as the Roctanelos D IP. and DFP, made by
  73. the Lines lying bermeen the Ordinates, and the
  74. Verrices of ihe Lacus Frarlrerlum.
  75. LeF E E De here Called ib, 25 F. L a25 Belore
  76. called e B, rhen ir wrill be plain From whac hach
  77. been Caid in che precedene Propolicion, That che
  78. Square CF, che Ordinace will be in eliis Noration
  79. = ei c d. AISO che Rectanele D F F. Wwii
  80. by mulciplyins D F (= 0b = ib) by FE (= i b)
  81. betound eobeoi bb = : i b b.
  82. Non since by Prop. T. the Square KI = 0CC d
  83. ece d, and here ve hare tound the Square ( F.
  84. 0i c8= cicd. H mte necdo be chac ihe
  85. quare

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/806933011:0287?run=74