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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: 0.84.

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The machine reads it as

  1. A F
  2. Proporrionals ill stand chus,
  3. Wrhich Was ihC ThinS ac sirA proposed 10 bc
  4. proved.
  5. bedt 25 2, 3. an rs 3
  6. bra meved r0 be very brietts chus.
  7. is clear; Becaule, From the ArIt ProPerEY oF the
  8. And this is a erue and rery shorr Onacrarune
  9. Parabola, P A =OO and P a == 00. WVhere
  10. FOre PA La ==OO = 00, From the Na-
  11. Fure OE EquariotIS. And thac last resolved inre
  12. P. O-6: : O-0
  13. OF the Parabola eF wotrich Archimedes Wvrore (0
  14. lons 290, al MTaII) ScoaS Mare LMICC
  15. expedired.Tis plain alto That CMIS LCIMONTEa
  16. tion id habertali alle cavcrnio lo dtg. Parabo
  17. licti dpaco.
  18. The Ouadrature Dt the Parabola by chie
  19. hod oE Fluxions, L have formeriy in my Alsen
  20. A PARABOLICK Space, iS ThaE ArCa COn
  21. rained Declveen ile Curve of the Parabola anc
  22. any Entire Ordinate CFI.
  23. And ThIS Space IS EO a Parallelogram ciroumseri
  24. c
  25. Tec che Parameter be p = r, che Abscissa BC
  26. Calsed x, and che Ordinare y.
  27. Lhen by che srst Properis oF ctie Paraboles
  28. -yy, Decause p
  29. And consequenir by che Exrraction ot chc
  30. 20 ihe Paralletozram L. LL . . 2. 3. BIL IO THC ROOES OF cach, and ulins che nem Noration,
  31. DEFH : : 25 4, 3.
  32. FOF, L. EF, eF. 8F, ec. are in continual A.
  33. rirhmerick Proportion trom the Nature oF Plain
  34. Friangles.
  35. 2.3
  36. SC
  37. :eh, (DY Cor. L. PrOP: 2
  38. OE che Parabora.) Buc he in che Axis F. F == b
  39. and in che Arst Parallel ef must be equal to = in
  40. the next ef, ic ill be equal to =; in chechire
  41. 10Z; and (o on in a duplicate Arithimerical PFO.
  42. GrelTIOn. FOr a8 es
  43. : (015 5e l
  44. fecond
  45. = 1
  46. 1). Ch l = =.) And as ehe
  47. 2) : : C5 2; t0
  48. eh = 4, (9c. And thus vill ic be it the Lines
  49. FS, ff, ecc. be 2gain bissected, (9c. ad Infini-
  50. cum. 50 chac aHI chie Indirilibles oF the Tri
  51. lincar Space P R II F will be in a duplicare
  52. Rrichmerical Progrestion increasins. BUE
  53. 3. LC Su OE à Rark oF such Ferrris 15
  54. suberiple ro a Rank oF as many equal ro rte
  55. x = y. Then multiplvins X By X che F
  56. xion oF etie Abscissa, ie will Rand chuS X X L
  57. eo the Fluxion oF che Area. ACrer Wohich And the
  58. Florine Ouantier ansverins eo chac Fluxion,
  59. wetrich all sire the area in tenoon Terms.
  60. Fodo which, cheFluxion being x x sirst Fate
  61. aWar the x, and there will remain x Hextin:
  62. creale che Index oF chac Pover by Oniiy, and
  63. it will sand chus X X =. Ttien divide X x= bY
  64. 1. + : or by 3 (etus 2) = = (3 X ∞ ) ne
  65. itie Ouorient You sec wist B 2 X X
  66. LastIY, Instead oE x Tubsiture WHaE WaS BC.
  67. Pore tound equal to ir, viz. y and ii will Be
  68. 2 X
  69. Torhie Area oF etic Semi-parabola VM P.
  70. grearest; (25 we proved in N. 7. OF arichme- And il rou double char, vou will fain the Area
  71. tical Procression, Wvhich sec) Wheretore che ertiole
  72. Trilinear SpaCC PK HIF is ro che Parallelo.
  73. Fram : = 25 F 20 3. And consequenels che re-
  74. ot che Wvhole Parabola M V O
  75. Wheretore che Parabolicte Area i5 LWo chirds
  76. oc a Rectansle under che abseissa and e Or-
  77. mainins Pacabolick Space must bc 10 it 20 2103. dinate. 8. Li. D.
  78. P. E. D.
  79. ratelogram 25 F EO 27 IE MUIC DC WOCIC Lala
  80. bola 25 1 3 4 8. F. D.
  81. Lec FFI che Semi-oru D avided into
  82. LarES, OF in108, 76, 69c. andt cntoushr thc
  83. Dirisiono utaW Lines, 25 ef, ef, ecc. parallelto
  84. the Axis L L. Suppose al(0 B F 10 bC 4.
  85. Then L las, the Parabock SPA LILL, IS
  86. And since the Friatiole F F EL is E0 the Pa.

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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/806933011:0597?run=74