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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. Series of che Progrestion is carried on. Thus che) And ao I the FOrmex RanK OL NNUMberS 2 WV
  2. Sum ot Phree LCttS, 1, 4, 9, 14, Llo pne ncon Mcspitet, in chis 2 is che Common
  3. 27, 25 Y 5 OF F 28, OF Y -)
  4. - 1= = 1. 10 3,
  5. (diridins boch sides by 9) che Sum oF Six Lerms,
  6. An 4, 9, 16, 25, 36, 9c. v1Z. 9F 10 SIX MMC
  7. 36, 1. c. 10 216, (diridins boch lides bY 72) 15
  8. 15 1 - . 2. -1- - = 103; and che Sum of Tvelre
  9. Terms 650, 10 12 times 144, 1. c. 1728, (diri
  10. dins boch lides by 576) 15 25 1 - - = --
  11. 03,
  12. C5c. the Fraction adherins co them thus constaney
  13. decreasins; fome by cheir TTaIE parES, Orhers by
  14. Threc quarrers: (FOr = I5 = Z; therefore che ArI
  15. Dirilor; Or, Wrhichis in effect che lame, the Com-
  16. ion MuluiplicE 15 =.
  17. ThC MIOIE Nacural and Simple Geomerrica) Pro-
  18. srestion, is when ic begins wich Cnits; 25,
  19. Decrement i5 = 3, and = = I5 ,3: cheretore che se- Former Progression, ic is in effect bur such a Pro-
  20. Cond Decrement is = 2 (90.) Wherctore che sum
  21. ot che lmce Prosrection will be coche Sum ol
  22. che like Number ot Lerms equal tothe sredtet;
  23. 5,
  24. grection as thislarter, mulciplied inco chac ArA Perm
  25. 2II alon8.
  26. 1. 1. 1. M. M. I. aC.
  27. When ie begins with any orher LCHM, as a inche
  28. LADEOSITION I
  29. IE chere are Threc Ouanricies continually PrO
  30. 1s. 66. 25 2 Bc. 10 3, bY C0.
  31. roil. 2d and 4eh, in Proeression Ceometrical.
  32. Buc ihe Sum oF a Friplicare Arichmetical PrO.
  33. prestion, (i. c. ascendins by che Cubes ol che C ae
  34. dinal Numbers) proccedins From F ThrO 27, 64,
  35. E8C. ad infinitum, is subquadruple oE the like Num-
  36. ber oF Terms equal co the greatest: For che Sum
  37. OE FOur TerMS, 1, 8, 27, 64, 1. c. 100, 10 4 times
  38. 64, 1. c. 256, (dividins boch sides by 64) Wvill
  39. be tound 1o be a5 r ) = -]- - 5 10 4; bur ehe Sum
  40. OF 8 TermS, 1, 8, 27, 64, 125, 216, 343, 512,
  41. 1. c. +296 10 8 rimes 5T2, 1. c. 4096, (dividins
  42. boch sides bY 1024) Will be tound 10 be 25
  43. i -f = 10 4, (9c. The adherins FractionS
  44. thus constaney decrealins, che one by cheir HTaIE
  45. Parr, che ochers by Three quarrers, (For 15 15 4,
  46. and= 15 -7, 5c. Wheretore the Sum of cheln.
  47. finite Prosrettion will be coche Sum oF a like (In-
  48. tinite) Number oE Terms, equalto che grearest;
  49. (90. = 335, (90. 10 4, b7
  50. Coroll. 2d and A1t, 25 7 20 4. 8. F.. D.
  51. Portional, the Reclansle ot the Eixtremes is equar
  52. roche Square oF the Mean Frem.
  53. TEs plain char the Fxrremes a, rra, mulciplied inco
  54. one anocher, are equal co rhe Mean ra mulciplied
  55. into it selF; Ox in Numbers, chat 3 times r2 is
  56. equat t0 6 rimes 6.
  57. the lame Conrinual Proporion a5
  58. EROORESSTONI Beomerrical, or Beometricat Ihe Rectanoles oF che Extremes made erols- ways
  59. Proportion Continued, is When Dumbers, Ox orher
  60. Duanciries, proceed by equal Proportion Or Ratio s,
  61. (property Cocalled) chat is, accordins ro onc Com-
  62. mon Mustiplier, Ox Exponent ot che Common Ra
  63. tio Whether Increatins Or Decreasine. AS,
  64. Hc equal 10 che Rectanse ot he Meaa Lerme
  65. beins erery way rrab, OF 48.
  66. Surface of a Rsht Cone i5 equat 10 a CHcte obost
  67. Radius is a Mean Proporcion Derveci ie stat of that
  68. Oe in Species, supposine a the First Perm, and Cone and the semi-diameter ot its Base.
  69. rche Ratio, here equal 1O 2.
  70. a. ra. rra. rrra. rerra. ritica, _C..
  71. For erery Term, burche first, arises From the mul-
  72. siplicarion of che Ratio, Or Pome Porver oF ic, in-
  73. 10. Ic.
  74. The Follomins Numbers are Conrinual PrOpOr-
  75. rions decreasins, accordins co che Common Ratio,
  76. oc 1.
  77. 128. 64. 32, 16. 8. 4,. 2. 16. 1
  78. l iii ini
  79. 2. 4. 8. 16. (32, 64. 6c. i
  80. As, Lupte
  81. a, ra, rra in Or, 3. 6. 12.
  82. oEADEFDM.
  83. AIIO, I Three Ouanicies on each side are in
  84. And From hence, Scurmius, in his Mathesis Fnu-
  85. cleata, PrOp. 17. OF BOOK r. Schol. very brieAy de
  86. monstrates chat Proposition ot Archimedes, That ibe

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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/806933011:0660?run=74