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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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  1. Caus, ir d a sete Realon ot, itich vort ae UN. ) Cor. 1. From hence have ve che DiHAHBS O
  2. che Sphiere and Cylinder, borh a5. 10 Solidiey and
  3. Surtace; tor let d be che Diamerer ot rhe Spherc
  4. and Cylinder, and rd the. Circumterence ot ehe
  5. Base oFrhe Cylinder, chen will the whole Ba(e b.
  6. =r d d (itrich also is che Area ot a grear Cirele ot
  7. cheSphere;) andchis Bale mulciplr d by d che AI.
  8. cirude, siresrd dd tor chesolidier ot che Cylin-
  9. der; and cheretore by chis Prop. Z Oi chac gives
  10. Ehe Sphere (1. c.) Erddd Solidir ot rhe Sptiere:
  11. andchai las Ouanciey divided by ? d (one sixch ot
  12. and in che orher D, che Solidies e eer (che Diamerer) giresrdd rhe Surtace ot chie Sphere.
  13. 2. Which Surtace rdd is manilesttus Ouadruxe
  14. Ot :rd due the Area oF a prear Circle oF rhc Sphere,
  15. char is, che Cylinders are as the Cubes ot cheir or che Bale ot che Cylinder.
  16. Diameters. L F. D.
  17. portion os sonds.
  18. 3. Wheretore, by mulcipixine r d (= 20 etic
  19. Periphery of che Base of che Crtinder by d che AI
  20. cirude, vou have rd d for ehe Curre Surtace et
  21. the Cylinder; itich cheretore is equat. (raken
  22. withour is proxer Bales) ro the Surtace ot the
  23. Sphere; and conlequenely, addins in the Bases
  24. (cach et nhich is =r d d) che wrhole Surtace ot che
  25. Cylinder, Bales and all, will be 1. = r d d; chac 15,
  26. coche Surtace oF the Sphere a5 3102.
  27. à Phe Square ot che Diamerer (d d) eoche
  28. Area oF the Circle =r d d, 15 a5 d. r d. (For d d
  29. rdd:: d. =r d) chac i5, a5 the Diameter 10 =
  30. Olche Circumterence.
  31. 5. Decause ihe Solidiry oF che estinder is. =r d dd.
  32. cheretore che Conc ot the lame Bale and Fleiptir
  33. Will be r.r d d d; which is plainsy che difference
  34. betveen =r d d d and. r d d d, che Solidiey oF che
  35. Cylinder and Sphere, (0 chac the Conc is equal t0
  36. the excess of the Cylinder above the Spbere: And
  37. he Conc, Sphere and Cylinder arc a5 3, 2, and +)
  38. (0 chac che Sphere is ruvo chirds ot che Cylinder.
  39. sec this proved much Morrer under che word
  40. Indivisibles.
  41. IL vou consider. a Colinder as compoled oF an in-
  42. tinire number oF Cylindrical Surfaces decreasine
  43. (a5 che Circles ot che Base on which chey Randi
  44. in Arichmerical Progrestion. IF rou call che ourer
  45. most or prearest Surtace S, and che Radius of rhe
  46. Baser, the Solidier ot the Cylinder will Be exprel
  47. sed by =rS. And ic will be diverrine co meature
  48. a Cylinder by borh oFrhele disterent mays, in order
  49. ro sec hon nearly chey will agree.
  50. EVETNDROTD, is a Solid Fixure, ich Ellip-
  51. rical Bases, parallel, and alikee siruarec
  52. CXLIHDROS, is a Plaitter made oblons:
  53. vohich some Phylicians call Masdaleo. Blans
  54. chard.
  55. EFLEOSIS: Sec C yllum.
  56. CXLLOM, senities a L es pur ouc oF joyne
  57. ourmaraly. Alsoone Lame and Crooked
  58. CTMA amone che Bocanists, sixnities thC cOP
  59. CXMATIOM, a Member ol Archirecture
  60. called Doucires Or Rixht Cula, che most advancee
  61. Pare ot which is Cencave; and rhe orher Palon Or
  62. Reversed Cula, whrich hach irs most advanced parr
  63. Convex, buc is hollon below, a5 che tirM is a
  64. bove.
  65. CTIBITORHEO: Sec O. Naviculare.
  66. CTMACHE
  67. des Circle:) And rhen il che Alcicude oF che Cylin
  68. der be called b (1. c. is heiptic) ehe Solidicy of rhe
  69. Cylinder will be expressed chus, r dd h.
  70. 2. HF heretore che Aleirudes ot any rvo CMm
  71. aers be cescalro ihe Diamerers ot cheir BalCo,
  72. Cylinders must be to onc anoret as iBe Cades s lseit
  73. Diameters or Alcitudes. et metes io nan
  74. beins che lame wich d, theDiameters ot CMes
  75. oF che Balc. IE in one Cylinder ic be called a
  76. will be 2Y dd d, and ot che lallet +r ;
  77. bur doubelels er beins a common FHicienE Or
  78. Mulciplier: 2r dd d. =rDDD:: ddd: D DD.
  79. 3. Lvery Cytinder is Priple ot a Cone of che
  80. tame Base and Heiphr; utich sec proved in ero
  81. 4. Every Cylinder i5 r0 a Sphere inceribed an.
  82. et ine same Bale and Fleiphe a5 3102.
  83. IF che Square and Ouadrane wich chie Diagona
  84. a d be supvoled ro revolve round che Axis b d.
  85. phe Square Will generare a Cylinder. ihe Oudata
  86. AH Hlehisphere and che Trianele a a. Cont
  87. l C ul hame Bale and Heiptic.
  88. And Cince Circles are a5 the Squares oF thei
  89. Diameters, and phar the Square oF e h(== VOF df)
  90. =Iha) F E Bf. by 47. cr. There
  91. fore the Circle delcribed by ch or is =c d, must
  92. be equal eo civo Circles described by sh and by
  93. bf. Takre awar chen the common Circle deleri-
  94. bed by hs trom boch, and ehere will remain che
  95. Circle delcribed by ch- to the Rins described by
  96. ef. And rhus ic vill alvays bc, chac (V. gr) che
  97. Circle described by Lm vill be equal eo the An
  98. nulus or Rino made by the Morion OF i l; Where-
  99. Fore all the Rines made by the Rerolurion ot ef
  100. ih, ecc. must be equal ro all che Circles delerib d
  101. by the Norion oF GB, m k, _cc. thac i5, aIl che
  102. Solid, compoled ot the Rings made by che Mori
  103. on oE ihe Parrs oC che Trilinear Fisure cflb a
  104. MaII be equai to all the Circles generared by che ot any Plane er Ilerb
  105. Elements ot che Friangle a d b: Wheretore Ance
  106. Heiphr, and chat che Solid made by che Frilinear cave: TherC arE EVO COrES OE Cymariums, viz. One
  107. cf1b a is allo anocher chird parr, as beins equat
  108. roche Cone. The FTemilphere mukbe Z oF che
  109. Cylinder, and consequentlr, it che Bale and Alri-
  110. rude ot che Cylinder vere equal to the Diameter of
  111. ede dplere, ihie wtiole sxtiere nould be, Ot e
  112. the Cone is : OF the Cylinder on che same Bale and Whereot onc halt is Convex, and che orher Con
  113. Cortinder.

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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/806933011:0239?run=74