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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. Rishe Sine in the Generarine Circle, (as BD, Space APL C Mus d ceual eo chree seni.
  2. bd) tocether with the Arch of that Sine, AD
  3. eriple oFrhe Generarins Circle.
  4. Ocherwile chus
  5. 8. F.
  6. The Rectanele AE is equal eo rmo Cirgles, al
  7. the Semi-Ellipsis AC C e eo onc, Wheretore che
  8. remainHS Space AeC F C must also be equal r
  9. cireles, and cheretore che whole Cycloidat SpaCe
  10. Manner ot Generacten et ine lctora abore de-
  11. Semi-circle, and consequens, e semi cycloidat
  12. Space equal ro chree demcireles. L. L. D.
  13. lirered: For since che Rishe Linc C F is equal co sition l had nom MP. Fumphry Diccon, Who is
  14. D F must be equal eo che Ouadrancal ACK AD;
  15. For che sereral Arks of che morins Circle do eve-
  16. ey where generare Righr Lines equal eo chem
  17. selres; Wheretore any Semi-ordinace drawn co
  18. Morr and plain, and depends on che Arictimerick
  19. OE Infinires. Thus
  20. che Curre ofthe Crcloid must be compounded oF do, do, dO; ecc. are suppoled eo be in Arichme.
  21. f Or D F, viz. 2 Righe Line equal ro rhe Parr rical Proporrions, and consequenty (o will che
  22. oftthe Ark chac hach revolved, and oE b d and Lines 00, 00, CO, ecc. Which trom the Nature
  23. BD che Righe Sine ot chac Ark in che Generatins (oF che Cycloid are all equal severally e0 rhole ArKS:
  24. Circle. R: F. D.
  25. Corollaries.
  26. cloid a Riehe Line may most calily be tound equal
  27. 2o any given ArK oF a Circle, op 1o ies whole Cir-
  28. cumterence; and consequently the Guadrarure ot
  29. che Circle may Geomerrically be had it chis Cyeloid
  30. be a true Ceometrical Curre, 25 indecd ir is HOE.
  31. evhere dranon equal co che Righe Lines bd, BD
  32. and bd; che Curve Line connectins cheir Exrre.
  33. miries will be an Elliphs (by a ProPOL. which vo
  34. vill find under che mora Elliprical Space) for the
  35. vohole Aporesare ot all Thele Righe Lines, or the
  36. Ellipeica lSpace wils be double ot che Semicircular
  37. One; 1. c. 25 Be is rO B B; and consequenty the
  38. cions, will bc 10 as matis eqsual 10 che Brentett
  39. 23F ED 2 (BV ProP. 2. OF DF. WV allis 5 Arith. Infi-
  40. Curvilincal Space Ae C D A Wis bc equal ro che nic.) Wheretore the space la S= =SV, bu
  41. Semicircular Space ADC. A.
  42. 2. DF (1. C. = DC L CF) Ouadrant D A, Where
  43. Fore since thae Whole BC= to a Semi-circle, che
  44. Remainder BD F FO must al(0 bC equal e0 a912-
  45. Cycloidal Space C DS must be equat t0 chcec
  46. Semi circles. 8. F. D.
  47. AFanE; buE BD =DC (by Cor. 2.) Wheretore cF che Curre Wc an lcars B0a) ou dcleti.
  48. vil be equal EO FO: and che lame way ot argu
  49. supposing it eo descend with the prearest pOstBL
  50. ing will alvays prove ef abore equal eo fe bc- Switrnets, IS IBC R 6) a Ca. LHIS f0Bi Bet
  51. tou; Wheresore all etie Indiritibles in each beins noulli, L Thinte, Arst proxosed, 25 a problem 10 be
  52. equal, the Space ee A f F will be equal ro che discovered, and ir hath otren been solved; but
  53. SpaCC FG L. HenCO,
  54. Cirele, (becaule one side is che Radius and the
  55. ortier the Semi-circumference) chac is, is equal 10
  56. the Semi-elliplis CDA; Wtctct H MC OF
  57. Philos. Transact. N. 268. In the Acta Fruditorum
  58. Inrectisarion Cor chis L’ine by Zames Bernoulli.
  59. CrONOS, the sman, a Constellacion in che
  60. Norchern Femisphere consictins Ot 35 Stars.
  61. CPLINDEK; che Hollon wichin every Piece
  62. EE VOU FaKC The Ouadran e LMIII DC CC S, OF Ordinance is called her Concave Cylinder.
  63. Wrhac remats, Wtieh is the Trapezium C CGL C,
  64. must be equal co the ocher Ouadrane of the FI-
  65. ExEINDER, is a Solid Body, made by che
  66. lipsis, or eo ille semicirele. Bur ic was proved in Rorarion ot a Rectanoled Paralle lopram about one
  67. 10 ec AfF; Wheretore che lrilinear Ligure
  68. F F F C A must 2ls0 be equal 10 the Semi-
  69. I. Since overy Cylinder hach a C ircle toc IIs
  70. ercte; are consequenls che inhoie semiepesoidal Bale, il vill be vecy proret 10 denoreis Bise
  71. ctiuo
  72. Fhis is proved trom che Consideration OF the
  73. P. Isence eis plain, thac by means et ee C).
  74. 2. It VousapPosc de, D e, ance ul 1odctes
  75. anorter Puch CHele, ana sES TOer HaIF EO Q SCMII
  76. circle as vell a5 iis upper one; bur in the love
  77. halt che Figure FG F. = to che Fieure ee Af F in
  78. the upper half; Wheretore couner-chanee chem
  79. and che SpACC C E A F A must also bC equal e 2
  80. The folloue Demonstration ot che lame Propo-
  81. very stiltul in chines ot chis nature. Tis very
  82. The Fixure is a SeMezeloid, where che ArKS
  83. Now rhele being a Selres et Arichmerical PrOPOE.
  84. ES D= 10 che Whole Circle; Wheretore the whole
  85. The Linea Celerimi Descensus, 25 Eis called, or
  86. very briesy and eahly by Mr. Zoln Crat
  87. 4.Z1s pran, that che Cycloidat Space is alvays Lips. FOr May 1690, p. 217 there is a Method ot
  88. Triple of the Generatins Circle.
  89. Fot IHC Rectanole BC F C is equal coche whole
  90. CVEMA, che same wvich Embroin.
  91. Cor. 3. TIaC CH LLHICat PACC LC L. lras equat set irs Sides.

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/806933011:0238?run=74