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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: 0.87.

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  1. Rerolurion eo be made ot the Line CarFMIHS HeCircle lO deteribed, 25 1 10273 10 a AFh, 2S L EO
  2. Poine, (0 EHac ther MaII enA THCIE MLOTIOM ac lasE
  3. rogether; there wvill be Formed a Double Spiral
  4. Line, and ruo Spiral Spaces as vou sec in chié fii
  5. sure. From the Cenesis oF which may casily be
  6. drawnchese Corollaries.
  7. kins equal Angles wich the first and second Spiral
  8. (25 2I(0B +2, B 10, B8, (95,) dre in Arichmeticat
  9. Proporrion.
  10. the Circle incercepred berwire B A and those Lines.
  11. Because Wvhacerer parts oF the Circumterence che
  12. Point A describes, a5 suppose 7, che Poine B wil
  13. al(o hare run over 7 Parts oF che Line A B.
  14. 3. Ans Les uaem B coe lecond Spiral,
  15. a5 B 18, B22, 690. are r0 each other, a5 che
  16. atorelaid Artes, rogecher wich che whole Peri-
  17. 48, 69c.
  18. ervo, enouxh on this Subject, ro sire cheReader
  19. 1
  20. phery added on boch sides: For ac che lame cime dian, must also (as ive Mewr in Prop. 7. OE Sphe-
  21. Thac che Point A runs over 12, Or the Whole Peri-
  22. pherr, and perhaps 7 pares more, Mall chac Poine
  23. B hare run over r2 anid7 parts oE che Line A B,
  24. extrichis nom suppoled eo be dirided into 24 equa
  25. PAFIS.
  26. med che Circle; and il thien rou imagine a new j ehie second Cirele will be 25 1 10r2: and r0 a 3 d
  27. F. That the Lines B +2, B FN, B 1O, (50. Ma
  28. 2. The Lines B7, B 1O, CdC. drawn any hoW 1O
  29. I. The first Spirat Line is equat eo hals ehre Deri-
  30. Phery of the first Cirele; for the Radii os the Se-
  31. Etors, and consequently rhe Arches are in simple
  32. Arithmeticte Prorression, vhile the Periphery of
  33. the Chiele contains as many arches equat to the
  34. Greatest; wherefore the Periphery to all those
  35. Arches, is to the Spiral- line a5 2 t0 L (b7 LI. 6. 0f
  36. Llum. ProgreHtiOn.)
  37. PehOPHE OnE ProxOsition, Wwich 2 Corollary Ox
  38. The Rel SpitaI, aEC Ed One anocher as the ArKS Ot
  39. Specimen oE thie Genest, a nd Properries, ard
  40. PROPOSTTTONS.
  41. L. IBc first Spirat Space A D CB is 10 the first
  42. Circte:: 45 L +0 3
  43. ar ot Demonitrarion uled abour spirat Lines.
  44. Thole chac vould see more, may consule Archime-
  45. des, Dr. WVallis S Arithmetick of Infinires, Ox Stur-
  46. minss Math. Fnucleat. lib. 2. Chap. 4.
  47. Proportional Spirals, are Cuch Spiral Lines as che
  48. Phumb Lnes on the Perrestrial Clobe, which be-
  49. cause thes makce equal Angles wich every Meri-
  50. rick Ceometer, Which scc) make equal Angles
  51. wich ehe Meridians in the Stereographick Projecti
  52. on the Plane ot the EquatOr; and cheretore wili
  53. ve, 25 the Learned C apr. Palley obserres, Propor-
  54. tional Spirals abour che Polar Point. From Whence
  55. that excellent Machemaricran aBIMOMNITateS, LHaE
  56. che Meridian Linc 1. a Scalc e L05. TangenEs
  57. Sec Meriatan L.M.
  58. ot che: Meridian complemenes ot elie Lacicudes.
  59. Diride itic Circumterence oF the C HCtC ITO:
  60. =ParES, by Lines drawn From the Ceniter B, bC
  61. Sinmins from ehe first Line B A; chen Wil (BY
  62. Cor. F.) BcbC == T, B D = 2, ana
  63. and he Sectors circumseribe d aboue the Spiral will
  64. be 25 The Squares oF che Radii, viz. C BC=
  65. DBd == 4. and AB a == 9; and (0 ir will bC a1.
  66. vays, il rou makce nerer so manx bissections ot che
  67. 3 first Dirisions ofche Circle. Phac is, che Lines
  68. drawn trom Bco rhe Spiral, Wvill bC 25 1, 2, 3, 4,5, 6.
  69. 5c. and the Sectors circumleribed, a5 X, 4, 25, 36
  70. Coc. alivars soins on in ehe order of Squares
  71. or in a duplicare Rario. Buc 2 Rank of Cuct
  72. PerIS, arc t0 a R ank of a5 many, equal ro che
  73. Greatest, aS L +0 3 (bY N, 7. OF Arithm. Progression.
  74. TVheretore che wwhole Spiral Space (Wrhich is Com
  75. In Proportional Spirals; the Angles B P D, BPd.
  76. (90. Or The Arches BD, B d, E3C. are Exponents
  77. OF Ehe Rarios OF B P EO P C. FOF FOr IE the ArCh
  78. BD De divided into innumerable equal ParES, ristE
  79. Lines dracon from them ro che Center P, MalI di-
  80. vide the Curre B cc C inco an infinier oF PFODOT-
  81. tionals; and all che Lines PC, P c, C9c. Tall BC
  82. an Intinier oF Proporrionals berween P B and BC
  83. vhose Number is equal eo all che Points d d, in
  84. the Arch B D: Buc ar intinire NumbeF OF PFOPOF-
  85. tionals becween the rvo terms ot the Rario, is eo
  86. Poled ot such Sectors) is ro che Whole Circle:: 25 chac infinice Number oF equal parrs between any
  87. 2103. L F. D.
  88. IE anoctier Circle be dravn wich a Radius dou
  89. Ble coche former, ies Area Wwill DC (aS eHe Square
  90. eF IES DLAMCECY) 4 rimeS aS GFCAE AS CHaE OF FhE FOF.
  91. Mer. Lheretore the Arst Cirele corhe second wil
  92. be 25 Y 10 4, OF 45 3lB +2. And since the Spira
  93. Orher Lvo TerMS : : 25 the Logarirtim ot che one
  94. Racio is co rhe Logarichm oFche ocher; theretore,
  95. 25 BD eO B d, Or a5 The Argle B PD tO thC AN
  96. Sle BP c; (0 isthe Logarictum ot the R ario OF P B
  97. E0PC, coche Locarictm oF che Rario OF P B 10
  98. Pc.
  99. e
  100. F. D.
  101. SPIRET, Which che Chrmists call Mercury,
  102. Is ore oF the s Principles separable From a MixI,
  103. by Fire; eis subeit, listr, penecrarine, and actire,
  104. F
  105. doaec id eo rhe hek Citede ad 1 10 3, phac done aee hacia 1e Paeveleo i a vers epiet Mogesii
  106. Etiis

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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/806933011:0770?run=74