Leibniz Legible

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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. F OC
  2. ac P, is asche sinc ot che respectire retracted An-, ac cach renth of an Inch distance From the AXis, the
  3. sle. Whence in all Cases oF Parallet RaYS, C F i5) Foci are as FolloWS.
  4. EOP F, in che lame constant Rario ot Retraction.
  5. IF ic Mall be desired ro effect in Numbers wtar
  6. re hare here done by Lines, ic will be most casie
  7. to adapt a Calculus ro the toresoins Ceomerrical.
  8. Construction.
  9. For it in che Frianele PO C, there De given the
  10. Radius C P equal 1o Vniey, CO che Distance ot
  11. the Object From che Centre of the Sphere, and che
  12. Perpendiculat P x, equal ro the Siné oF che Anole
  13. P CO, che Side PO = OR, will be equat EO
  14. VEO FCP F 2COin VCP =PF
  15. Then aS OR OF PO EO P x:: So C R 10 che
  16. Sinc oF the Angle C OR, and the Complemenero
  17. 180 Degrees ofthe Sum of the Angles C PO and
  18. COR, is ihc Ansle C R Q equal C F P; and a5
  19. P X 1O PO, (0 is the Sine OF the Anple C RO EO
  20. CQ; and aS C QTO C. P, IOC REOC F, which
  21. is the Distance of the respectire Focus oF ai the
  22. RayS P O from the Centre oF che Sphere C.
  23. Burche Foci oE Rays parallel roThe AXIS, may
  24. De compured more readily follomine rhe Foorexs
  25. ot che Construction, For chereby ic ill appear,
  26. Mharche Radius oE che Cirele H F, viZ. a F, 15 c.
  27. qualeo- C P, and C a = = CP,
  28. For Fmersins RayS, a5 in Fis. I. but For Tmmer-
  29. sins RaYS, 25 in Fis. 2. C a will be tound to be
  30. ==C P: And supposins che Distance oF he
  31. RayS From che AXis = P X, in the CasC OF Parallel
  32. RayS Fmergins, rhe Distance of theFocus will be
  33. Found,
  34. PF =
  35. Thatis, r 2O s Beins a5 3 102,
  36. PF= SV CP = ex L VECP =3P~
  37. And Cor Immersins Rays, the Focal Distance i
  38. Coundby alitre Rule:
  39. PF
  40. er
  41. CP = L +
  42. er = 55 CP = er - 55 x C P.
  43. Thac is, r and s bcins 25 3 102, 25 betore.
  44. PF = 3 V CF = Pv F V5CP -2P~
  45. CF
  46. These Canons are (0 casly deduced From che
  47. Constructions, thacchere is no necd corrouble che
  48. Reader wich cheir Demonstrarions, onty vou have
  49. here added ero Fables compured trom them, wwirhr
  50. lirele more Work than a continual Addirion; wtrick
  51. may by ar of Example, serre ro instruet and ex
  52. ercileche rouns Scudene in chis parr ot che Mache-
  53. Cussiciene Satisfaction.
  54. FODTNTA, is the Labyrinch in che BMC OE the
  55. RaES.
  56. FAECOTA, Signities a Poder erhich subsidesto
  57. maricks.
  58. Suppole CP ihe Ractius ot ihe Sphere or Ctass) Porder whichis ro be aryed lixhely
  59. 2 Ineties, and che Rario ot Retraction 25 3 202;
  60. ILKK 2
  61. si A C
  62. Por Fmersine Rays.
  63. 2. 92.76+ V 5. 7276
  64. V 12. 8304 + V 5.6304. 2
  65. V 12.6634. + V 5. 4684: L
  66. V 12. 4.4. 16 +- V 5. 2.4.16.2
  67. 12. 1500 = V 4. 9500 2
  68. VTT. 7936+ V 4. 5936.2
  69. IT. 3724 + V 4. 1724
  70. V 10. 3864. + V 3,6864.
  71. V 10. 3356 + Y31356-2
  72. V 9. 7200.+ V 2.. 5200-
  73. For Immergins Rays.
  74. 4. V5. 7344 +
  75. V2.5024 + V5. 7024+
  76. V 2. 4576 + v5.6576+
  77. 4000 + V5.6000.+
  78. 2.3296 V5. 5296.+
  79. V2. 2.464 + V5
  80. V 2. 1504
  81. V
  82. V2.04.16 + V5.
  83. 10 lV 1. 9200 + V5. 1200+2
  84. Butic is co be Nored, Thac these Foci For Im.
  85. mergins Rars must nor be caken For the Foci OF a
  86. Llano Correa, en n cnreau ls comards
  87. the Object, For che Plane- Side by irs Retractian
  88. does conrraet the Focal Lengch, by about a semi-
  89. diamerer dt elle oplele, cele lupose bous
  90. et Clals concinued.
  91. The Came Ingenious Author, as an Inltance
  92. the Lxcellence oF che Modern Algebrae, gires al(o
  93. in Philos. Fransact. N. 205, a Way ro And the Foci
  94. Ot all prick Colasses univertally; and ews oF
  95. Wrhar sieat usc his and tuch Theorems are: BUE
  96. lavins cMlarsed (o muest altcaus, L Cast only reter
  97. ee Alsebraieat leacer c, where he will ind
  98. the Borrom in cerrain Hraimings of Vegetables;
  99. For ic is prepared ot lome ercen, wathed, alu pa-
  100. red Roors Deac rogether ich a licrle WVarer, then
  101. Strained, that chere may sublide a evtrire Tort ob
  102. EOEKVS,

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/806933011:0351?run=74