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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: 0.86.

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The machine reads it as

  1. dra chrouph K the Center ot the Sphere, 2 rigHE
  2. Line 25 9 d, perpendicular 1oB C, wtrich chere-
  3. fore will be che Axis ol che obque Circle; ihen a
  4. Rulex laid From A chrouch O and S, che Pole ot
  5. chac Axis MaII Project he Polar FOII L
  6. and Z.
  7. F0 Project the Poles oF the oblique Circle BC, j... 1
  8. P ROP. VIII.
  9. lies oblique ro the Primirire (in the Projection)
  10. is so far discant tom C, the Center of the Pri-
  11. P. (12o 01 l
  12. Problem 2.
  13. To Project a Lesser, or Parallet Circle l L, Whose
  14. Poles are in the Line of Measures, C, r: repre
  15. Senns che Plane of the Projection.
  16. Lult, Project the Diamerer oF the Lesser Cirele
  17. P L, intothac oF the Projection in che POIs a ahl,
  18. and deam a Line from P coN; eo which erea
  19. P C ac Righe Angles; (0 Mall, C be the true C M-
  20. rex oF che plosclted CixClE.
  21. The Center (P) of every Preat Circle (BG) whicb
  22. rion of its Plan, abodee lan of the Pri-
  23. mitive.
  24. micire, as is the Tansent of the ArK OE Plera-
  25. Make thC ArK B u = C I, che Complemene oF
  26. che Angle et tlerarion, and draw u A, Wilch vil
  27. tind che Poinc P, che Cenrer ot ihe Ltojecle
  28. Cirele.
  29. .2
  30. i 100
  31. DE MONSFR AYFON.
  32. The AngIC N A P, is equal to che Angle O Pr;
  33. because A N is parallel 10 P O: AIIO che Arele
  34. A e P, is equal EO THC AIFerNaTO AnGIC C PL: BUF
  35. the Angle c AP, added to the Anslec, is equalto
  36. a RighE one. Wheretore che Anole O P r-
  37. Pr O, = a RighE AnelC: THaE is, The ATOlC
  38. d Pr, is a Rishe Angle. Wheretore dr, is thc
  39. Diameter oF a Circle.
  40. Because the Anole B A u = Anele C A C, (25 NTon NPC, Beins righeby Construction, cakC FTONL
  41. Beins on equal ArChes) and e AnSle A B C equal ) those ro RighE AnGles, che common one dPC.
  42. Eo rhe AnBleS A d e, (BY THC SUBCOMEFAEY POMTION)
  43. cheretore che Triangles B A S and AC d are Simi-
  44. lar, and consequenely che Anese D Cirtich is
  45. equal cothe Anole A C a) IS d FISHC Onc.
  46. Deam B L perpendicular 10 B C, Wherefore.
  47. the Priangles B L C and AP C are Similat; FOF
  48. Ansle L B C = Anele P C A, 25 beins bochrist
  49. ones, and the Angle AP C = B L C, because
  50. BL and AP, are Parallels; Wheretore che Ansle
  51. BCL = Anole P AC.
  52. Buc P C is che Tangent olthe AHSIC P AC, and
  53. ThCTEFOR OF IES egual che Anole BC L, OF OF the
  54. ArK BK, Which is equal co the obligue Circlés
  55. Eleration abore the Plane oF e d; Wheretore Pthe
  56. Lenter OF the obsique CIrClC IS aIITANE FrOm C bY
  57. che Tangent of ies Fleratton avore Lca C
  58. 3
  59. and che Angle NP a (= L e) must remain equal
  60. 10 che Anele C Pr, and che Ansler, is = co che
  61. Angle es because che Triangles NI d e, and P dr.
  62. are smilar: Wheretore che Trianales P Cr, and
  63. NP e, are similar; and consequenty, c N: NY P
  64. :: PC: Cr; butCN = N P; ThCretOre PC = CY.
  65. Theretore bochare Radii ot a Circle. 8. F. D.
  66. and +0 prove PC = dC, and consequently that
  67. they also are Radii.
  68. FCay, The Friansle d P C, is an TCosceles, Be-
  69. cause cheAnsle P a C, is equalto che Ansle d PC;
  70. Wrtich Lchus prOvC.
  71. The Anele P d 0 - 1 - L d P0 = RighE AnBIC,
  72. ==La P C -) LCPY, BUECPN = L e = d P0;
  73. Thecetore cakins avar che common Ansle aP0,
  74. (Or its equal C Pr) d P C must remain equal 10
  75. P d C: TVhereFOre P C (= C r) = C d. Wrtere
  76. Pore cisthe crue Cenrre os rheprojected Circle.
  77. GOROLL ARZ I.
  78. F. Denec Tis plain, Phar makine N D ehe Ra-
  79. dius ot a Circle, whole Cenrre is NI, The proie-
  80. Ated Circles Cenere C, is distane From N, the C en-
  81. Pb, Or oF chat lesser Circles Diltance Erom iis
  82. Pole b.
  83. 2. Lhc
  84. D E M ONS Y R A X LB N.
  85. E Do
  86. COKOL.
  87. AIIO, because the Friangles e P A and A C C
  88. are Similar, (a5 having Ansle C = Angle C, by
  89. SubContrarY POBtiOn) and the AnelC B A P = AN-
  90. Ele C AC (as beins on equat ArKS) cheretore will
  91. P: PA:: AC: C 6, thac 1S, e P =P A. But
  92. LA is the SCCaHE OF the AnOle P AC, OF OF chc
  93. et set trom e, Mall find P rhe Center 25 betore;
  94. ArK BK; WHeretOre thC SCCANE OF the Fleration cer oF the Primitire, by NC, cheSecanc Of che ArK
  95. PG, P A, or P d beins ies Radtius.

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/806933011:0761?run=74