Leibniz Legible

Machine transcription of the Leibniz Nachlass

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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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The machine reads it as

  1. IIL. I a Scalenous Cone ABC DE Cut B LEuta
  2. in a subcontrary Position to its Base, the Sectu
  3. DEH nou be a C irelem
  4. Ra75.
  5. 4. An Olique Circle, votiose Plane lies osde le
  6. 3. A Rixht Circle, vohose Plare is coincidete
  7. Axis oE 23 et WM EnC VIUa
  8. che AXis oF che Fre, P0 chac ic makes unequal An-
  9. 8les wich ir
  10. Fo Project the Sphere truly in Plano, is a PAFF OF
  11. Perspective; Whereot chere are several kinds; bui
  12. the most usual is what is proxerty called the Stereo:
  13. graphicte, Ox Solid Projection of the Sphere; aud the
  14. Orthorraphick, or che analemma: The Lallet Ot
  15. ertrich, sec in analemma.
  16. Inche Former, che Circles ot thelo atc arabon
  17. ex reprelenced on a Plane, erhich passes cibuph
  18. irs Center, and hach the Fye, supporec ro be in
  19. che Pole or 900 distant from ic; Poechine the lere
  20. ral Circles or Arks oF Circles on char Planc, Ox on
  21. any one parallel to it.
  22. In ehis Projection, it a Line pals Mouph che
  23. Fiye, or be coincident or Palatus d C XIS, ir wil
  24. be represented by a Point.
  25. IV. Is a Line be direct 1o the Ereq it ill be pro–
  26. i
  27. 1. The Section A BC made chroust che Axis,
  28. is a Friangle.
  29. 2. The Friangle A F D is Similar E0 A B C,
  30. tho placed a contrary ray, (by che Supposion)
  31. (Whichis called Subcontrary Posicion.))
  32. 3. F D beins the mutual Intersection OF EO
  33. Planes wilt be a Riphr Linc, on Which cake any
  34. PoinE, 25 (i) and chroueh ic deaw F i C parallel 10
  35. BC, and ehere ler the Cone be cur al(o, etien the
  36. Plane chac curs ic beins parallel 1o che Bale oF the
  37. Section, P HIC must be a Circle, and F C a Dia-
  38. meter.
  39. Nou, because boch chele Interlectine Planes
  40. arc Righero che Plane ot che Triangle AB C theix
  41. common Incersection IFI, Will allo be a Righe
  42. Linc, and perpendicular co the Plane oF che Fri
  43. anele, and eo the rvo Lines P D and FC. And
  44. then, because che Triansles ABC, A B D and
  45. A F C arc all Similar, che Angles at C and P must
  46. be equal; and che Verrical ones at i beins (0r00,
  47. che Triansse F P I must be Similar e0 ID.
  48. Wheretore D I: IG : : F I: T F. theretore
  49. IDIE = () FIG5 bur because F C is the
  50. Diameter oF a Cirele, and I FI perpendicular ro it,
  51. and cerminared ac che Circumterenco, twill be a
  52. midole Proportional berreen the Segments of the
  53. Diameter, and hare ies Square equal ro the Rect.
  54. angle FIG, (a5 aI(0 eO iEs Bqual F ID) where-
  55. Fore che Poine II is in the Circumterence of a Cir-
  56. cle, wohose Diameter is D F. 8. F. D.
  57. DEFENETIONT
  58. ACirole of the Sphere, as eo its Projection on any
  59. Plane, is oF tour Kincs.
  60. I. The Primitive Circlo, or Limb ehich bounds
  61. ehe Projection, and wichin wrtich ris alvars
  62. made.
  63. 2. A Direct Circle, whole Plane is directiy oppo-
  64. sirero che Fyc, or iotien che Ere is in chc Axis ot
  65. The Plane.
  66. merer ot a larallel Circle) is luppolea cone lalal
  67. telto D F, and is projected into ir from the Lye at
  68. A, il rou deaw rhe LineS AD, A F, and AF, che
  69. Triangles ABC and AD F will be Similar; 25
  70. also will A CFC and A F F; Wheretore aS AB
  71. AD:: BC: D F. and as AB: AD:: AC3
  72. (+ L. dd L 5 2L~:: BC: DP :: C
  73. L F. Trasct ad CHC. Wose BC Wo che Wvhole
  74. F 116 L at BL.. 6C.
  75. sected into a t LMe, nisse lals be in
  76. the same Proporrion to one another, as those os
  77. the Primitive Line, os which it is the Repre-
  78. sentation.
  79. Fo, Since The Line B C (WIIICM LLIA) DE LHCBIa-
  80. PRO

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/806933011:0759?run=74