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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: 0.89.

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The machine reads it as

  1. 2. The Semidiamerer of this projected Cilele
  2. C d) is equal+o (C P) Whic
  3. eticT.
  4. Laid Ark P B, or oF char Cireles Distance from irs
  5. All Angles made by Circles on the Supersicies of the
  6. Sphere, are equal vo chose made by cheir Represen-
  7. racives on che elino os che Projection.
  8. Polc.
  9. OP. Z
  10. The Angle of the intersection of any tuo Cireles on a
  11. Plain, is equal to the angle made by their Radi
  12. drann from their Centers ro the Point of Inter
  13. section.
  14. TCaY, IHe Kectilineal Ansle cTn; made by
  15. thervo RadiicT, and Fn, is equal toche Curri
  16. lincal Anele oTC, made by che Arks oT, and
  17. eT; Wwhich is equal also coche Currilineal Ansle
  18. n Y an made by che Arksn Y, and L a.
  19. Deav o F, and P a, Fangenes co che imersect.
  20. Ing Circles.
  21. Thenthe Angles oF Contact, o FC, and n I a-
  22. Wvhich are made by che Tangenes and che Curres
  23. being less chan any Acure ones, and indecd no
  24. Ouantiry; che Pangenco T0, and d T a, will Fal
  25. in wich che Circles, and makre etre same Angles
  26. wich onc anocher, a5 the Acks ot those Circles do:
  27. Wheretore che Currilineal Ansleo TC, is equal 10
  28. the Rectilineat ore o J d; andi on the ortier side
  29. che Currilineal Auslen Pa, is equal rothe Recti
  30. lincal one a P c.
  31. Wheretore since che Rishr lin d Angles d TC,
  32. and o T n, are boch Riphe Angles, and equal: IH
  33. rou cate avay che common Angle oTC, the AN-
  34. Ele d To, must be equalco che Anslec Pn; and
  35. consequeney che Anele cTn, is equal to che AN
  36. fle oF Incersection oY c. 8: H. D.
  37. Texthere be ruo Circles, C and F, interlectine
  38. cach orher ac d.
  39. TCaY, TheAnele Od T, made By che PIaneS OF
  40. these Circles, is equal ro che Angle osh, made by
  41. their Tangenrs od, and d h, Wvhen projected.
  42. Lerrhe Fye be ac A, and che poinc ot incerlecti-
  43. on d; chendraw dh, a Tangene cothe outer C ir-
  44. cle d F, and d o, a Fangent r0 che Inner Circle
  45. de
  46. Then snce che Plane oF che Projection e ∞, 25 al
  47. (0 chat made by the Tangenes a h, and do, (Whick
  48. are in che lame Plane) are boch perpendicular 10
  49. the Plane oF che Circle cT d R; FheIE COIIOI
  50. Incersection oh, must be a Rishe Line, and al(o
  51. Perpendicular 10e 8.
  52. Dran all che Lines, as in theFigure; then will
  53. the Anole A d m, (made by the Tangent and Se-
  54. Cant) be equal coche Anele q. (in he oppolite Ses-
  55. menc) wrhichis equal 10 q d A, becaule the Tri-
  56. ansle q A d, is ani Isosceles; bur che Anole 9 d A
  57. L h8d, becaule q d is parallelro cg: There.
  58. Fore the Anole he d = l Ad m Verrical AN-
  59. ele hd g: Wrheretore che Priane lc h d 5, i5 a1t 1so-
  60. sceles, and consequenes d h = B 8.
  61. Fence che Frianole od B, hach avo Sides,
  62. oh, and ha, and the RighE Anole oh d, equal 10
  63. evo Sides, and one Anssc, in che Trianele obs:
  64. NVheretore all chinss are equal, and consequently
  65. the Ansle osh, is equal co che Angle o d h, equal
  66. co che Currilineal AnslC C dY. 8. F. B.
  67. tR OP. XII.

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/806933011:0762?run=74