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: 0.89.

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The machine reads it as

  1. RC
  2. T0 Project a lesser Cirele, nohen ils Poles are no
  3. the Plane os che Projection.
  4. P R O P. XIII.
  5. Al Great Circles of ihe Sphere, passins throuch ans
  6. Point 2, in the Diameter of the Projection, sate
  7. Sall have their C’entres in the Line 8F, which is
  8. perpendicular tothe Diameter 8 b, and their C en-
  9. ters will be distane fromthe Point 5, the Centre 0)
  10. the Cirele A C D, by the Pansent os the Ansle os
  11. cheir Intersection wich the Savet .
  12. Pet OF be the Diamerer oF such a Circle, a
  13. Ruter From che Poined, Wrhere chie Fye is suppoled
  14. to bc placed, to O, Will project the Point a; and
  15. Fromt d to L, will proicet che Point b: Pheretore
  16. a b, 25 the projected Diamerer, and consequen
  17. ies midale Point e, will Bethe Cenere oF chac Cir-
  18. cte in che Projection.
  19. The Demonstration sou hare univertally in
  20. Prop. 4.
  21. Or, since b7 (Prob. L.) C a, and Cb, Will Beche
  22. haIF Langens oF che AEHS AO, and R L, (For che
  23. Primitire Circle is righr to che PyC ac d:) There.
  24. Fore ro proicet such a Fesser Oblique Circle, vou
  25. necd oniy calce chehale l’angenes ot the Distance oF
  26. each end of theDiameter oF luch alesser Circle From
  27. che Point A, oppotce ro the Fre, Cupposed acd;
  28. and set ehem from the Centre C, and ther wrill find
  29. che Poines a and b, che ends of the projected Dia-
  30. mecex; and a b bissected, will sive he C’en
  31. Ere c.
  32. dits 311s
  33. st is plain from what hath been proved in PrODOSI
  34. tion 10, chac che Ansle oFthe Radii os any evo Cir-
  35. eles is equal io rhe Angle ofthe incersection oF cheir
  36. Peripheries.: And cheretore il it vere required 10
  37. draw a great Circle chro the Poine a wetrich
  38. Mali mate ans siren Ansle wich che Circle
  39. A a d.
  40. Set the FaHGENE OF Etat AMPIC, Trom C the CeH-
  41. Ter oF the Circle A a D, Found by chemakino a
  42. Cirele palschro chechree PointS A, a and D, and
  43. chac Mall End che Poinc s, ihie Cetitre oF ihe Ciccte
  44. required.
  45. COROLL ARY.
  46. Fence, it a Be supposed eo be the Polar Poine
  47. OFthe Worid projected, and it vere required thro
  48. iE, to project all the FTour Circles: A a L, will be
  49. the FTour Circle of siX, Whose Center is in s; and
  50. by Terrins che Tangents oF 15, 30, 45, 60, (9c.
  51. boch mars Erom ecorards fandh, (agreable tothe
  52. Radius a 5) all che ocher FTour Circles maybe de-
  53. scribed on the Plane ot the Projection; trom cheir
  54. Cencers in che Line f B.
  55. Which is the Foundation oE all Dyalline, Or thC
  56. True Projection OF che Four Circles of the Sphere On
  57. any siven PlanC.
  58. itie sie regis Oti
  59. R OP. XNV.

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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/806933011:0763?run=74