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. But is
  2. Provor
  3. s.
  4. ue 1o the Lye, the Parts
  5. ction mill not be in the same
  6. se in the Line it sels, but
  7. it hich lic nearest to the Fye
  8. u in the Projection appear longer thanth
  9. WhteB lic more remote from it.
  10. Ference, Which are sererally che halres oF the AN
  11. Eles LE C, B E C, H E C, (90. ac the C CnErC: 0
  12. ettch laccer Ansles, che Arks ot che Circle giren
  13. C L, C B, and C HI, are che proper mealures
  14. Wheretore MC LISHE LineS OL, DL LE, C9C
  15. us thal CVery Diamerer ot a great Circle, OF IIS
  16. Parts wichin or wichour che Primiere, 15 tO BC
  17. meatured on the Scale oF FTaIF Pangenes; and thar
  18. che Dirisions oF ic begin ac the Centre ot ille Frimi
  19. are the Tangenes oF halt thole ArkS; which MewS
  20. ure Circle.
  21. Circle placed oblique to ihe Fye at A, will be a
  22. true Circle in tho Projection; but ils true Cen
  23. ter is different from ils apparent one-
  24. Fet BC De che Diamerer oF an oblique CIr
  25. cle, wtrich is eo be Projected from thc BBC S
  26. A, On a Plane Represented by che Line F R, wrtict
  27. Mr. Oushered calls the Line of Measures.
  28. donser chan PF, che RepreleMCarion OL IHC OIHeF HAII
  29. Wrtich lies remore trom cho lre; a5 is in a mannet
  30. Telferident.
  31. coincident ich, or parallel e0 us Axis, ic will b
  32. Projected inco an intinire righe Line.
  33. PROBL FMt L.
  34. Lexthe Circle siven Bc A B CD; and lex it be
  35. dirided into cighe equal ParrS, as in the Figure;
  36. and lec che Ere be ac A. DraW FC ac ristie An
  37. glesto AC, the Axis of che Lye, io represene rhe
  38. Plane oF che Projection; and deam al(o From A
  39. AF, AB, AI, A C, A H, AD, AO, chroue
  40. che sererat Diritions oF the siren Circle; then wil
  41. E B, BO, O E, F P, P D, and D C, bc cho
  42. proxer Representarions ol che Pans sr
  43. Circleo
  44. T.Tis plain ihe Diamerer B C ill be repre
  45. Tented by che Line FP. Tis allo plain, char il ript
  46. Lines vere drann from A ro all the ParrS OF cto
  47. oblique Cirele, OF wrhich B C is the Diameter, thez
  48. ould makre an oblique Cone oE RaYS, 25
  49. ABC.
  50. 2. BuF P Cay thac the Ccalenous Conc OF RayS
  51. A B C is cur by che PIanC F, R, subcontrarily EO it
  52. Base, and consequentty the Section will be a Circle
  53. (by che 34) Wheretore che siren oblique Circle
  54. will alvars be represented by a Circle on the Plane
  55. OFthe Projection.
  56. Thac the Scalenons Cone A B C is cut SubcOn-
  57. crarily eo ies Base, may be chus proved.
  58. Dran AD chroush the Center OF the Sphere R,
  59. and join BD and C D.
  60. The Ansle A C D is a righeone, (beins in a Se-
  61. micirele) and the Angle A H is righe, by Suppo-
  62. sirion and Construction; and the Angle D AC is
  63. common roche rwo Triangles AH F and AD C
  64. Wheretore cheyare Similar, and consequenty che
  65. Ansle ADC is equal rothe Angle AFK
  66. But che Angle AD C is equal to the AnSIC ABC
  67. as beins in the same Segmene; and the Angle ADC
  68. ras betoreproved =ro the Angle A PK; Wvheretore
  69. the Angle A B C = Angle AF K; and since the
  70. Angle ABC is common co boch, cheretore the
  71. Ansle F must be equal ro che Angle C, and Con
  72. seguentiy the Conc A B C is cur subcontrarily, and
  73. cheretore LP is the Diameter ot a crue Circle
  74. wtose real Centre wilt be in Pche midale Poinr;
  75. buc che apparent Centre of the Circle will be aE L.
  76. ertiere the Poine O (tich is che midele Poine ot
  77. BC) is projected.
  78. There are several otter ays oF cndins P che
  79. Cenere ot che Projected Cirele; buc chis is AS expe-
  80. 70
  81. TMS, IE the Eye BC AE A, FCayE
  82. CLir
  83. eBC
  84. Iying oblique eo ic, will be projected into che L inc
  85. D F; and its halF B F, Which lies nearer co che
  86. Ere, Mall De represenced by Line D F, wrtich i
  87. IF a Circle be righe tothe Fre, Or hath irs Plane
  88. L1OP. O. Forepresent on the Plane of che Projectio
  89. Rishe Circle, and to distinsuist there sue
  90. Parts and Ordisions as salt truly corresporutn
  91. those osue sto.
  92. di
  93. And is on A as a Center vich che Distance A F
  94. another Circle be described, tis plain, chat O F
  95. E B and F F, (3C. Wwill bC Tangenrs oF the An
  96. Bles O A F, BAF, FAF, 8C. ac ihC CC dirious aS arY.

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/806933011:0760?run=74