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: 0.88.

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The machine reads it as

  1. eAt L
  2. The difference of the versed Sines of tmo Arts m
  3. olied by hals the Radius, is equal to the Sine of ha
  4. the dum of tbose artis multiplied by the vine.
  5. hals che aisselence os ehe Arks.
  6. Suppose, A F, AL Ly CHC EVO ArKS; the ditte.
  7. rence OF the versed Sines is A C - A IL = C F
  8. BF, and che Sine oF halt the Sum oF the ArK
  9. iS A D, FOF F P = F A, the Sine oF halF the dit.
  10. Terence OF the AFkS is FO. Nou che Triangles
  11. NCD, F F B, are Similar, (For che Frianoles a CC
  12. P oaare Similar, cherefore the Angle C equalrothe
  13. AnolC F) TheretOre, aS A C: AD:: F P: F B. OF
  14. AC: AD:: Z F F (1. c. F 0): F B. cheretore
  15. AC XFB = F O X AD. FOT SINCC A C. A
  16. But AF: AC:: bL: B M.
  17. AndmF: ac :: B m: y a.
  18. Therelore mulcipirins he Correlpondent terms oE
  19. boch Proportions,
  20. A EXmF: ACKaC:: (BF. X Bm: B mX7a
  21. 25 bL : y a.
  22. C AS F XI.
  23. : F E, PB. cherctore AC X PB = AD X F F.The Three Sides os any Spherick Friansle beins siven,
  24. and consequencty : A C X FB = = AD X F P: 1o find an Anele.
  25. ahar is = ADX L F F. = ADXOF. P. L. D.
  26. AXIOM NV.
  27. Ihe Rectanete os che Pines os che LeeS, is 10 che
  28. Square osthe Radius:: as the Sine of ? Base more
  29. diff. of the Lees multiplied by the sine of= Base
  30. The Rectangle or Product oE the Sines oEche less = diff. os be Less is 1o ihe Square os ibe Sine os
  31. Less, is to the Square oF the Radius: : a5 the hals the ansle required.
  32. difserence of the versed Sines oF the Bale, and ol
  33. che disterence ot ihe Leso, 10 ihie versed Sine of che
  34. verricat Ansie.
  35. Demonstration.
  36. Resume che Foresaid Circles oF Pastboard, ane
  37. suppose chere, B the Arole required, B A, B P.
  38. sequal B M) its LCGS, P A che Basero be any way
  39. Oblique rothe Plane B A, and not Perpendicular a5
  40. besore. Then vill B P a be un oblique Pri
  41. anste.
  42. Lec Fall P B perpendicular to B m, and Xy per
  43. pendicular t0 C a, and P b rob A, and in L. perpen-
  44. dicular 1o0 A; cheretore B b is perpendicular 10
  45. e A, and bL equat bA = L A equal E0 the versec
  46. Sine of the Bale, lels the rersed Sine of the Disse.
  47. rence. OF che L. C85.
  48. Demonstration.
  49. BL X2L : y R X E R. (1, e. bY cheforesoe
  50. Temman and che tirst in Mr. CasivellS Lrisono.
  51. etEY:)
  52. AF X m F: R g :: S, = BalC X = dif. CY X S,
  53. = Base = 3 dif. or 10Sg = Angle.
  54. Example in Numbers.
  55. Suppose B Pequal 60 d. 10, D Pequal 46d. 42
  56. BD equa
  57. equired.
  58. 87 d. 30 vere given, and clic Anele P
  59. 2 che Bale is
  60. the DiH. OF che SIdeS 15
  61. EtheBase-) Z Dif. OF the Sides is
  62. the Base = = DiH. OF the Sidesis
  63. Rad. 59.
  64. 20, 0000000
  65. S, = bale :t = disE. Cr. X S, = bale 2 19. 6669325
  66. Sum
  67. E diff.
  68. Subrract IhCLOL IAC SICOI CHC L. C8513, 6062354
  69. Remainder = Sg. OF the Sine OF = = P 19, 866679F
  70. The = OF Wwtich is che Sine oF 59d. 03 9. 9333395
  71. That iS = the Angle required.
  72. Therelore beins doubledis 118 4. 061 =7.
  73. A FX m F: R9; :: (BY A~. 4.) bL: y
  74. 43.
  75. 50, 29
  76. 37. OF
  77. 39, 6669325

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/806933011:0864?run=74