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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: 0.85.

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The machine reads it as

  1. III.
  2. Gent oF the Anele ca d (1. c. the FanSCMC OI HIdIF
  3. the Sum ot opposire Angles;) and in che licele Tri
  4. L L I
  5. arxesad. 8 d Will be Tangenc ot che Ansle z a
  6. ins proporrional, eb: ea : : c d : d 5: PHaE 15, 11
  7. NVords, TTalS the Sum of ibe Lecs, is toss Ber
  8. Difference:: as the Tangent of hals theSum of the
  9. opposite angle, is to the Pangent of hals their Diffe-
  10. rence; bur Wholes are as cheir Hlalres: Where.
  11. Fore the Sum oF the Legs is to their Diference:
  12. 25 the Pansent oF hals the Sum oF che opposi
  13. (1. C. The FAnOCHE OF haIF the DifferenCC OF OpPO-
  14. sice Angles.) Bur the Segments oF rtre Legs ol
  15. any Friangle cur by Lines Parallelco che Ba(C, BC-
  16. As che Sum os che L add le siven, is 1
  17. their Difference:: Sois the Tansent os hals il.
  18. hals their Difference.
  19. beins Whacche siren nsle Was 100 olo
  20. and their Lifterence is non found; add TheretOr
  21. their halF Sum, and half Difterence rogether, ai
  22. ic sires rou che greater os the tuo Aneles souht
  23. and half che Difference subrracted trom ihe hal
  24. Sum, leares the lesser Angle Cought. And chus
  25. havins Found che Angles; il the Side oppolice to
  26. ehe former siren Anele be Poughe, ic will be tound
  27. casily by Pardies axiom, Thar che Sides areas the
  28. Sines of the Angles.
  29. TheDemonstrarion oF rhe Third Axiso, ls VILCL
  30. Ix chus.
  31. their ViHerence: aS FC LaHSCHE OL HAIL MMC SUII
  32. ot their oppolice Aneles, isro che Tansent oF halt
  33. their Difference.
  34. required.
  35. 10 20
  36. solred.
  37. Sum os the ocer o Aneles, to the Tansent
  38. Non che Sum ol c L. ex tvo Angles isknonn
  39. Arisles, is to the TalSe et Ma CCM CLCMCL
  40. Wrhence che ruo followins Cases ut caus l
  41. llay che Sum of the Legs ot any Angle a iS re
  42. Giren FI, O and a. Required c, b3
  43. FOr HI - 1 - O, IT -O:: 25 F, halEZ Opposite
  44. Angles, is to T, half X opposice Angles, and ille
  45. alEZ. ) halF X = b: and haCL.
  46. Demonstration.
  47. Produce O, one ot the siren L egs oF che Angle
  48. siven, eill as become equal iO FY Or C a and che
  49. Drav a d bohich wiil De Lespeet s (2.
  50. 16.) and draw d e, wrhich Wvill be Parallel 10cb:
  51. Siven FF O, and a. Required Bd
  52. First sind che Angles by che Former Case, anc
  53. bisect bf in e, join c f, and bisect ic alo in d: chen 5, b: HI: : S, a: B: OFS, 6: O:: S, A: B:
  54. ed Ede Debbired addtorito
  55. (6. 92.) Then wwill che Anele c a d == d a f: L. C. tC
  56. ehe halt oFc a f, Which external Angle c a f-
  57. I b: Tharis, eo che Sum oC rhe oppolice Ansles
  58. A X IO M 1I
  59. The Base is to che sum os che L eps:: as ehe Dise
  60. rence ef the Lers is rothe Difference of the Serment
  61. os the Base made by a Perpendicuat let sall fron
  62. the Ansle opposite ro the Base.
  63. Forthere is allo anorter Case, in Plain Oblique-
  64. Triangles, wtich requires 2 parriculat LLX IMM l
  65. solre ic; and thac is, Where aII chree Sides are BI
  66. ven ro tind che Angles. Flere lec Falt d Perpena
  67. cula trom any AnslerOis ide ds d P:
  68. Oram then 5 a Parallel ro cb; (0 will the Angle
  69. 5ac, bc equal roche alcernare one c. Andictrom
  70. halE esle Sum oEche opposie Angles, ron calre che
  71. sesser Angle: 1. 0. IE trom c a d, You cate 8c
  72. chere will remain the Ansle s a d, equal ro hal
  73. theDitterence OL u Opposte AIIBICS.
  74. and then (ay, A5 the Side d ois 10 d a- ac, th
  75. Sum ot ine oetet l silles.. Soisthe Ditference
  76. FTaIF oF wrtich addca W HaIF a c,
  77. halF d c, ic will leare the Mher Sesment pc. AnC
  78. ate cay had thus: d a : Radius :: d. P. C0.
  79. And (0 alto, il trom b e, halt che Sum oF thie sinc orthe Ansle C.
  80. Legs, rou rake, O the lesser Leg, there will te
  81. main a c equal ro halt che Ditterence ot the Le9s.
  82. And ihen since the Triansle c a d is Righr-anglec
  83. it a d be made Radius, cd Will be che Tan.
  84. ofthole ruo sidesu ao a tourch Number
  85. fires rou cho
  86. Scoment ot the Bale ut P, and l Lubrracted Fron
  87. Wotien etose Segmienes ale cluo sou, che Anoles
  88. sine oF rhe Ansled: And a c: Radi:: pC: C0.
  89. ahis.
  90. The Demonstratibu bt Woie la r
  91. Demonstracion.

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/806933011:0851?run=74