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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: 0.87.

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The machine reads it as

  1. r4. The Poles oF the Sides of any Triatee
  2. CTID, do on che Suatace oF chelrlobe, contitule
  3. another Friangle nx m, erhich may be called Sup.
  4. plemental ro che Triansle CHID; For che Sup
  5. Plements oE che Angles and Sides oF che Triangle
  6. nxm, are equal 10 che sides and Aneles ot che
  7. Trianele C D HI.
  8. DEMONSTRATION.
  9. quener, che ruo Pomes ot incerlection ale al cu
  10. distance of a Semicirele From each orher.
  11. Frianele must be less chan a Semicircle.
  12. 9. The oppolite Angles at the intersection ol
  13. cvo Circles are alivars equal, because the same
  14. Planes constiture boch Angles; chacis, che Angle a
  15. is equalto che Ansle b. Sec Figure belovr.
  16. 20. In a Spherical Triansle, it che Sum oF che
  17. Less oF any Angle be Grearer, equal, or lels tham
  18. a Semicircle; the internal Angle at the Base is aC.
  19. cordingly grearer, equal, or less than the ourvard
  20. and opposite one; and consequenur, the Sum o
  21. ihe cvo incernal Angles at che Baseis grearer, equal
  22. or less chancvo Rixhr Anpses.
  23. B. AII preat Circles must cut cach orher inro
  24. EO equal Parrs; becaule cheir common Inter-
  25. section is a Diameter OF the Sptere; and conse
  26. EOROLLARY.
  27. Hlence eis plain, Thar everr Side oF a Spheric
  28. DE MONSTR ATYON.
  29. From che Poinrs CHD, 25 Poles, deseribe cree
  30. preac Circles X A y,
  31. ib b27
  32. RT m n, X B n Z, then id
  33. Ouadrane = A
  34. because m is the Pole
  35. OF HI Cy, and x Or P che Pole OFC A, cheretore
  36. Ouadrant = M LC, Meretore n m = lR = Sus
  37. and 21 Lo Oua
  38. supplem
  39. IE OFC A == AnelC TTOD
  40. C = B ∞, cherctore n X = B 3
  41. E oE Ansle IIOD, and n Y =
  42. plemene oE che Ansle D H6.
  43. , Lhac che Friangle n F im constimred Be-
  44. crcch chechreenexe Poles, has its chrec Sides
  45. longer chan cb, and consequents, CC AlIlC
  46. = a) ill be bisser than che Angle c d b. Pro-
  47. perry 3. Bur il a c-I c d be equal ro a Semicircle.
  48. chen dc will beequal ro c b, and che angle
  49. Anslec d b. And in the Trianele d c b, becaule
  50. 0-)= cb is lelsthan ab; theretore a c is greate
  51. than c d, aud consequenty che exrernal Ansle ad
  52. is grearer chanche Anslea; chac is, chanthe An
  53. sle b, the internal anele at the Base.
  54. Alo, since the Angle a dc-- the Angle C d
  55. ervo righe Angles, cheretoreche Ansle a d c-
  56. ehe Angle a is greater than evo Righe Ansles, (o
  57. 22. In an Tolceles Sph. Friangle, il one oF che
  58. equal Lces is greater, equal, or lels than a Qua-
  59. dranc, che Angle is accordinsly greater, equal, or
  60. dels than a Rishe one.
  61. Ansle L and che Ansle Lihe dupplement et
  62. che side CD.
  63. 13. Any Angle oF a Friangle, wich che ditter-
  64. tence os the oter tvo, 1s sels chan rvo RiphE An
  65. Bed. Foe, an is tels canx m + mn.
  66. That i6,
  67. 2L = D =2L = 6- F 2L -FI.
  68. Theretore,
  69. C HT -- D =2 l
  70. 12. The Sum oC che chree Sides os evers Sph. (For sinee 2 L = D = 2L = C + 2L - H:
  71. Friansle, is lels chana Circle.
  72. FOF C d I5 le (S chan c b: I b d, Woheretore a c-
  73. dc d an must be less chanche Sides a c b adb
  74. Sec che Figure abore.
  75. Thac is,
  76. 2L = D = + L = C - H
  77. 12 THC HCAIMIE OL AHIY SpDerCK Anere, IS AII YDY EtAIISICLHI L, C, atia LL CWIII DC2 l-
  78. Ark OF 2 great Cirele described From the Angular I II = 4L Y D; ihen by cakins awar. 2 l
  79. Point, and precilelr 90 Deg. distane trom ic; char
  80. se matiue ihe Auguloe boue ve Edle ot rra,
  81. Eucte.
  82. trom boch Sides, and cranstering D You il have
  83. C HI = D =2L. Q. F. D.
  84. 16. TFruo Friangles are mutually Equiangular,
  85. ches nec allo auenatis Eguilarecal: hoc becante
  86. iher
  87. and Angles equal ro the Angles and Sides ot
  88. che Lllansle CFlD, lare chac che srearell
  89. Side n m iS che Supplement oF the greatest
  90. IEa C. Jc d De preater than a b, d c must be

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/806933011:0856?run=74