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: 0.81.

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The machine reads it as

  1. Ihe Third may.
  2. L(a7, 4c9; = ab 93 b09
  3. 2. ANet 00 = PB. E. a
  4. 3. Bucbb-- 00 = bb- a a - ] P P.
  5. L. L.. D.
  6. Wherctore BB ehcccllo ie late diet d 2du
  7. P R O P. VIII.
  8. In an Acute aneled Friangle, est Square os the
  9. Side (H) subtendins an ACure- disC, is less thanthe
  10. Sum of the Squares os the other d sous, by dou
  11. blethe Rectansle under the nhole Base, (B-) 2
  12. the dcure ansle
  13. and the Serment of the Base (2) which is next te
  14. all ehre
  15. culaF pP.
  16. Make B k = 10 e b, aliet compleat alt cheSquare:
  17. Ttien will,
  18. 1ac = D - X 7 27 l.
  19. Dab = X ] R. p. O.
  20. 060 = Z -] II.
  21. Wheretore cakins aay what is common, l
  22. mains D. I Y = R ] II. ]- O. Bur chen,
  23. R = T, Bec, a0 = d e, a5 = ab, and L5 = b.
  24. Remains co be prorec, chat
  25. t. bb- pp - 2 a aF 2 a b, 15 ehc dum Ot
  26. D = HI.-]- O. Which ic is, becaule D = R che Squares OF che LeBS.
  27. (aS havins 2 = Sides and one L) and R WaS prO.
  28. ed = T, and T = O-) FI, becaule a c == 6c
  29. che Angle at b = k, and the Ansle a c b = eck
  30. (becaule cach writh bce makes a l.)
  31. Wheretore, che Square oF a c = ab 9; -] - b09;
  32. P. L. D.
  33. PROP. VII.
  34. in an Obrule aneled Frianple, ihe Square s che Side
  35. subtendins tbe Obtase Ansle, excceds the Sum of
  36. Rectanete, (2 b a) under ihe Basen alca cide paio
  37. added t0 it.
  38. Tet Fall che Perpendieular p, and produce b, ril
  39. le mec vernaie.
  40. the Squares of the ether evo Sides by the double
  41. Demonseration.
  42. Demonstration.
  43. 2. 11+F
  44. 2. b = p p. 1 e a.
  45. 3. b. F a 2 .
  46. WHeretore Bh is less chan thal B) 2 a a -F 2 ab,
  47. Wrhich is plainly equal ro che Double Rect. angle
  48. underche whole Base, and he PaHE a.
  49. L R OP. LX.
  50. . Lb = bb + 2b a + aa + 2Y.
  51. The Side ab os an Equilareral Frianele, ab C, in
  52. Scribed in a Circle, is in Pover Triple of the Ra-
  53. aldo; or its square is equal 1o chriee che Square os
  54. the andius, 2 d.
  55. .0. -..
  56. Tec he Racius be called R, nud conlequemis
  57. o dguaee K R.
  58. r

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/806933011:0842?run=74