« ForrigeFortsett »
Steps of the Demonstration. 1. Prove that FA, FB, FE, bisect KS CBA, BAE, AED, 2 that , FCD = L CDF, 3. that .. FC = FD, 4. that the five right lines, FA, FB, FC, FD, FE
= each other; and :: a o described from centre F and distance any one of them, will pass through the points A, B, C, D, E and be described about the given pentagon.
Problem. To inscribe an equilateral and equiangular hexagon in a
Steps of the Demonstration. 1. Prove that A EGD is equilateral, 2. that Z EGD = } of 2 right Zs, and similarly
_ DGC = 1 of 2 right ZS, 3. that coB = 1 of 2 right ZS,
and :: ZS EGD, DGC, CGB = each other, 4. that the Zs vertical to these are = to them,
and , the six ZS = each other, 5. that :. AB, BC, CD, DE, EF, FA, = each other, 6. that the hexagon is equilateral, 7 that FBD = ECA, and :: 2 AFE = _ FED, 8. that the hexagon is equiangular; and it is
inscribed in the given circle.
Steps of the Demonstration * 1. Prove that if the o be divided into 15 equal parts,
ABC will contain 5 such parts, and AB will contain 3 such parts, and .. their differ
ence Bc will contain 2 such parts. 2. that :: BC being bisected, be or Ec will con
tain one such part. 3. that :. if right lines be or Ec be drawn, and
their equals extended round the whole o; an equilateral and equiangular pentagon will be inscribed in it.
* It should be observed that the triangle and pentagon must be so placed in the circle, that one angle of each may meet in the same point A.
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