Plane and solid geometry . s left as an exercise for the student. 527. Cor. I. A regular pentagon is formed by joiningthe alteimate vertices of a regular inscribed decagon. Ex. 978. Construct a regular inscribed polygon of 20 979. The diagonals of a regular inscribed pentagon are 980. Construct an angle of 36° ; of 72*.Ex. 981. Divide a right angle into five equal 982. The seven diagonals of a regular decagon drawn from anyvertex divide the angle at that vertex into eight equal angles. Ex. 983. Circumscribe a regular pentagon about a circle. Ex. 984. Circumscribe
Plane and solid geometry . s left as an exercise for the student. 527. Cor. I. A regular pentagon is formed by joiningthe alteimate vertices of a regular inscribed decagon. Ex. 978. Construct a regular inscribed polygon of 20 979. The diagonals of a regular inscribed pentagon are 980. Construct an angle of 36° ; of 72*.Ex. 981. Divide a right angle into five equal 982. The seven diagonals of a regular decagon drawn from anyvertex divide the angle at that vertex into eight equal angles. Ex. 983. Circumscribe a regular pentagon about a circle. Ex. 984. Circumscribe a regular decagon about a circle. Ex. 985. On a given line as one side, construct a regular pentagon. Ex. 986. On a given line as one side, construct a regular decagon. Ex. 987. The side of a regular inscribed decagon is equal toJ B (\/5 — 1), where B is the radius of the circle. Hint. By cons., B : s = s : B — s. Solve this proportion for s. Proposition Y. Problem528. To inscribe a regular pentedecagon in a circle. E. Given circle O. To inscribe ill circle O a regular pentedecagon. I. Construction 1. Prom A, any point in the circumference, Idiy off chord AKequal to a side of a rej;ular inscribed hexagon. § 523. BOOK V 253 2. Also lay off chord AF equal to a side of a regular inscribeddecagon. § 526. 3. Draw chord FE, 4. FE is a side of the required pentedecagon. II. Proof Argument 1. Arc AE = ^ of the circumference. 2. Arc AF = ^Iq of the circumference. 3. arc FE = \ K, -^^ of the cir- 10^ TS^ 4. 5. cumference. , the circumference may be divided into fifteen equal parts. the polygon formed by joining the points of division will be a regular inscribed pentedecagon. III. The discussion is left as an exercise for the student. Reasons 1. By cons. 2. By cons. 3. § 54, 3. 4. Arg. § 517, a. 529. Note. It has now been shown that a circumference can bedivided into the number of equal parts indicated below: 2, 4, 8, 16,... 2^ 3, 6, 12, 24,... 3x 25, 10, 20, 40,
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