Plane and solid geometry . parallelopiped ? State the theorem and corol-laries in Book IV that correspond to §§ 778, 779, 782, 783, and 784. Willthe proofs given there, with the corresponding changes in terms, apply-here ? Compare the entire discussion of §§ 406-480 with §§ 769-786. Ex. 1304. Find the volume of a cube whose diagonal is SVS ; d. Ex. 1305. The volume of a rectangular parallelopiped is F; eachside of the square base is one third the altitude of the parallelopiped. Findthe side of the base. Find the side of the base if Y = 192 cubic feet. Ex. 1306. The dimensions of two rectangula
Plane and solid geometry . parallelopiped ? State the theorem and corol-laries in Book IV that correspond to §§ 778, 779, 782, 783, and 784. Willthe proofs given there, with the corresponding changes in terms, apply-here ? Compare the entire discussion of §§ 406-480 with §§ 769-786. Ex. 1304. Find the volume of a cube whose diagonal is SVS ; d. Ex. 1305. The volume of a rectangular parallelopiped is F; eachside of the square base is one third the altitude of the parallelopiped. Findthe side of the base. Find the side of the base if Y = 192 cubic feet. Ex. 1306. The dimensions of two rectangular parallelopipeds are 6,8, 10 and 5, 12, 16, respectively. Find the ratio of their volumes. Ex. 1307. The total area of a cube is 300 square inches; find its volume. Ex. 1308. The volume of a certain cube is F; find the volume of acube whose edge is twice that of the given cube. Ex. 1309. The edge of a cube is a ; find the edge of a cube twice aslarge; containing twice the volume of the given cube. BOOK VII 365. Plato 787. Historical Note. Plato (429-348 ) was one of the first todiscover a solution to that famous problem of antiquity, the duplicationof a cube^ the finding of theedge of a cube whose volume isdouble that of a given cube. There are two legends as tothe origin of the problem. Theone is that an old tragic poet rep-resented King Minos as wishingto erect a tomb for his son Glau-cus. The king being dissatis-fied with the dimensions (100feet each way) proposed by hisarchitect, exclaimed : The in-closure is too small for a royaltomb ; double it, but fail not inthe cubical form. The other legend asserts thatthe Athenians, who were suf-fering from a plague of typhoid fever, consulted the oracle at Delos as tohow to stop the plague. Apollo replied that the Delians would haveto double the size of his altar, which was in the form of a cube. A newaltar was constructed having its edge twice as long as that of the old pestilence became worse than befo
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