Hippocrates of Chios (c. 430 B.C.), the discoverer of the square of a lune, showed that the problem reduced to the determination of two mean proportionals between two given lines, one of them being twice the length of the other. [Please select]
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8 and 27; and the mean proportionals between these, viz. [Please select]
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In the first, B is named twice; and so, if, as in the second, B is actually written twice, the proportionals will be four): and the Just likewise implies four terms at the least, and the ratio between the two pair of terms is the same, because the persons and the things are divided similarly. [Please select]
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So then the joining together of the first and third and second and fourth proportionals is the Just in the distribution, and this Just is the mean relatively to that which violates the proportionate, for the proportionate is a mean and the Just is proportionate. [Please select]
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