No. 8.*—*Isosceles of Carthage:* De Orbe Quadrata (On the Squaring of the Circle).*

ISOSCELES OF CARTHAGE was apparently a third-century geometer, to judge by certain internal evidence in his writing. The sole work of his that remains to us in any form is his *De Orbe Quadrata,* a Greek treatise that we know only from a fourth-century Latin epitome by an unknown hand. In a short preface, this anonymous epitomist describes how he found a number of scrolls by Isosceles in the library of Alexandria that purported to contain a solution to the ancient problem of squaring the circle; and, having been intrigued by the possibility of finding a solution to that puzzle, he prepared a summary of the argument in the books as he read them.

Book 1, our epitomist informs us, introduced the notion of squaring the circle, summarizing the failures of past geometers who studied the problem, and containing many personal animadversions which the epitomist did not think it proper to repeat.

Book 2 explained how to construct a circle. Forsaking the usual Euclidean method, Isosceles eschewed compasses and other tools (which he called decadent) in favor of laying a bowl in the sand and tracing the outline of it.

Book 3 similarly explained how to construct a square, for which Isosceles followed the same method as in the case of the circle, except that for the bowl he substituted what he described as some sort of square thing.

Book 4 compared the square to the circle, showing by means of diagrams how they differed. Our epitomist skips lightly over this book, devoting only two lines to it, although he remarks that it was the longest among the original scrolls.

Book 5 introduced the *diameter,* which Isosceles, alone among geometers, appears to have considered a property of the square rather than of the circle.

Book 6 invoked the aid of the Muses, and was cast in hexameters of very indifferent quality, according to our epitomist, who admits, however, that he is not as competent a critic of poetry as he would like to be.

Book 7 was a historico-mythological treatise explaining how the moon had once been square until the time of Jason of *Argonautica* fame; our epitome does not tell us what Jason did to make it round, or indeed whether its change of shape was merely a coincidence having nothing to do with Jason himself.

Book 8 explained how, by the inspiration of the god Dionysius, Isosceles had discovered that other round objects, such as bowls and marbles, could be seen as square if the observer’s head was tilted at precisely the right angle: an assertion which he proved in what he described as an elegant diagram, although our epitomist, reproducing it, reckons it for a lewd caricature of the emperor Pupienus Maximus.

Book 9 was an examination of the properties of the small hippopotamus which Isosceles said followed him everywhere, and which he described as bright red in color, wearing a crown of gold studded with lapis and carbuncles, and no more than two spans tall at the shoulder. He apologized for the apparent digression, but explained that the information would prove relevant to the argument when we reached Book 863.

Book 10, though written in Greek characters, did not appear to be in Greek, and our epitomist candidly admits his inability to construe the language of the scroll.

So ended the magnum opus of Isosceles; for the epitomist informs us that there were no more scrolls to be found in Alexandria, and that his correspondents in Carthage wrote back to inform him that the name of Isosceles was unknown there. Whether there were at one time 853 more books, or some larger number, we do not know; and the apparently unique manuscript perished when the library in Alexandria was stormed by a mob of violent fundamentalist geometers, who had vowed to purge it of all heresy contrary to the received text of Euclid.