Anaxagoras appears to have been the first who dared this enterprise, and it was when he was in prison at Athens. Plutarch says positively that he achieved it; but this must be looked upon only as a general expression. Aristotle in many places mentions the efforts of the Pythagoreans Bryson and Antiphon, who likewise flattered themselves with having found out the square of the circle. Aristophanes jeers the learned of his time for attempting to resolve this problem. One of the nearest approximations to the solution of this problem is that of Archimedes. He found the proportion of the diameter to the circumference to be as 7 to 22, or somewhat between 21 and 22; and it is in making use of Archimedes’s method, that Wallis lays down rules for attaining nearly the square of the circle; yet they bring us not fully up to it, how far soever we advance. Archimedes contented himself with what he had in view, which was to find out a proportion that would serve all the purposes of ordinary practice. What he neglected to do, by extended approximations was afterwards performed by Apollonius, and by Philo of Gadare, who lived in the third century.
The Squaring of the Parabola is one of the geometrical discoveries which has done most honour to Archimedes. It is remarked to have been the first instance of the reducing a curve figure exactly into a square, unless we admit of Hippocrates’s squaring the lunulæ to have been of this sort.
The Burning Glasses, employed by Archimedes to set fire to the Roman fleet at the siege of Syracuse, Kepler, Naudéus, and Descartes have treated as fabulous, though attested by Diodorus Siculus, Lucian, Dion, Zonaras, Galen, Anthemius, Eustathius, Tzetzes, and other eminent authors. Some have pretended to demonstrate by the rules of catoptrics the impossibility of it; but Kircher, attentively observing the description which Tzetzes gives of the burning glasses of Archimedes, resolved upon an experiment; and having, by means of a number of plain mirrors, collected the sun’s rays into one focus, he by an increased number of mirrors produced the most intense degree of solar heat. Tzetzes says, that “Archimedes set fire to Marcellus’s navy, by means of a burning glass composed of small square mirrors, moving every way upon hinges; which, when placed in the sun’s rays, directed them upon the Roman fleet so as to reduce it to ashes at the distance of a bow-shot.” Buffon’s celebrated burning glass, composed of 168 little plain mirrors, produced so considerable a heat, as to set wood in flames at the distance of two hundred and nine feet; melt lead, at that of one hundred and twenty; and silver, at that of fifty.
Anthemius of Tralles in Lydia, celebrated as an able architect, sculptor, and mathematician, who in the emperor Justinian’s time built the church of St. Sophia at Constantinople, wrote a small treatise in Greek, which is extant only in manuscript, entitled “Mechanical Paradoxes,” wherein is a chapter respecting burning glasses, with a complete description of the requisites, which, according to this author, Archimedes must have possessed to enable him to set fire to the Roman fleet. His elaborate description demonstrates the possibility of a fact so well attested in history. Zonaras, speaking of Archimedes’s glasses, mentions those of Proclus, who, he says, burnt the fleet of Vitellius at the siege of Constantinople, in imitation of Archimedes, who set fire to the Roman fleet at the siege of Syracuse. He intimates that the manner wherein Proclus effected this, was by launching upon the vessels, from the surface of reflecting mirrors, such a quantity of flame as reduced them to ashes.
Refracting Burning Glasses were certainly known to the ancients. Pliny and Lactantius speak of glasses that burnt by refraction. The former tells of balls or globes of glass, or crystal, which exposed to the sun transmit a heat sufficient to set fire to cloth, or corrode away the dead flesh of those patients who stand in need of caustics; and the latter, after Clemens Alexandrinus, takes notice that fire may be kindled, by interposing glasses filled with water between the sun and the object, so as to transmit the rays to it. Aristophanes, in his comedy of the Clouds, introduces Socrates as examining Strepsiades about the method he had discovered for getting clear for ever of his debts. The latter replies, that he thought of making use of a burning glass, which he had hitherto used in kindling his fire; for, says he, should they bring a writ against me, I’ll immediately place my glass in the sun, at some little distance from the writ, and set it a fire.
Erratum.
[Col. 455], line 10 from the bottom, for “Hartley Common,” read “Startley Common.”
For the Table Book.