Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/402

Rh 380 A K C A 11 C men he was reverenced as the equal of Homer, and statues of these two poets were dedicated on the same day. The fragments of Archilochus are to be found in the collections of smaller Greek poets by Jacobs, Bergk, and Gaisford, and have been published separately by Liebel, Archilochi Rdiquice, Leipsic, 1812, 1818. ARCHIMANDRITE (from ^avSpa, a fold, cloister, or convent), is a title in the Greek Church applied to a superior abbot, who has the supervision of several abbots and cloisters. The name has sometimes been applied generally to superiors of large convents. In Russia the bishops are selected from among the archimandrites. Although the title is peculiar to the Greek Church, it has found its way into Western Europe. It is used in Sicily, Hungary, and Poland, and has even been applied to bishops of the Latin Church. ARCHIMEDES, the greatest mathematician and the most inventive genius of antiquity, was born at Syracuse, in Sicily, about 287 B.C. In his youth he went to Alexandria, and completed his education there under Conon, at the royal school of the Ptolemies, of which Euclid had been the ornament some half a century before. On his return to his native city he devoted himself to geometrical investigations, and by his great energy and inventiveness carried the science far beyond the limits it had then attained. Combined with his remarkable faculty of analysis was a power of practical application which enabled him to establish the science of engineering upon a solid mathematical basis. Of the facts of his private life we have but a few disconnected notices. He was the devoted friend, and, according to some accounts, the relative of Hiero, king of Syracuse ; and he was ever ready to exercise his ingenuity in the service of his admirer and patron. Popularly, Archimedes is best known as the inventor of ingenious contrivances, though many of the stories handed down about these are probably fabulous. He devised for Hiero engines of war, which almost terrified the Romans, and which protracted the siege of Syracuse for three years. There is a story that he constructed a burning mirror which set the Roman ships on fire when they were within a bow-shot of the wall. This has been discredited because neither Polybius, Livy, nor Plutarch mention it ; mirrors may, however, as Buffon showed, be so arranged as to burn at a considerable distance, and it is probable that Archimedes had constructed some such burning instrument, though the connection of it with the destruction of the Roman fleet is more than doubtful. Among the most celebrated of his contributions to practical science are his discoveries in hydrostatics and hydraulics. The account usually given of one of these is remarkable. Hiero, it is said, had set him to discover whether or not the gold which he had given to an artist to work into a crown for him had been mixed with baser metal. Archimedes was puzzled till one day, as he was stepping into a bath and observed the water running over, it occurred to him that the excess of bulk occasioned by the introduction of alloy could be measured by putting the crown and an equal weight of gold separately into a vessel filled with water, and observing the difference of overflow. He was so over joyed when this happy thought struck him that he ran home without his clothes, shouting, &quot; evpyxa, cvpy/ca,&quot;- I have found it, I have found it. It may have been this that led to his establishing the fundamental principle still known by his name, that a body immersed in a liquid sustains an upward pressure equal to the weight of the liquid displaced. Among a number of other mechanical inventions ascribed to him, the water-screw may be mentioned, which still bears his name. His estimate of the capabilities of the lever is expressed in the saying attr.buted to him, Aos TTOV CTTW, KOL rrjv y?]v &quot; Give me a fulcrum on which to rest, and I will move the earth.&quot; The life of this philosopher ends with the capture of Syracuse by Marcellus, 212 B.C. In the general massacre which followed the fall of the city, Archimedes, whilo engaged in drawing a mathematical figure on the sand, was run through the body by a Roman soldier. No blan:e attaches to the Roman general, Marcellus, since he had given orders to his men to spare the house and person of the sage ; and in the midst of his triumph he lamented the death of so illustrious a person, directed an honourable burial to be given him, and befriended his surviving relatives. In accordance with the expressed desire of the philosopher, his tomb was marked by the figure of a sphere inscribed in a cylinder the discovery of the relation between the volumes of a sphere and its circumscribing cylinder being regarded by him as his most valuable achievement. When Cicero was quaestor in Sicily (75 B.C.), he found the tomb of Archimedes, near the Agrigentine gate, overgrown with thorns and briers. &quot; Thus,&quot; says Cicero (Tusc. Disp. v. 23), &quot; would this most famous and once most learned city of Greece have remained a stranger to the tomb of one of its most ingenious citizens, had it not been discovered by a man of Arpinum.&quot; The range and importance of the scientific labours of Archimedes will be best understood from a brief account of those writings which have come down to us ; and it may be remarked that though some useful and important works may have perished, it is probable that these are chiefly details of his mechanical inventions, and that all his most valuable mathematical discoveries have been preserved. The follow ing treatises have escaped the ravages of time : (1.) On the Sphere and Cylinder (irfpl TT^ cr^aipa? KOL TOV KvA.ii/8pov). This treatise consists of two books, dedi cated to Dositheus, and containing a number of propositions relative to the dimensions of spheres, cones, and cylinders, all demonstrated in a strictly geometrical method. The first book contains fifty propositions, the most important of which are : Prop. XIV. on the measure of the curve surface of a cylinder ; Props. XV. and XVI. on the surface of a cone ; Prop XVII. of a frustrum of a cone ; Prop. XXII. of a circle; Prop. XXXV. of the surface of a sphere ; and Prop. XXXVII. of the relation between a sphere and its circumscribing cylinder. The second book contains ten proposition?, which chiefly relate to plane spherical sections. (2.) The Measure of the Circle (KIKOV jucVp^crt?) is a short book of three propositions. Prop. I. proves that the area of a circle is that of a triangle whose base is equal to its circumference, and height equal to its radius; Prop. II. shows that the circumference of a circle exceeds three times its diameter by a small fraction, which is less than its circumscribing square nearly as 11 to 14. He arrived at these wonderfully accurate results by inscribing in and circumscribing about a circle two polygons, each of 96 sides ; and, assuming that the perimeter of the circle lay between these of the polygons, he obtained by actual measurement the limits he has assigned. (3.) Conoids and Spheroids (jrepl Ktoi/oetSewv KO.I ox/&amp;gt;a&amp;lt;poi- SeW) is a treatise in forty propositions, on the superficial and solid dimensions of the solids generated by the revolu tions of the conic sections about their axes. (4.) On Spirals (trepl eAt /cwv), is a book, in twenty-eight propositions, upon the properties of the curve now known as the spiral of Archimedes, which is traced out by a radius vector, whose length is proportional to the angle through which it has turned from the initial position. (5.) Equiponderants and Centres of Gravity (irepl tcroppOTrirtwv ry Kt vTpo. yQapuiv eVtTredojv). ililS Con-
 * and greater than ffi ; and Prop. III. that a circle is to