TRIPTYCH. 473 TRISECTION OF AN ANGLE. was .a form much in use for altar-pieces during the Gothic and early Kcnaissance periods. The three panels were usually of heavy wood, with an architectural framework, often in the form of a pointed arch, surrounding the painted or carved composition. Giotto, Orcagna, Gaddi, Fra An- gelico, and many other famous artists painted triptyehs. The German and Flemish wood-carv- ers and the Tuscan stuecoists of the Kenaissance often retained the form, which vanished com- pletely, however, in the sixteenth century. TRIREME (Lat. triremis, galley with three banks of oars, from ires, three -|- retniis, oar). In ancient times, a galley with three banks of oars; the common form of the ancient ship of war in the fifth and fourth centuries B.C. The credit of the invention was given to the Corin- thians, who were said to liave used triremes in their war with Corcyra in the seventh century B.C. The details of the structure of the Athenian trireme are still luicertain, as the statements of the ancient writers leave many points obscure, and the testimony of works of art is likewise full of uncertainties. It seoms clear that the banks of oars were arranged one above the other, though not perpendicularly, that there was only one man to an oar, and that all the oars could be, and in battle were, used at the same time. For ordinary purposes the crew was, of course, divided into watches. The ancient trireme was of light draught, and could be easily hauled on shore, so that a high freeboard seems improbable, for reasons of stability ; while the difficulty of keeping an efl'ective stroke with oars of widely different lengths also speaks against any such mode of construction. The trireme was provided with a mainmast which carried a large square sail, that wis lowered with its yard, or if pos- sible left on shore, before going into action. In the latter' case the mast also was unstepped and laid along the deck. There was also a small foremast, which seems to have projected some- what like a bowsprit and likewise carried a square sail. The Attic trireme of the fourth cen- tui-y carried 170 oars, but probably not over 150 were actually used, the rest being a reserve equipment. Officers, sailors, and ten or twelve hoplitcs brought the total crew up to about 200 men. The ship was steered by large paddles on either side of the stern, connected inboard so that they could be handled b.v a single man. The time was given to the rowers by a special officer, the kclciisfcs. The lowest rank of rowers were called thaJaniitcr. the second ;:eugita;, and the uppermost thraiiifrr, and these received the highest pay, as handling the longest oars. In the early battles, such as Salamis, the chief endeavor was to lay the ships aboard and fight from the decks, trusting little to manoeuvring, in which the Greeks seem to have felt themselves inferior. Later the Athenians developed a high degree of skill in handling their long, light ves- sels, and preferred to regard the trireme as the ■weapon, and to aim at disabling or sinking the enemy by the use of the ram, which projected at the water line or below. The attack was aimed at the quarter or side of the hostile ship, and to meet bows on was held unskillful and even dangerous, as the bow was not strongly built. Against the Carthaginians the Romans used boarding bridges in order to neutralize the sea- manship of their opponents, and bring about a conflict of soldiers. Consult: Graser, Dc Vcteruni Re Xdvuli (licrlin, 18ti4), and in I'kilologtis, Sppl. Bd. iii. ; Serre, Lcs marines dc guerre de I'tiiiliquild et du muyeti-6ge (Paris, 1885, 1891) ; Breusing, Die Xaiitilc der Alien (Bremen, 1880), and Die Ddsuiig dcs Trirrcnriitsrls (lircmen, 1889) ; Assmann, s. v. "Seewesen," in Bau- meister's Denkmiilcr des klasxischen Altertums (Munich, 1889) ; Luebeck, Das Seewesen der Grieehen und Homer (Hamburg, 1890, 1891) ; C. Torr, Ancient f<hips (Canduidge, 1894). TRISECTION OF AN ANGLE (from tri- sect, from Lat. tres, tlirce + sect us, p. p. of secare, to cut). One of the three famous prob- lems of antiquity, the others being the duplica- tion of the culie (q.v.) and the squaring of the' circle. (See Cibcle; Quadrature.) This prob- lem, like the quadrature of the circle, is almost as old as geometry itself, but first received thorough investigation at the hands of the Soph- ists (B.C. 400). Hippias of this school invented the quadratrix ( see Qu.dr.vture ) , by wbieli any angle may be trisected. In the figure BD is a quadrant of a circle, BG is an arc of the quadratrix, and the construction involves the relation =-=- — ==: . Hence by dividing B. FD EH into segments having any given ratio, the quad- rant or any arc BD can be divided into arcs having the same ratio. If the arc is to be tri- sected the line corresponding to BA is tri- sected. The trisection of an angle is also accom- plished by means of the concluiid (q.v.) of Ni- comcdes (B.C. 180). If AOB in the figure 13
