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* HYPATIA. 402 HYPERIDES. Ihe city. At this time the Bishop of Alexandria was Cyril (q.v.), between whom and Orestes tlicre had arisen a dissension on the <|Uestion of jurisdiction. "It was conimonly roportcd among the Cliristians," says Socrates, the Cluirch his- torian, "Ih-it it was by lier inlhuMue he [Oresles] was prevented from heinp reconeih'd with Cyril. ISonic of them, therefore, wliose rinjileador was a reader named Peter, linrried away by a lieree and bijioted zeal, entered into a eonspiracy against her; and observing her as .she returned liome in a carriage, they dragged her from it and carried her to a eluii'ob ealU'd Osareiim. where they eomplctiOy strijiped lier and then murdered her with slii'ils. .ftcr tearing her body to pieces, they took her mangled limbs to a place called Cinaron. and there burned them." This occurred in March, 415. As at the time Synesius (q.v.) met her (about 395) she had Ix-en for twenty years a famous lecturer, and as she lived twenty years after that, she nuist liave been at least si.xty years old when murdered, but in legend and fic- tion she is represented as of unfaded physical charm. She is the lieroine of Charles Kingsley's lliijtatin, or .Ycio Foes villi an Old I'ltcr (1853). Synesius has preserved a few of her letters. Con- stilt Meyer. Ili/pntia roii Alexandria, ein Beitrag &ur Ceichichte des ^euplatonismus (Heidelberg, ISSfi). HYPERjESTHE'SIA (Xco-I.at.. from Gk. Wip, hyper, over + atae-ijatt, aislhfms, sensi- bility, ifrom ahBdvcaffai, aixthnneslhai. to per- ceive through the senses) and Hvi'EHAI.gesia. Hyperirsthcsia is a term connnonly tliougb less correctly used to designate increased sensibility to [Tain, the proper term being hyperalgesia. It is believed that there is no increase of sensibil- ity to touch or to heat and cold over the normal, though tactile and thermal sensibility may be diminished under various eonditions. Unpleasant sensation or actual pain may be caused by a light totieh on the surface, and is due to irrita- tion of over-sensitive end-organs of common sensi- bility (that is. pain), and not to increased per- ception of touch. Ilyi)eralgosia is due to periph- eral, spinal, or cerel)ral irritation of sensory nerve-fibres. Increased eutaneous sensiliility oc- curs in meningitis, cerebral or spinal; tetanus, hysteria, traumatic neuroses, hy.>€tv, hyperbaUein, to exceed, from inrf-p. hyper, over 4- pa'/.'^eiv, bnllcin, to throw). One of the conic section;! (q.v.). Analytically, the hyperbola is the locus of a point which moves so that its dis- tance from a fixed point, railed the focus, bears a constant ratio greater than unity to its dis- tance from a fixed .straight line, called the directrix. In the figure. V is the focus and d the directrix for the branch on the right: V is the foeiis and d' the directrix for the branch on the left: XX' is the transverse axis: YY' the conjueate axis: and I is the latiis rectum. The equation of the hyperbola referred to the rec- tangular axes XX', YY' isl' j.. ?'J_.= I, in which a ^OV. and e is the given ratio. Since e>l, o°(I — c')is negative. Putting — 6= for this negative quantity, the standard form of the equation is — — 'jl =1. The curve MX, PQ is the conjugate hyperbola with reference to the hyperbola AB, CD. (Sec Conjugate.) The HYPKItnOLA. hyperbola is the only conic section having real a-ymptoles. These are the lines TT, T'T' in the figure. The equation of the liyperbola referred to its asymptotes is xy = uh. An hy- ])erbola whose asymptotes are perpendicular to each other is called a reelantitilar or ciiiiiliileral hyperbola. These asymptotes have the following remarkable jiroperty: if, starting from O, the asymptotes 1* divided in continued proportion, and from the ])oints of section lines be drawn parallel to the other a.symptote, the areas con- tained by two adjacent parallels and the corre- sponding parts of the asymptote and curve are equal. HYPERBOLE, ht-per^)6-fe The name given to a figure of rhetoric, by which expressions are employed that, taken literally, signify more than is really meant. The use of the figure is to ar- rest the attention. Hyperbole is the basis of many metaphors. Thus, we call Nero a 'mon- ster''; Tamerlane, a 'tiger'; and so on. See KllETORIC, FlOlRES OF. HYPERBOLIC LOCKARITHMS. See Loo- ABITIIM. HY'PERBO'REANS (Gk. •rirepp6pcoi. By- perhoreoi, beyoinl llie north wind, from I'jrf/), hyper, beyond + liopiac, boreas, north wind). A name given by the ancients to a mytliical people dwelling in the distant north, beyond the Rhi- pa-an M<iuiitains. where it was everlasting day and per])etnal s]iring. and where sorrow and old age were never found. The name was often ap- plied to any people who lived in the far north. The Hyperboreans may have been originally those who brought to Apollo gifts and sacrifice. Con- sult Crusius. "Kvperboreer," in Roscher, Lexikon (Leipzig, 1884-97). HYTERCAWINISM. Tliat form of Cal- vinism which carries the system to its extreme logical conclusions, holding, for example, to a double predestination (to evil as well as good), and atonement only for the elect. The more moderate Calvinists seek to soften some of the results of their principles. HYPER-GEOMETRY. See Geometbt, sec- tion Ihiiii r-r,i iiiiii-lry. HY'PERITJES (T.at., from Gk. 'TTrrpeiSnc, Tfypereidi'-i). An Athenian orator of the fourth eentnrv n.c. one of the ten comprised in the Alexandrian canon. After studying philosophy