Page:The New International Encyclopædia 1st ed. v. 10.djvu/206

* HOMOLOGY. 17« HOKIOFTESA. cepts, G (geometric) aod A (algebraic), euch Ihat to every concept in set Ci (for cxauiple, a rectangle, or a line) shall corrcspund a concept in sot A (say, a product, or a nunilicr; ; and to every relation between any two of one set (for example, equality) a relation (in tliis case equality) between the corrchp^nding two of the other, then all lan;,'uage, reasoning, and conclu- sions as to the one set may be applied to the other set. This correspondence of one symbol, one opera- tion, one result, etc., of algebra, to one symbol, one operation, one result, etc., of geometry, or, as it is called, tiiis 'one-to-one correspondence,' sug- gests many tbeorcms of geometry that would otherwise remain unnoticed. E.g.: Oboubtric Tueobems. n X, y, r. . . . are liiii' 8eg- meMt«, ami -v.r, a'z. . . . rep- resoitt the ri-i'tiiuylcH of x and ,r, .v and x and X Cr + «) rcpresentB tht; rec- tangle of X and y + z. and x* repreaeutfi the square uu x, then 1. x(y + i) = xy + iz. 2. ( X + >•)» = i» f .r' -f 2 1.1-. 3. i»— .I' — ix +.1) (.V— J). Algebraic Treoueub. If It, b, c, . . . are nunibere, and lib, ua . ., represent the pruduetH of a and /', /i and c and u (/> + e) repre- seutH the prodin-t of a and b -f c, nad u'^ reprtHenta tiie flecond power of a, then 1. a {b+r)=ab + nc. 2. (a + b)' — a'+b' + 2ab. a. a' — b''=(a+b){a — b). HOM'ONYMS (Lat. homonymus, from Gk. A^iiwyuos, having the same name, from i/jis, ho- mos, same -|" ivotia, unomit, name). Words that agree in form, but dilTer in origin and meaning. A familiar example of this class of words is sound, which in its didVrent meanings goes back to the Latin soniis. Scanilinavian siiiid, and Anglo-Saxon fiiauiid and miiitlinii. Many liomonyms are often distinguished by the accent, as absent, the adjective, and absent, the verb. Strictly speaking, these are not homonyms, but homographs, since the exact correspondence is eontined to the spelling. A third term is also used — 'homophones.' words that agree in the sound, but not necessarily in the spelling. Thus write, wriffhl, and rite are homophones. HOMOOUSION, ho'niA-on'sI-on (Gk. ifwoi., liiiinoiiusi'in. consubstantial, from oiiAt, homos, same + oi/ff/a, ounia, essence). A tenn of Greek theology, employed against the Arians at the Council of Xicaea (A.n. .S2.t). to denote that in the doctrine of the Trinity the !Son is "of the same essence for substance] with the Father." According to the received text of what we call the Xieene Creed, the article in question reads: "And fl believe] in one Lord Jesus Christ . . . being of one substance with the Father." The word hontooiision is much older than the Council of Nic.Tpa. Not to sj>eak of its employment by Gnostics, like Rasilides. it is found in the •writings of Ircnicus. in the latter half of the second century, and not infrequently in llie third century. II was rejected by a synod held in Antioch. against I'aul of Samosata (208 or 200), where it seems to havp borne a meaning some- what diirerent from that which was applied to it by Athanasiiis. In the fourth century the word aroused a long and bitter controversy. The Athanasian party defended it; the Ariana at- tacked it on every side. In the progress of the struggle various alternatives were proposed. Some extreme .rians wished to substitute heteroousion (of a difTerent substance) for h(imooui>i'm. thus alTirniing the direct opposite of what the orthodox party insisted upon. Others, less radical and largely indifferent to the real issue involved, .suggested the colorless term honwioii (similar), meaning simply the tjou "is like' the Father. Others still were willing to go so far as to use the word homuiuusion (i.e. the Son Is "of a like essence, or substance,' with the Father ). After nearly sixty years of theological warfare, the Church, at the Council of Constantinople (liSlj, rcallirined its allegiance to the homuuiision doc- trine, and now applied it not simply to the Son, but also to the Holy (iliost. thus completing the dogma of the Trinity, wliieli has evi'r since re- mained the orthodox faith of Christendom. Consult: liarnack, History of Uoijma, vol. iv., translation (London, 1898); Athanasiiis, Hcteel Works, translation in the Xieene ami I'ostMei nc fathers, second series, edited by ScluilF and Wacc, vol. iv. (New York, 18il2) ; Dubose, The Ecu- menical Councils (2d ed.. New York, 1897). Seo Attn s and Xicknk Creed. HO MOPH'ONY (Gk. ofjJxpwyoc, homophonos, having the same .sound, from o^ii, homos, same + ipuvq, phone, sound). The style of modern music where one voice or melody ]iiedomiiiates. The other voices arc not iiide]iendenl. but serve chielly to furnish the harmonic basis for the leading voici'. Thus it is directly opposed to the older polyphony (q.v. ), where all voices were independent and of equal importance. See Ak- TipiioNV ; Monody. HOMOP'LASY. A term proposed by Lan- kester to e.|iriss, as he says, 'the ))arallelisin of genetically distinct organs.' Its meaning by some is expressed liy the word ■convergence,' now in frequent use. It is due to the action of similar or identical habits or environment on a part or parts of an animal or on the entire animal. I.an- kester's definition is: "When identical or nearly similar forces, or environments, act on two or more parts of an organism which are exactly or nearly alike, the resulting modi/ieations of the various jiarts will be exactly or nearly alike." Lankester illustrates homoplasy by the easp of the remarkable coincidence in the pteropod raol- lusks and eeplialopod mollusks of ap[)endages around or near the mouth provided with suckers. Osborii asserts tlial homophisy lias been confused with 'parallelism' and 'convergence,' which may affect absolutely non-homologous structures. IhimopUisii. he says, should be confined to struc- tures in which there is an element of homology. Converf/enrc may be restricted to cases of 'paral- lelism' between animals of entirely tinrelatcd groups or classes, like the following: l^larsupial mice, and other animals of that group exactly resemble placental mice, etc.; whales resemble fishes owing to their similar ad;>ptation to the water. Many cases of so-called mimicry (q.v.) appear to be instances of convergence. Tx»glcss lizards may be mistaken for snakes. There are nuilfitudcs of such examples, and the resem- blance or narnllelism is so exact as to have often misled well-trained zoologists. HOMOP'TERA (from Gk. A^j, /lomos. same + TrrepSv. i/lmni. wing). . suborder of the Hemiptera inclurling insects with winjrs (when present) of uniform thickness throughout. It contains some of the most destructive of insects and others that arc the most henefiei;!!. It in- cludes the cicadas, lantern-flics, spittle-insects, leafhoppers and treehoppers. plant-lice, scale-ia- sects, and others. A few of the scale-insects fur-