Chapter X: "1. Then, after being filled, thus give ye thanks (2)

But the covenant instituted by Jesus on the eve of his death was hardly intended as a new covenant with God, superseding the old. This reconstruction of its meaning seems to have been the peculiar revelation of the Lord to Paul, who viewed Christ's crucifixion and death as an atoning sacrifice, liberating by its grace mankind from bonds of sin which the law, far from snapping, only made more sensible and grievous. This must have been the gist of the special revelation which he had received from Christ as to the inner character of a supper which he already found a ritual observance among believers. The Eucharist of the synoptists is rather a covenant or tie of communion between Jesus and the twelve, such as will cause his life to survive in them after he has been parted from them in the flesh. An older prophet would have slain an animal and drunk its blood in common with his followers, or they would all alike have smeared themselves with it. In the East, even now, one who wishes to create a blood tie between himself and his followers and cement them to himself, makes under his left breast an incision from which they each in turn suck his blood. Such barbarisms was alien to the spirit of the Founder, who substitutes bread and wine for his own flesh and blood, only imparting to these his own quality by the declaration that they _are_ himself. He broke the bread not in token of his approaching death, but in order to its equal distribution. Wine he rather chose than water as a surrogate for his actual blood, because it already in Hebrew sacrifices passed as such. "The Hebrews," says Robertson Smith (_op. cit_. p. 230), "treated it like the blood, pouring it out at the base of the altar." As a red liquid it was a ready symbol of the blood which is the life. It was itself the covenant, for the genitive [Greek: tes diathekes] in Mark xiv. 24 is epexegetic, and Luke and Paul rightly substitute the nominative. It was, as J. Wellhausen remarks,[11] a better cement than the bread, because through the drinking of it the very blood of Jesus coursed through the veins of the disciples, and that is why more stress is laid on it than on the bread. To the apostles, as Jews bred and born, the action and words of their master formed a solemn and intelligible appeal. It belongs to the same order of ideas that the headship of the Messianic _ecclesia_ in Judea was assigned after the death of Jesus to his eldest brother James, and after him for several generations to the eldest living representative of his family.

To the modern mind it is absurd that an image or symbol should be taken for that which is imaged or symbolized, and that is why the early history of the Eucharist has been so little understood by ecclesiastical writers. And yet other religions, ancient and modern, supply many parallels, which are considered in the article SACRAMENT.

Authorities.--Robertson Smith, _Religion of the Semites_; Goetz, _Die
Abendmahlsfrage_; G. Anrich, _Das antike Mysterienwesen_ (Goettingen,
1894); _Sylloge confessionum_ (Oxford, 1804); Duchesne, _Origins of
Christian Culture_; Funk's edition of _Constitutiones Apostolicae_;
Hagenbach, _History of Doctrines_, vol. ii.; Geo. Bickell, _Messe und
Pascha_; idem. "Die Entstehung der Liturgie," _Ztsch. f. Kath. Theol_.
iv. Jahrg. 94 (1880), p. 90 (shows how the prayers of the Christian
sacramentaries derive from the Jewish Synagogue); Goar, _Rituale
Graecorum_; F.E. Brightman, _Eastern Liturgies_; Cabrol and Leclercq,
_Monumenta liturgica, reliquiae liturgicae vetustissimae_ (Paris,
1900); Harnack, _History of Dogma_; Jas. Martineau, _Seat of Authority
in Religion_, bk. iv. (London, 1890); Loofs, art. "Abendmahlsfeier" in
Herzog's _Realencyklopaedie_ (1896.) Spitta, _Urchristentum_
(Goettingen, 1893); Schultzen, _Das Abendmahl im N.T._ (Goettingen,
1895); Kraus, _Real-Encykl. d. christl. Altert_. (for the
Archaeology); art. "Eucharistic"; Ch. Gore, _Dissertations_ (1895);
Hoffmann, _Die Abendmahlsgedanken Jesu Christi_ (Koenigsberg, 1896);
Sanday, art. "Lord's Supper" in _Hastings' Dictionary of the Bible_;
Th. Harnack, _Der christl. Gemeindegottesdienst_. (F. C. C.)

RESERVATION OF THE EUCHARIST

The practice of reserving the sacred elements for the purpose of subsequent reception prevailed in the church from very early times. The Eucharist being the seal of Christian fellowship, it was a natural custom to send portions of the consecrated elements by the hands of the deacons to those who were not present (Justin Martyr, _Apol_. i. 65). From this it was an easy development, which prevailed before the end of the 2nd century, for churches to send the consecrated Bread to one another as a sign of communion (the [Greek: eucharistia] mentioned by Irenaeus, _ap_. Eus. _H.E._ v. 24), and for the faithful to take it to their own homes and reserve it in _arcae_ or caskets for the purpose of communicating themselves (Tert. _ad Uxor_. ii. 5, _De orat_. 19; St Cypr. _De lapsis_, 132). Being open to objection on grounds both of superstition and of irreverence, these customs were gradually put down by the council of Laodicea in A.D. 360. But some irregular forms of reservation still continued; the prohibition as regards the lay people was not extended, at any rate with any strictness, to the clergy and monks; the Eucharist was still carried on journeys; occasionally it was buried with the dead; and in a few cases the pen was even dipped in the chalice in subscribing important writings. Meanwhile, both in East and West, the general practice has continued unbroken of reserving the Eucharist, in order that the "mass of the presanctified" might take place on certain "aliturgic" days, that the faithful might be able to communicate when there was no celebration, and above all that it might be at hand to meet the needs of the sick and dying. It was reserved in a closed vessel, which took various forms from time to time, known in the East as the [Greek: artophorion], and in the West as the _turris_, the _capsa_, and later on as the _pyx_. In the East it was kept against the wall behind the altar; in the West, in a locked aumbry in some part of the church, or (as in England and France) in a pyx made in the form of a dove and suspended over the altar.

In the West it has been used in other ways. A portion of the consecrated Bread from one Eucharist, known as the "Fermentum," was long made use of in the next, or sent by the bishop to the various churches of his city, no doubt with the object of emphasizing, the solidarity and the continuity of "the one Eucharist"; and amongst other customs which prevailed for some centuries, from the 8th onward, were those of giving it to the newly ordained in order that they might communicate themselves, and of burying it in or under the altar-slab of a newly consecrated church. At a later date, apparently early in the 14th century, began the practice of carrying the Eucharist in procession in a monstrance; and at a still later period, apparently after the middle of the 16th century, the practice of Benediction with the reserved sacrament, and that of the "forty hours' exposition," were introduced in the churches of the Roman communion. It should be said, however, that most of these practices met with very considerable opposition both from councils and from theologians and canonists, amongst others from the English canonist William Lyndwood (_Provinciale_, lib. iii. c. 26), on the following grounds amongst others: that the Body of Christ is the food of the soul, that it ought not to be reserved except for the benefit of the sick, and that it ought not to be applied to any other use than that for which it was instituted.

In England, during the religious changes of the 16th century, such of these customs as had already taken root were abolished; and with them the practice of reserving the Eucharist in the churches appears to have died out too. The general feeling on the subject is expressed by the language of the 28th Article, first drafted in 1553, to the effect that "the sacrament of the Lord's Supper was not by Christ's ordinance reserved, carried about, lifted up or worshipped," and by the fact that a form was provided for the celebration of the Holy Eucharist for the sick in their own homes. This latter practice was in accordance with abundant precedent, but had become very infrequent, if not obsolete, for many years before the Reformation. The first Prayer-Book of Edward VI. provided that if there was a celebration in church on the day on which a sick person was to receive the Holy Communion, it should be reserved, and conveyed to the sick man's house to be administered to him; if not, the curate was to visit the sick person before noon and there celebrate according to a form which is given in the book. At the revision of the Prayer-Book in 1552 all mention of reservation is omitted, and the rubric directs that the communion is to be celebrated in the sick person's house, according to a new form; and this service has continued, with certain minor changes, down to the present day. That the tendency of opinion in the English Church during the period of the Reformation was against reservation is beyond doubt, and that the practice actually died out would seem to be equally clear. The whole argument of some of the controversial writings of the time, such as Bishop Cooper on _Private Mass_, depends upon that fact; and when Cardinal du Perron alleged against the English Church the lack of the reserved Eucharist, Bishop Andrewes replied, not that the fact was otherwise, but that reservation was unnecessary in view of the English form for the Communion of the Sick: "So that reservation needeth not; the intent is had without it" (_Answers to Cardinal Perron, &c._, p. 19, Library of Anglo-Catholic Theology). It does not follow, however, that a custom which has ceased to exist is of necessity forbidden, nor even that what was rejected by the authorities of the English Church in the 16th century is so explicitly forbidden as to be unlawful under its existing system; and not a few facts have to be taken into account in any investigation of the question. (1) The view has been held that in the Eucharist the elements are only consecrated as regards the particular purpose of reception in the service itself, and that consequently what remains unconsumed may be put to common uses. If this view were held (and it has more than once made its appearance in church history, though it has never prevailed), reservation might be open to objection on theological grounds. But such is not the view of the Church of England in her doctrinal standards, and there is an express rubric directing that any that remains of that which was consecrated is not to be carried out of the church, but reverently consumed. There can therefore be no theological obstacle to reservation in the English Church: it is a question of practice only. (2) Nor can it be said that the rubric just referred to is in itself a condemnation of reservation: it is rather directed, as its history proves, against the irreverence which prevailed when it was made; and in fact its wording is based upon that of a pre-Reformation order which coexisted with the practice of reservation (Lyndwood, _Provinciale_, lib. iii. tit. 26, note q). (3) Nor can it be said that the words of the 28th Article (see above) constitute in themselves an express prohibition of reservation, strong as their evidence may be as to the practice and feeling of the time. The words are the common property of an earlier age which saw nothing objectionable in reservation for the sick. (4) It has indeed been contended (by Bishop Wordsworth of Salisbury) that reservation was not actually, though tacitly, continued under the second Prayer-Book of Edward VI., since that book orders that the curate shall "minister," and not "celebrate," the communion in the sick person's house. But such a tacit sanction on the part of the compilers of the second Prayer-Book is in the highest degree improbable, in view of their known opinions on the subject; and an examination of contemporary writings hardly justifies the contention that the two words are so carefully used as the argument would demand. Anyhow, as the bishop notes, this could not be the case with the Prayer-Book of 1661, where the word is "celebrate." (5) The Elizabethan Act of Uniformity contained a provision that at the universities the public services, with the exception of the Eucharist, might be in a language other than English; and in 1560 there appeared a Latin version of the Prayer-Book, issued under royal letters patent, in which there was a rubric prefixed to the Order for the Communion of the Sick, based on that in the first Prayer-Book of Edward VI. (see above), and providing that the Eucharist should be reserved for the sick person if there had been a celebration on the same day. But although the book in question was issued under letters patent, it is not really a translation of the Elizabethan book at all, but simply a reshaping of Aless's clever and inaccurate translation of Edward VI.'s first book. In the rubric in question words are altered here and there in a way which shows that its reappearance can hardly be a mere printer's error; but in any case its importance is very slight, for the Act of Uniformity specially provides that the English service alone is to be used for the Eucharist. (6) It has been pointed out that reservation for the sick prevails in the Scottish Episcopal Church, the doctrinal standards of which correspond with those of the Church of England. But it must be remembered that the Scottish Episcopal Church has an additional order of its own for the Holy Communion, and that consequently its clergy are not restricted to the services in the Book of Common Prayer. Moreover, the practice of reservation which has prevailed in Scotland for over 150 years would appear to have arisen out of the special circumstances of that church during the 18th century, and not to have prevailed continuously from earlier times. (7) Certain of the divines who took part in the framing of the Prayer-Book of 1661 seem to speak of the practice as though it actually prevailed in their day. But Bishop Sparrow's words on the subject (_Rationale_, p. 349) are not free from difficulty on any hypothesis, and Thorndike (_Works_, v. 578, Library of Anglo-Catholic Theology) writes in such a style that it is often hard to tell whether he is describing the actual practice of his day or that which in his view it ought to be. (8) There appears to be more evidence than is commonly supposed to show that a practice analogous to that of Justin Martyr's day has been adopted from time to time in England, viz. that of conveying the sacred elements to the houses of the sick during, or directly after, the celebration in church. And in 1899 this practice received the sanction of Dr Westcott, then bishop of Durham. (9) On the other hand, the words of the oath taken by the clergy under the 36th of the Canons of 1604 are to the effect that they will use the form prescribed in the Prayer-Book and none other, except so far as shall be otherwise ordered by lawful authority; and the Prayer-Book does not even mention the reservation of the Eucharist, whilst the Articles mention it only in the way of depreciation.

The matter has become one of no little practical importance owing to modern developments of English Church life. On the one hand, it is widely felt that neither the form for the Communion of the Sick, nor yet the teaching with regard to spiritual communion in the third rubric at the end of that service, is sufficient to meet all the cases that arise or may arise. On the other hand, it is probable that in many cases the desire for reservation has arisen, in part at least, from a wish for something analogous to the Roman Catholic customs of exposition and benediction; and the chief objection to any formal practice of reservation, on the part of many who otherwise would not be opposed to it, is doubtless to be found in this fact. But however that may be, the practice of reservation of the Eucharist, either in the open church or in private, has become not uncommon in recent days.

The question of the legality of reservation was brought before the two archbishops in 1899, under circumstances analogous to those in the Lambeth Hearing on Incense (q.v.). The parties concerned were three clergymen, who appealed from the direction of their respective diocesans, the bishops of St Albans and Peterborough and the archbishop of York: in the two former cases the archbishop (Temple) of Canterbury was the principal and the archbishop of York (Maclagan) the assessor, whilst in the latter case the functions were reversed. The hearing extended from 17th to 20th July; counsel were heard on both sides, evidence was given in support of the appeals by two of the clergy concerned and by several other witnesses, lay and clerical, and the whole matter was gone into with no little fulness. The archbishops gave their decision on the 1st of May 1900 in two separate judgments, to the effect that, in Dr Temple's words, "the Church of England does not at present allow reservation in any form, and that those who think that it ought to be allowed, though perfectly justified in endeavouring to get the proper authorities to alter the law, are not justified in practising reservation until the law has been so altered." The archbishop of York also laid stress upon the fact that the difficulties in the way of the communion of the sick, when they are really ready for communion, are not so great as has sometimes been suggested.

See W.E. Scudamore, _Notitia eucharistica_ (2nd ed., London, 1876);
and art. "Reservation" in _Dictionary of Christian Antiquities_, vol.
ii. (London, 1893); _Guardian_ newspaper, July 19 and 26, 1899, and
May 2, 1900; _The Archbishops of Canterbury and York on Reservation of
the Sacrament_ (London, 1900); J.S. Franey, _Mr Dibdin's Speech on
Reservation, and some of the Evidence_ (London, 1899); F.C. Eeles,
_Reservation of the Holy Eucharist in the Scottish Church_ (Aberdeen,
1899); Bishop J. Wordsworth, _Further Considerations on Public
Worship_ (Salisbury, 1901). (W. E. Co.)

FOOTNOTES:

[1] Ps. lxxx. 8-19.

[2] Acts iv. 25, 27.

[3] 1 Cor. x. 17; Soph. iii. 10.

[4] Matt. vii. 6.

[5] Matt. xxiv. 31.

[6] 1 Cor. xvi. 22.

[7] We should probably omit the words bracketed.

[8] The codex Othobonianus omits the words bracketed.

[9] See Nerses of Lambron, _Opera Armenice_ (Venice, 1847), pp. 74,
75, 101, &c.

[10] This represents the views of Calvin.

[11] _Das Evangelium Marci_, p. 121.

EUCHRE, a game of cards. The name is supposed by some to be a corruption of _ecarte_, to which game it bears some resemblance; others connect it with the Ger. _Juchs_ or _Jux_, a joke, owing to the presence in the pack, or "deck," of a special card called "the joker"; but neither derivation is quite satisfactory. The "deck" consists of 32 cards, all cards between the seven and ace being rejected from an ordinary pack. Sometimes the sevens and eights are rejected as well. The "joker" is the best card, i.e. the highest trump. Second in value is the "right bower" (from Dutch _boer_, farmer, the name of the knave), or knave of trumps; third is the "left bower," the knave of the other suit of the same colour as the right bower, also a trump: then follow ace, king, queen, &c., in order. Thus if spades are trumps the order is (1) the joker, (2) knave of spades, (3) knave of clubs, (4) ace of spades, &c. The joker, however, is not always used. When it is, the game is called "railroad" euchre. In suits not trumps the cards rank as at whist. Euchre can be played by two, three or four persons. In the cut for deal, the highest card deals, the knave being the highest and the ace the next best card. The dealer gives five cards to each person, two each and then three each, or vice versa: when all have received their cards the next card in the pack is turned up for trumps.

_Two-handed Euchre_.--If the non-dealer, who looks at his cards first,
is satisfied, he says "I order it up," i.e. he elects to play with his
hand as it stands and with the trump suit as turned up. The dealer
then rejects one card, which is put face downwards at the bottom of
the pack, and takes the trump card into his hand. If, however, the
non-dealer is not satisfied with his original hand, he says "I pass,"
on which the dealer can either "adopt," or "take it up," the suit
turned up, and proceed as before, or he can pass, turning down the
trump card to show that he passes. If both players pass, the
non-dealer can make any other suit trumps, by saying "I make it
spades," for example, or he can pass again, when the dealer can either
make another suit trumps or pass. If both players pass, the hand is at
an end. If the trump card is black and either player makes the other
black suit trumps, he "makes it next"; if he makes a red suit trumps
he "crosses the suit"; the same applies to trumps in a red suit,
_mutatis mutandis_. The non-dealer leads; the dealer must follow suit
if he can, but he need not win the trick, nor need he trump if unable
to follow suit. The left bower counts as a trump, and a trump must be
played to it if led. The game is five up. If the player who orders up
or adopts makes five tricks (a "march") he scores two points; if four
or three tricks, one point; if he makes less than three tricks, he is
"euchred" and the other player scores two. A rubber consists of three
games, each game counting one, unless the loser has failed to score at
all, when the winner counts two for that game. This is called a
"lurch." When a player wins three tricks, he is said to win the
"point." The rubber points are two, as at whist. All three games are
played out, even if one player win the first two. It is sometimes
agreed that if a score "laps," i.e. if the winner makes more than five
points in a game, the surplus may be carried on to the next game. The
leader should be cautious about ordering up, since the dealer will
probably hold one trump in addition to the one he takes in. If the
point is certain, the leader should pass, in case the dealer should
take up the trump. If the dealer "turns it down," it is not wise to
"make it," unless the odds on getting the point against one trump are
two to one. With good cards in two suits, it is best to make it
"next," as the dealer is not likely to have a bower in that suit. The
dealer, if he adopts, should discard a singleton, unless it is an ace.
If the dealer's score is three, only a very strong hand justifies one
in "ordering up." It is generally wise in play to discard a singleton
and not to unguard another suit. With one's adversary at four, the
trump should be adopted even on a light hand.

_Three-handed (cut-throat) Euchre_.--In this form of the game the
option of playing or passing goes round in rotation, beginning with
the player on the dealer's left. The player who orders up, takes up,
or makes, plays against the other two; if he is euchred his
adversaries score two each; by other laws he is set back two points,
and should his score be at love, he has then to make seven points. The
procedure is the same as in two-handed euchre.

_Four-handed Euchre_.--The game is played with partners, cutting and
sitting, and the deal passing, as at whist. If the first player
passes, the second may say "I assist," which is the same as "ordering
up," or he may pass. If the first player has ordered up, his partner
may say "I take it from you," which means that he will play alone
against the two adversaries, the first player's cards being put face
downwards on the table, and not being used in that hand. Any player
can similarly play "a lone hand," his partner taking no part in the
play. Even if the first hand plays alone, the third may take it from
him. Similarly the dealer may take it from the second hand, but the
second hand cannot take it from the dealer. If all four players pass,
the first player can pass, make it, or play alone, naming the suit he
makes. The third hand can "take it" from the first, or play alone in
the suit made by the first, the dealer having a similar right over his
own partner. If all four pass again, the hand is at an end and the
deal passes. The game is five up, points being reckoned as before. If
a lone player makes five tricks his side scores four: if three tricks,
one: if he fails to make three tricks the opponents score four. It is
not wise for the first hand to order up or cross the suit unless very
strong. It is good policy to lead trumps through a hand that assists,
bad policy to do so when the leader adopts. Trumps should be led to a
partner who has ordered up or made it. It is sometimes considered wise
for the first hand to "keep the bridge," i.e. order up with a bad
hand, to prevent the other side from playing alone, if their score is
only one or two and the leader's is four. This right is lost if a
player reminds his partner, after the trump card has been turned, that
they are at the point of bridge. If the trump under these
circumstances is not ordered up, the dealer should turn down, unless
very strong. The second hand should not assist unless really strong,
except when at the point of four-all or four-love. When led through,
it is generally wise, _ceteris paribus_, to head the trick. The dealer
should always adopt with two trumps in hand, or with one trump if a
bower is turned up. At four-all and four-love he should adopt on a
weaker hand. Also, being fourth player, he can make it on a weaker
hand than other players. If the dealer's partner assists, the dealer
should lead him a trump at the first opportunity; it is also a good
opportunity for the dealer to play alone if moderately strong. If a
player who generally keeps the bridge passes, his partner should
rarely play alone.

_Extracts from Rules_.--If the dealer give too many or too few cards
to any player, or exposes two cards in turning up, it is a misdeal and
the deal passes. If there is a faced card in the pack, or the dealer
exposes a card, he deals again. If any one play with the wrong number
of cards, or the dealer plays without discarding, trumps being ordered
up, his side forfeits two points (a lone hand four points) and cannot
score during that hand. The revoke penalty is three points for each
revoke (five in the case of a lone hand), and no score can be made
that hand; a card may be taken back, before the trick is quitted, to
save a revoke, but it is an exposed card. If a lone player expose a
card, no penalty; if he lead out of turn, the card led may be called.
If an adversary of a lone player plays out of turn to his lead, all
the cards of both adversaries can be called, and are exposed on the
table.

_Bid Euchre_.--This game resembles "Napoleon" (q.v.). It is played
with a euchre deck, each player receiving five cards, the others being
left face-downwards. Each player "bids," i.e. declares and makes a
certain number of tricks, the highest bidder leading and his first
card being a trump. When six play, the player who bids highest claims
as his partner the player who has the best card of the trump suit, not
in the bidder's hand: if it is among the undealt cards, which is
ascertained by the fact that no one else holds it, he calls for the
next best and so on. The partners then play against the other four.

EUCKEN, RUDOLF CHRISTOPH (1846- ), German philosopher, was born on the 5th of January 1846 at Aurich in East Friesland. His father died when he was a child, and he was brought up by his mother, a woman of considerable activity. He was educated at Aurich, where one of his teachers was the philosopher Wilhelm Reuter, whose influence was the dominating factor in the development of his thought. Passing to the university of Goettingen he took his degree in classical philology and ancient history, but the bent of his mind was definitely towards the philosophical side of theology. Subsequently he studied in Berlin, especially under Trendelenburg, whose ethical tendencies and historical treatment of philosophy greatly attracted him. From 1871 to 1874 Eucken taught philosophy at Basel, and in 1874 became professor of philosophy at the university of Jena. In 1908 he was awarded the Nobel prize for literature. Eucken's philosophical work is partly historical and partly constructive, the former side being predominant in his earlier, the latter in his later works. Their most striking feature is the close organic relationship between the two parts. The aim of the historical works is to show the necessary connexion between philosophical concepts and the age to which they belong; the same idea is at the root of his constructive speculation. All philosophy is philosophy of life, the development of a new culture, not mere intellectualism, but the application of a vital religious inspiration to the practical problems of society. This practical idealism Eucken described by the term "Activism." In accordance with this principle, Eucken has given considerable attention to social and educational problems.

His chief works are:--_Die Methode der aristotelischen Forschung_
(1872); the important historical study on the history of conceptions,
_Die Grundbegriffe der Gegenwart_ (1878; Eng. trans. by M. Stuart
Phelps, New York, 1880; 3rd ed. under the title _Geistige Stroemungen
der Gegenwart_, 1904; 4th ed., 1909); _Geschichte der philos.
Terminologie_ (1879); _Prolegomena zu Forschungen ueber die Einheit des
Geisteslebens_ (1885); _Beitraege zur Geschichte der neueren
Philosophie_ (1886, 1905); _Die Einheit des Geisteslebens_ (1888);
_Die Lebensanschauungen der grossen Denker_ (1890; 7th ed., 1907; Eng.
trans., W. Hough and Boyce Gibson, _The Problem of Human Life_, 1909);
_Der Wahrheitsgehalt der Religion_ (1901; 2nd ed., 1905); _Thomas von
Aquino und Kant_ (1901); _Gesammelte Aufsaetze zu Philos. und
Lebensanschauung_ (1903); _Philosophie der Geschichte_ (1907); _Der
Kampf um einen geistigen Lebensinhalt_ (1896, 1907); _Grundlinien
einer neuen Lebensanschauung_ (1907); _Einfuehrung in die Philosophie
der Geisteslebens_ (1908; Eng. trans., _The Life of the Spirit_, F.L.
Pogson, 1909, Crown Theological Library); _Der Sinn und Wert des
Lebens_ (1908; Eng. trans., 1909); _Hauptprobleme der
Religionsphilosophie der Gegenwart_ (1907). The following of Eucken's
works also have been translated into English:--_Liberty in Teaching in
the German Universities_ (1897); _Are the Germans still a Nation of
Thinkers_? (1898); _Progress of Philos. in the 19th Century_ (1899);
_The Finnish Question_ (1899); _The Present Status of Religion in
Germany_ (1901). See W.R. Boyce Gibson, _Rudolf Eucken's Philosophy of
Life_ (2nd ed., 1907), and _God with Us_ (1909); for the historical
work, Falckenberg's _Hist. of Philos_. (Eng. trans., 1895, index);
also H. Poehlmann, _R. Euckens Theologie mit ihren philosophischen
Grundlagen dargestellt_ (1903); O. Siebert, _R. Euckens Welt- und
Lebensanschauung_ (1904).

EUCLASE, a very rare mineral, occasionally cut as a gem-stone for the cabinet. It bears some relation to beryl in that it is a silicate containing beryllium and aluminium, but hydrogen is also present, and the analyses of euclase lead to the formula HBeAlSiO5 or Be(AlOH)SiO4. It crystallizes in the monoclinic system, the crystals being generally of prismatic habit, striated vertically, and terminated by acute pyramids. Cleavage is perfect, parallel to the clinopinacoid, and this suggested to R.J. Hauey the name euclase, from the Greek [Greek: eu], easily, and [Greek: klasis], fracture. The ready cleavage renders the stone fragile with a tendency to chip, and thus detracts from its use for personal ornament. The colour is generally pale-blue or green, though sometimes the mineral is colourless. When cut it resembles certain kinds of beryl (aquamarine) and topaz, from which it may be distinguished by its specific gravity (3.1). Its hardness (7.5) is rather less than that of topaz. Euclase occurs with topaz at Boa Vista, near Ouro Preto (Villa Rica) in the province of Minas Geraes, Brazil. It is found also with topaz and chrysoberyl in the gold-bearing gravels of the R. Sanarka in the South Urals; and is met with as a rarity in the mica-schist of the Rauris in the Austrian Alps.

EUCLID [EUCLEIDES], of Megara, founder of the Megarian (also called the eristic or dialectic) school of philosophy, was born c. 450 B.C., probably at Megara, though Gela in Sicily has also been named as his birthplace (Diogenes Laertius ii. 106), and died in 374. He was one of the most devoted of the disciples of Socrates. Aulus Gellius (vi. 10) states that, when a decree was passed forbidding the Megarians to enter Athens, he regularly visited his master by night in the disguise of a woman; and he was one of the little band of intimate friends who listened to the last discourse. He withdrew subsequently with a number of fellow disciples to Megara, and it has been conjectured, though there is no direct evidence, that this was the period of Plato's residence in Megara, of which indications appear in the _Theaetetus_. He is said to have written six dialogues, of which only the titles have been preserved. For his doctrine (a combination of the principles of Parmenides and Socrates) see MEGARIAN SCHOOL.

EUCLID, Greek mathematician of the 3rd century B.C.; we are ignorant not only of the dates of his birth and death, but also of his parentage, his teachers, and the residence of his early years. In some of the editions of his works he is called _Megarensis_, as if he had been born at Megara in Greece, a mistake which arose from confounding him with another Euclid, a disciple of Socrates. Proclus (A.D. 412-485), the authority for most of our information regarding Euclid, states in his commentary on the first book of the _Elements_ that Euclid lived in the time of Ptolemy I., king of Egypt, who reigned from 323 to 285 B.C., that he was younger than the associates of Plato, but older than Eratosthenes (276-196 B.C.) and Archimedes (287-212 B.C.). Euclid is said to have founded the mathematical school of Alexandria, which was at that time becoming a centre, not only of commerce, but of learning and research, and for this service to the cause of exact science he would have deserved commemoration, even if his writings had not secured him a worthier title to fame. Proclus preserves a reply made by Euclid to King Ptolemy, who asked whether he could not learn geometry more easily than by studying the _Elements_--"There is no royal road to geometry." Pappus of Alexandria, in his _Mathematical Collection_, says that Euclid was a man of mild and inoffensive temperament, unpretending, and kind to all genuine students of mathematics. This being all that is known of the life and character of Euclid, it only remains therefore to speak of his works.

Among those which have come down to us the most remarkable is the _Elements_ ([Greek: Stoicheia]) (see GEOMETRY). They consist of thirteen books; two more are frequently added, but there is reason to believe that they are the work of a later mathematician, Hypsicles of Alexandria.

The question has often been mooted, to what extent Euclid, in his _Elements_, is a discoverer or a compiler. To this question no entirely satisfactory answer can be given, for scarcely any of the writings of earlier geometers have come down to our times. We are mainly dependent on Pappus and Proclus for the scanty notices we have of Euclid's predecessors, and of the problems which engaged their attention; for the solution of problems, and not the discovery of theorems, would seem to have been their principal object. From these authors we learn that the property of the right-angled triangle had been found out, the principles of geometrical analysis laid down, the restriction of constructions in plane geometry to the straight line and the circle agreed upon, the doctrine of proportion, for both commensurables and incommensurables, as well as loci, plane and solid, and some of the properties of the conic sections investigated, the five regular solids (often called the Platonic bodies) and the relation between the volume of a cone or pyramid and that of its circumscribed cylinder or prism discovered. Elementary works had been written, and the famous problem of the duplication of the cube reduced to the determination of two mean proportionals between two given straight lines. Notwithstanding this amount of discovery, and all that it implied, Euclid must have made a great advance beyond his predecessors (we are told that "he arranged the discoveries of Eudoxus, perfected those of Theaetetus, and reduced to invincible demonstration many things that had previously been more loosely proved"), for his _Elements_ supplanted all similar treatises, and, as Apollonius received the title of "the great geometer," so Euclid has come down to later ages as "the elementator."

For the past twenty centuries parts of the _Elements_, notably the first six books, have been used as an introduction to geometry. Though they are now to some extent superseded in most countries, their long retention is a proof that they were, at any rate, not unsuitable for such a purpose. They are, speaking generally, not too difficult for novices in the science; the demonstrations are rigorous, ingenious and often elegant; the mixture of problems and theorems gives perhaps some variety, and makes their study less monotonous; and, if regard be had merely to the metrical properties of space as distinguished from the graphical, hardly any cardinal geometrical truths are omitted. With these excellences are combined a good many defects, some of them inevitable to a system based on a very few axioms and postulates. Thus the arrangement of the propositions seems arbitrary; associated theorems and problems are not grouped together; the classification, in short, is imperfect. Other objections, not to mention minor blemishes, are the prolixity of the style, arising partly from a defective nomenclature, the treatment of parallels depending on an axiom which is not axiomatic, and the sparing use of superposition as a method of proof.

Of the thirty-three ancient books subservient to geometrical analysis, Pappus enumerates first the _Data_ ([Greek: Dedomena]) of Euclid. He says it contained 90 propositions, the scope of which he describes; it now consists of 95. It is not easy to explain this discrepancy, unless we suppose that some of the propositions, as they existed in the time of Pappus, have since been split into two, or that what were once scholia have since been erected into propositions. The object of the _Data_ is to show that when certain things--lines, angles, spaces, ratios, &c.--are given by hypothesis, certain other things are given, that is, are determinable. The book, as we are expressly told, and as we may gather from its contents, was intended for the investigation of problems; and it has been conjectured that Euclid must have extended the method of the _Data_ to the investigation of theorems. What prompts this conjecture is the similarity between the analysis of a theorem and the method, common enough in the _Elements_, of _reductio ad absurdum_--the one setting out from the supposition that the theorem is true, the other from the supposition that it is false, thence in both cases deducing a chain of consequences which ends in a conclusion previously known to be true or false.

The _Introduction to Harmony_ ([Greek: Eisagoge harmonike]), and the _Section of the Scale_ ([Greek: Katatome kanonos]), treat of music. There is good reason for believing that one at any rate, and probably both, of these books are not by Euclid. No mention is made of them by any writer previous to Ptolemy (A.D. 140), or by Ptolemy himself, and in no ancient codex are they ascribed to Euclid.

The _Phaenomena_ ([Greek: Phainomena]) contains an exposition of the appearances produced by the motion attributed to the celestial sphere. Pappus, in the few remarks prefatory to his sixth book, complains of the faults, both of omission and commission, of writers on astronomy, and cites as an example of the former the second theorem of Euclid's _Phaenomena_, whence, and from the interpolation of other proofs, David Gregory infers that this treatise is corrupt.

The _Optics_ and _Catoptrics_ ([Greek: Optika, Katoptrika]) are ascribed to Euclid by Proclus, and by Marinus in his preface to the _Data_, but no mention is made of them by Pappus. This latter circumstance, taken in connexion with the fact that two of the propositions in the sixth book of the _Mathematical Collection_ prove the same things as three in the _Optics_, is one of the reasons given by Gregory for deeming that work spurious. Several other reasons will be found in Gregory's preface to his edition of Euclid's works.

In some editions of Euclid's works there is given a book on the _Divisions of Superficies_, which consists of a few propositions, showing how a straight line may be drawn to divide in a given ratio triangles, quadrilaterals and pentagons. This was supposed by John Dee of London, who transcribed or translated it, and entrusted it for publication to his friend Federico Commandino of Urbino, to be the treatise of Euclid referred to by Proclus as [Greek: to peri diaireseon biblion]. Dee mentions that, in the copy from which he wrote, the book was ascribed to Machomet of Bagdad, and adduces two or three reasons for thinking it to be Euclid's. This opinion, however, he does not seem to have held very strongly, nor does it appear that it was adopted by Commandino. The book does not exist in Greek.

The fragment, in Latin, _De levi et ponderoso_, which is of no value, and was printed at the end of Gregory's edition only in order that nothing might be left out, is mentioned neither by Pappus nor Proclus, and occurs first in Bartholomew Zamberti's edition of 1537. There is no reason for supposing it to be genuine.

The following works attributed to Euclid are not now extant:--

1. Three books on _Porisms_ ([Greek: Peri ton porismaton]) are mentioned both by Pappus and Proclus, and the former gives an abstract of them, with the lemmas assumed. (See PORISM.)

2. Two books are mentioned, named [Greek: Topon pros epiphaneia], which is rendered _Locorum ad superficiem_ by Commandino and subsequent geometers. These books were subservient to the analysis of loci, but the four lemmas which refer to them and which occur at the end of the seventh book of the _Mathematical Collection_, throw very little light on their contents. R. Simson's opinion was that they treated of curves of double curvature, and he intended at one time to write a treatise on the subject. (See Trail's _Life of Dr Simson_).

3. Pappus says that Euclid wrote four books on the _Conic Sections_ ([Greek: biblia tessara Konikon]), which Apollonius amplified, and to which he added four more. It is known that, in the time of Euclid, the parabola was considered as the section of a right-angled cone, the ellipse that of an acute-angled cone, the hyperbola that of an obtuse-angled cone, and that Apollonius was the first who showed that the three sections could be obtained from any cone. There is good ground therefore for supposing that the first four books of Apollonius's _Conics_, which are still extant, resemble Euclid's _Conics_ even less than Euclid's _Elements_ do those of Eudoxus and Theaetetus.

4. A book on _Fallacies_ ([Greek: Peri pseudarion]) is mentioned by Proclus, who says that Euclid wrote it for the purpose of exercising beginners in the detection of errors in reasoning.

This notice of Euclid would be incomplete without some account of the
earliest and the most important editions of his works. Passing over
the commentators of the Alexandrian school, the first European
translator of any part of Euclid is Boetius (500), author of the _De
consolatione philosophiae_. His _Euclidis Megarensis geometriae libri
duo_ contain nearly all the definitions of the first three books of
the _Elements_, the postulates, and most of the axioms. The
enunciations, with diagrams but no proofs, are given of most of the
propositions in the first, second and fourth books, and a few from the
third. Some centuries afterwards, Euclid was translated into Arabic,
but the only printed version in that language is the one made of the
thirteen books of the _Elements_ by Nasir Al-Din Al-Tusi (13th
century), which appeared at Rome in 1594.

The first printed edition of Euclid was a translation of the fifteen
books of the _Elements_ from the Arabic, made, it is supposed, by
Adelard of Bath (12th century), with the comments of Campanus of
Novara. It appeared at Venice in 1482, printed by Erhardus Ratdolt,
and dedicated to the doge Giovanni Mocenigo. This edition represents
Euclid very inadequately; the comments are often foolish, propositions
are sometimes omitted, sometimes joined together, useless cases are
interpolated, and now and then Euclid's order changed.

The first printed translation from the Greek is that of Bartholomew
Zamberti, which appeared at Venice in 1505. Its contents will be seen
from the title: _Euclidis megaresis philosophi platonici
Mathematicaru[z] disciplinaru Janitoris: Habent in hoc volumine
quicuq[z] ad mathematica substantia aspirat: elemetorum libros xiii cu
expositione Theonis insignis mathematici ... Quibus ... adjuncta.
Deputatum scilicet Euclidi volume xiiii cu expositioe Hypsi. Alex.
Itideq[z] Phaeno. Specu. Perspe. cum expositione Theonis ac mirandus
ille liber Datorum cum expostioe Pappi Mechanici una cu Marini
dialectici protheoria. Bar. Zaber. Vene. Interpte._

The first printed Greek text was published at Basel, in 1533, with the
title [Greek: Eukleidou Stoicheion bibl. ie ek ton Theonos synousion].
It was edited by Simon Grynaeus from two MSS. sent to him, the one
from Venice by Lazarus Bayfius, and the other from Paris by John
Ruellius. The four books of Proclus's commentary are given at the end
from an Oxford MS. supplied by John Claymundus.

The English edition, the only one which contains all the extant works
attributed to Euclid, is that of Dr David Gregory, published at Oxford
in 1703, with the title, [Greek: Eukleidou ta sozomena]. _Euclidis
quae supersunt omnia_. The text is that of the Basel edition,
corrected from the MSS. bequeathed by Sir Henry Savile, and from
Savile's annotations on his own copy. The Latin translation, which
accompanies the Greek on the same page, is for the most part that of
Commandino. The French edition has the title, _Les Oeuvres d'Euclide,
traduites en Latin et en Francais, d'apres un manuscrit tres-ancien
qui etait reste inconnu jusqu'a nos jours. Par F. Peyrard, Traducteur
des oeuvres d'Archimede_. It was published at Paris in three volumes,
the first of which appeared in 1814, the second in 1816 and the third
in 1818. It contains the _Elements_ and the _Data_, which are, says
the editor, certainly the only works which remain to us of this
ever-celebrated geometer. The texts of the Basel and Oxford editions
were collated with 23 MSS., one of which belonged to the library of
the Vatican, but had been sent to Paris by the comte de Peluse
(Monge). The Vatican MS. was supposed to date from the 9th century;
and to its readings Peyrard gave the greatest weight. What may be
called the German edition has the title [Greek: Eukleidou Stoicheia].
_Euclidis Elementa ex optimis libris in usum Tironum Graece edita ab
Ernesto Ferdinando August_. It was published at Berlin in two parts,
the first of which appeared in 1826 and the second in 1829. The above
mentioned texts were collated with three other MSS. Modern standard
editions are by Dr Heiberg of Copenhagen, _Euclidis Elementa, edidit
et Latine interpretatus est J.L. Heiberg_. vols. i.-v. (Lipsiae,
1883-1888), and by T.L. Heath, _The Thirteen Books of Euclid's
Elements_, vols. i.-iii. (Cambridge, 1908).

Of translations of the _Elements_ into modern languages the number is
very large. The first English translation, published at London in
1570, has the title, _The Elements of Geometrie of the most auncient
Philosopher Euclide of Megara. Faithfully (now first) translated into
the Englishe toung, by H. Billingsley, Citizen of London. Whereunto
are annexed certaine Scholies, Annotations and Inventions, of the best
Mathematiciens, both of time past and in this our age_. The first
French translation of the whole of the _Elements_ has the title, _Les
Quinze Livres des Elements d'Euclide. Traduicts de Latin en Francois.
Par D. Henrion, Mathematicien_. The first edition of it was published
at Paris in 1615, and a second, corrected and augmented, in 1623.
Pierre Forcadel de Bezies had published at Paris in 1564 a translation
of the first six books of the _Elements_, and in 1565 of the seventh,
eighth and ninth books. An Italian translation, with the title,
_Euclide Megarense acutissimo philosopho solo introduttore delle
Scientie Mathematice. Diligentemente rassettato, et alla integrita
ridotto, per il degno professore di tal Scientie Nicolo Tartalea
Brisciano_, was published at Venice in 1569, and Federico Commandino's
translation appeared at Urbino in 1575; a Spanish version, _Los Seis
Libros primeros de la geometria de Euclides. Traduzidos en legua
Espanola por Rodrigo Camorano, Astrologo y Mathematico_, at Seville in
1576; and a Turkish one, translated from the edition of J. Bonnycastle
by Husain Rifki, at Bulak in 1825. Dr Robert Simson's editions of the
first six and the eleventh and twelfth books of the _Elements_, and of
the _Data_.

AUTHORITIES.--The authors and editions above referred to; Fabricius,
_Bibliotheca Graeca_, vol. iv.; Murhard's _Litteratur der
mathematischen Wissenschaften_; Heilbronner's _Historia matheseos
universae_; De Morgan's article "Eucleides" in Smith's _Dictionary of
Biography and Mythology_; Moritz Cantor's _Geschichte der Mathematik_,
vol. i. (J. S. M.)