[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.