The baud is then played as at whist, four cards constituting a trick. The eldest hand has the next deal. If a player has a very strong hand he may play alone single-handed against the two adversaries. His partner cannot object. A player can declare to play alone when he or his partner orders up, or when his partner assists, or when he makes the trump, or (if dealer) when he takes up the trump, but not when the adversary orders up, assists, or makes the trump. If the lone player wins a march he scores four, if he wins three or four tricks he scores one; if he fails to win three tricks the opponents score two.
Hints. 1. The chances are that the dealer has one trump in hand; if you order up, you must expect to meet two trumps. Therefore, you should not order up unless your hand gives you a two to one chance of winning three tricks against two trumps, and your cards are such that you would have a worse chance if you made the trump. If strong in trumps and equally strong in another suit, it is always right to pass. Also, if you have the point certain, whether you make the trump or not, you should pass, in hopes the dealer may take up the trump.
2. If you pass and the dealer turns it down, you should not make the trump unless you have a two to one chance of winning three tricks against one trump.
3. I f you hold good cards in two suits of different colours, and you make the trump, you should make it next. For, the dealer having turned it down in one colour, is less likely to hold a bower of that colour than of the other. At the four-handed game the non dealer and his partner should also avoid crossing the suit. But if the dealer's partner makes the trump, he should not hesitate to cross the suit, as the dealer, having turned it down, has probably no bower in that suit.
4. At four-handed euchre, the eldest hand should be very strong to order it up; but the second player should assist if he has some thing more than one trick, e.g., an ace and a trump, or two aces. If, however, he is strong in the non-trump suits, he should not assist unless he can be pretty sure of making two tricks. The third hand should be cautious of ordering up, as his partner, having passed, must be weak. This applies with still more force to taking up by the dealer, as his partner, not having assisted, must be very weak. To take up the dealer should be pretty sure of two tricks, and have a chance of a third.
5. If the dealer takes up the trump he should keep two. cards of a suit, unless his single card is an ace. Thus, with queen, seven of one suit and king single of another, the king should be discarded.
6. Lead from a guarded suit unless in fear of losing a march, when lead your highest single card. Lead from a sequence of three trumps. At four-handed euchre always lead a trump with three. Also lead a trump if you have made it next; if your left hand adversary has assisted (unless a bower is turned up); and if your partner orders up, assists, takes up, or makes the trump. Further, lead a trump if you have lost two tricks and won the third, unless your partner has dealt and still has the turn up in hand.
7. As a rule make tricks when able. Passing or finessing is seldom good play.
8. If your partner orders up, assists, takes up, or makes the trump, trump the trick whenever you can.
9. In discarding during the play, as a rule, keep a guarded card in preference to a single one, except a single ace.
10. If the adversary is at three do not order up unless you have very good cards. If the adversary is at four take up the trump on a light hand.
11. At four-handed euchre, if the dealer is one or two, and the eldest hand four, he should order up, unless he has one certain trick, in order to prevent the opponent from playing alone. This position is called the bridge.
12. At four-all, if the eldest hand or third hand has a trick and the chance of a second, and such cards that he would be no better off if he made the trump, he should order it up.
13. The eldest hand, and next to him the dealer, may play alone on weaker hands than the other players. The leader, with a lone hand, should lead his winning trumps; if two tricks are thus made, and the leader has a losing trump, he should then lead his best card out of trumps. When playing against a lone hand, lead an ace. If you have not one, lead your highest card out of trumps, except with a guarded king and another suit, when lead the latter. Also, keep cards of the suits your partner discards, but do not throw an ace, even if your partner keeps your ace suit.
Laws of Euchre. Dealing.- 1. If the dealer gives too many or too few cards to any player, or if he turns up two cards, it is a misdeal, and the next player deals. 2. If the dealer exposes a card, or if there is a faced card in the pack, there must be a fresh deal. Playing. 3. .Any one playing with the wrong number of cards can score nothing that hand. The same if, when the trump is ordered up, the dealer omits to discard before he or his partner plays. 4. When more than two play, exposed cards can be called. Also a card led out of turn may be called, or a suit from the side offending at their next lead. 5. A player not following suit when able may correct his mistake before the trick is turned and quitted or he or his partner plays to the next trick, the card played in error being an exposed card. If the error is not corrected a revoke is established. A player revoking is euchred, and cannot score anything that hand. 6. A player making the trump must abide by the suit first named. 7. If, after the trump is turned, a player reminds his partner that they are at the point of the bridge, the latter loses the right to order up. 8. Each player has a right to see the last trick. (h. j.)
EUCLID. Of the lives of the Greek mathematicians generally very little is known, and among the number Euclid is no exception; we are ignorant not only of the dates of his birth and death, but also of his parentage, Lis teachers, and the residence of his early years. In some of the editions of his works, as will be seen, 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, the Neo-platonist (412-485 A.D.), is the authority for most of our information regarding Euclid, which is contained in his commentary on the first book of the Elements. He there states 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, whose date is rather uncertain, but is probably a century earlier than that of Proclus, 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 (Sroi^eta). 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. At the outset of the first book occur the definitions or explanations of the meanings of the terms employed; the postulates, which limit the instruments to be used in the constructions to the ruler and the compasses; and the axioms or common notions, the fundamental principles from which mathematical truths are deduced. The propositions, which consist of both theorems and problems, deal with rectilineal figures, principally the triangle and the parallelogram, and the book concludes with the celebrated Pythagorean theorem and its converse. The second book is occupied with the consideration of the rectangular parallelograms contained by the segments of straight lines, and their relation to certain squares. It contains only two problems, the one to divide a straight line in medial section ("the divine section," as it was afterwards called), and the other which shows how to effect the quadrature of any rectilineal area. The third book, prefaced with a few definitions, discusses the properties of circles. The fourth book contains no theorems. The problems are on the inscription in, and circumscription about, circles of triangles, squares, and certain regular polygons, and on the inscription of circles in, and the circumscription of circles about, some of these figures. Though, in the definitions preliminary to this book, Euclid explains when a rectilineal figure is in-
