in Logic. The extremes, or extreme terms of a syllogism, are the predicate and subject. They are called extremes from their relation to another term, which is a medium or mean between them. Thus, in the syllogism, "Man is an animal; Peter is a man; therefore Peter is an animal; the word animal is the greater extreme, Peter the less extreme, and man the medium.

EXTREME AND MEAN PROPORTION; in Geometry, is when a line is so divided, that the whole line is to the greater segment as that segment is to the other; or, as it is expressed by Euclid, when the line is so divided that the rectangle under the whole line and the lesser segment, is equal to the square of the greater segment.

EXTREME UNCTION has been since the twelfth century one of the seven sacraments of the Roman Catholic Church. The ceremony is performed as follows:—When a person is supposed to be at the point of death, his eyes, ears, nostrils, mouth, and hands are successively anointed with the sacred oil by the priest. At each anointing the priest says: "By this holy unction, and through His great mercy, Almighty God forgive thee whatever sins thou hast committed by sight, smell, hearing, touch," &c. At the same time the priest has the power of absolving the dying person from all sins, even from those which in the seventh chapter of the decree on penance are reserved to the decision of the Supreme Pontiff. The oil used in extreme unction is supposed to represent the grace of God poured down into the soul, and the prayer offered up at the time of anointing to express the remission of sins thereby granted to the sick person. The Council of Trent has decreed extreme unction to be a sacrament, and declares that, "Whoever shall affirm that extreme unction is not truly and properly a sacrament, instituted by Christ our Lord, and published by the blessed apostle James, but only a ceremony received from the fathers, or a human invention, let him be accursed." And it denounces a similar anathema against all who "shall affirm that the sacred unction of the sick does not confer grace, nor forgive sin, nor relieve the sick, but that its power has ceased, as if the gift of healing existed only in past ages" (Sess. xiv. Can. I. et seq.). As this unction has, according to the tenets of the Romish Church, sacramental efficacy, purifying the dying person from his sins, and communicating to him divine forgiveness, it can only be administered by a bishop or priest, and is not to be given to infants or to excommunicated persons, or to those who die impenitent, or in the actual commission of mortal sin. Roman Catholics found their opinion of the efficacy of extreme unction on the custom of the apostles, who "anointed with oil many that were sick, and healed them," and on the exhortation of the apostle James (v. 14): "Is any sick among you? let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord." On the other hand, Protestants deny the sacramental significance and efficacy of this ceremony, because nothing is known of a formal establishment of it by Christ himself. They allege that "extreme unction," from its very nature, is to be administered only in the immediate prospect of death, and when the patient is past all hope of recovery; whereas the anointing practised by the apostles and other early ministers of religion was with a view not to the death but the recovery of the sick person—not that he might be prepared to die, but that he might be restored to health: "and the prayer of faith shall save the sick, and the Lord shall raise him up" (Jas. v. 15). The Orientals are strongly persuaded of the sanative properties of oil; and it was under this impression that the Jews anointed the sick and applied oil to wounds (Isa. i. 6, Mark vi. 13; Luke x. 34). Anointing was therefore employed as a cure for various disorders, as well as for the purpose of promoting the general health of the body. This custom still prevails in the East. The Jews in Mocha assured Mr Forskal that the Mohammedans as well as the Jews in Sana, when they were sick, were accustomed to anoint the body with oil; and Niebuhr states that, "in Yemen the anointing of the body is believed to strengthen and protect it from the heat of the sun, by which the inhabitants of this province, as they wear but little clothing, are very liable to suffer. Oil, by closing up the pores of the skin, is supposed to prevent that too copious transpiration which enfeebles the frame; when therefore the intense heat comes on, the Arabs always anoint their bodies with oil." In the Greek Church unction is administered not only to dying persons, but generally in diseases of all kinds, as tending to promote the restoration of health, as well as the forgiveness of sins.