PYTHAGOREANS, the school of philosophy founded by Pythagoras, “the fundamental thought of which,” according to SCHWEGLER, “was that of proportion and harmony, and this idea is to them as well the principle of practical life, as the supreme law of the universe.”  It was a kind of “arithmetical mysticism, and the leading thought was that law, order, and agreement obtain in the affairs of Nature, and that these relations are capable of being expressed in number and in measure.”  The whole tendency of the Pythagoreans, in a practical aspect, was ascetic, and aimed only at a rigid castigation of the moral principle in order thereby to ensure the emancipation of the soul from its mortal prison-house and its transmigration into a nobler form.  It is with the doctrine of the transmigration of souls that the Pythagorean philosophy is specially associated.

PYTHEAS, a celebrated Greek navigator of Massilia, in Gaul, probably lived in the time of Alexander the Great; in his first voyage visited Britain and Thule, and in his second coasted along the western shore of Europe from Cadiz to the Elbe.

PYTHIAN GAMES, celebrated from very early times till the 4th century A.D. every four years, near Delphi, in honour of Apollo, who was said to have instituted them to commemorate his victory over the Python; originally were contests in singing only, but after the middle of the 6th century B.C. they included instrumental music, contests in poetry and art, athletic exercises, and horse-racing.

PYTHON, in the Greek mythology a serpent or dragon produced from the mud left on the earth after the deluge of Deucalion, a brood of sheer chaos and the dark, who lived in a cave of Parnassus, and was slain by Apollo, who founded the Pythian Games in commemoration of his victory, and was in consequence called Pythius.

PYTHONESS, the priestess of APOLLO AT DELPHI (q. v.), so called from the PYTHON (q. v.), the dragon slain by the god.

PYX, the name of a cup-shaped, gold-lined vessel, with lid, used in the Roman Catholic churches for containing the eucharistic elements after their consecration either for adoration in the churches or for conveying to sick-rooms.  Pyx means “box.”  Hence TRIAL OF THE PYX is the annual test of the British coinage, for which purpose one coin in every 15 lbs. of gold and one in every 60 lbs. of silver coined is set aside in a pyx or box.

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QUADRAGESIMA (i. e. fortieth), a name given to Lent because it lasts forty days, and assigned also to the first Sunday in Lent, the three Sundays which precede it being called respectively Septuagesima, Sexagesima, and Quinquagesima.

QUADRANT, an instrument for taking altitudes, consisting of the graduated arc of a circle of ninety degrees.

QUADRATIC EQUATION, an equation involving the square of the unknown quantity.

QUADRIGA, a two-wheeled chariot drawn by four horses abreast, used in the ancient chariot races.