came chamber musician to Queen Charlotte, he also won considerable distinction as a composer.
ABEL, HI)?], Niels Henrik (1802'2n). One
of the most brilliant mathematicians of the first
part of the nineteenth century. He was born
at Findö, Norway. After a course of study at
the University of (hristiania. he spent two years
in Paris and Berlin, and in 1S2T was made in-
structor at the university and at the school of
enfrineerinj; in Christiania. lie wa.s the first to
demonstrate with rigor the impossibility of
solving by the elementary processes of algebra
general equations of any degree higher than the
fourth. His chief contributions were made to
the theory of functions, of which he was
one of the founders. An important class of
elliptic functions (see Functions) are known
as Abelian. from their discoverer. There are
also Abelian groups and bodies. The Binomial
Theorem (q.v. ), proved by Newton and Euler,
received at the hands of Alicl a wider generaliza-
tion, including the cases of irrational and im-
aginary exponents. Abel's works, in two volumes, were published by the Norwegian Government (Christiania, first edition, 1839; second edition, 1881).
ABELARD (Engl, ab'f-ljird; Fr. d'bfl'lar'),
Pierre (1079-1142). A scholastic philosopher
and theologian, the boldest thinker of the twelfth
century. His name is commoidy given in the
French form, Abélard or Abailard; in Latin, Abai-
lardus or Bajolardus. But these are epithets of
uncertain meaning, the latter form perhaps from
bajulus, "teacher," the former from abeille, a
bee. He had properly the single name Peter,
Petrus, to which was added de Palais, from the
place of his birth, Le Pallet, or in Latin form
Palatinus, a village eight miles southeast of
Nantes, Brittany, western France. He was born
in 1079. His father was the knight Berengar,
lord of the village; his mother was Lucia, and
they both later on entered monastic orders. An
irrepressible thirst for knowledge and a special
pleasure in scholastic logic moved Abélard to
resign his rights of primogeniture in favor of
his younger brothers. His first teacher was Ros-
cellin, the Nominalist, during the latter's stay
at Vannes. He wandered about in search of
knowledge until he arrived in Paris, where he
became a pupil of William of Champeaux, the
Realist. the head of the cathedral school of Notre
Dame there, but soon incurred the hatred of his
master, whom he puzzled by his wonderful subtle-
ty. He fled to Melun, where he started a school
of his own, and afterward to Corbeil, admired, yet persecuted, wherever he went. He then returned home for the restoration of his health.
With renewed strength, he returned to Paris,
reconciled himself with his opponents, and
molded, by his influence as a lecturer, some of
the most distinguished men of his age, among
whom were the future Pope Celestine II., Peter
Lombard, Berengar, his future apologist, and
Arnold of Brescia.
At this time, however, there also lived in Paris with her uncle, the canon Fulbert, Héloïse, the eighteen-year-old natural daughter of a certain canon John, of Paris, already remarkable for her beauty, talents, and attainments. At Fulbert's invitation Abélard made his home with him and instructed Héloïse. She soon kindled in the breast of Abélard, then thirty-eight years old, a violent and overwhelming passion, which was returned by Héloïse with no less fervor. The lovers were happy together until Abélard's ardent poetical effusions reached the ears of the canon. He sought to separate the lovers; but it was too late. They fled together to Abélard's home, where, in his sister Dionysia's house, Héloïse gave birth to a son, and was privately married to Abélard with the consent of her uncle. Not long after, Héloïse returned to Fulbert's house, and denied the marriage, that her love might be no hindrance to Abélard's advancement in the Church. Enraged at this, and at a second flight which she took with Abélard to the Benedictine nunnery at Argenteuil, where she had been educated, a flight which Fulbert interpreted as showing Abélard's desire to rid himself of his wife. Fulbert, in order to make him canonically incapable of ecclesiastical preferment, caused Abélard to be emasculated. In deep humiliation Abélard entered as a monk the abbey of St. Denis, in Paris, and induced Héloïse to take the veil at Argenteuil.
But the lectures which he began to give soon after exposed him to new persecutions. The synod of Soissons (1121) declared his opinions on the Trinity to be heretical. In punishment he had to throw the offending treatise into the fire, to read publicly the Athanasian Creed, and to endure a brief imprisonment. The charge seems to have been that he declared Cod the Father alone omnipotent. But what cost him more was his declaration that St. Dionysius, the patron saint of France, had been bishop of Corinth, and not of Athens, for this stirred up court opposi- tion. He fled from St. Denis to the monastery of St. Aigulph, near Provins, but was brought back and compelled to retract his opinions concerning St. Dionysius. He was then allowed to go, and went to Nogent-sur-Seine, and there built of reeds and rushes a little chapel to the Trinity, and later, on account of the press of hearers, who planted their huts about him. a structure of wood and stone, which he called the Paraclete, the ruins of which exist to this day. But as everything he did caused adverse criticism, so the name that he gave the building — because it brought into unusual prominence the Holy Spirit — involved him in fresh trouble, and he left the Paraclete and accepted the abbotship of St. Gildas de Rhuys, on the coast of Lower Brit- tany. It was a sore trial for him to contend with the Tinruly monks. Meanwhile, the eon- vent at Argenteuil, where Hfloise was prioress, had been broken up. Ab^'lard transferred H^lolse and her nuns to the Paraclete and made her abbess of the nunnery he established. It was a long distance from St. Cildas. but, as spiritual director, he frequently went thither. Naturally, he fell under suspicion of renewing his intimacy with H^'lolse, and so the lovers finally restricted, themselves to writing. The correspondence has been preserved. On his part it was sternly re- pressive, to the point of coldness; on her part the heart expressed its love, which was an inex- tinguishable passion, both of body and soul, and tyrannical in its demands upon the monk who had ceased to share it.
After ten more years, Abélard, fearing an attack upon his life, left his monks and became a wandering teacher again. Two men, Norbert and the much more famous Bernard of Clairvaux, were always on his track. The Council of Sens, held in 1141, under the influence of Ber-
