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 limits of the angle and perpendicular to each other. These rays are therefore harmonic with regard to the limits of the given angle and with regard to the rays through the circular points. Thus perpendicularity and bisection of an angle have been stated in a projective form.

It must not be forgotten that the circular points do not exist at all; but to introduce them gives us a short way of making a statement which would Otherwise be long and cumbrous.

We can now generalize any theorem relating to metrical properties. For instance, the simple fact that the chord of a circle is touched by a concentric circle at its mid point proves the theorem:— If two conics have double contact, then the points where any tangent to one of them cuts the other are harmonic with regard to the point of contact and the point where the tangent cuts the chord of contact.

PROKOP, the name of two of the most prominent Hussite generals

1., surnamed “ Veliky ” (the great) or “ Holy ” (the bald), was a married utraquist priest who belonged to an eminent family of citizens of Prague. Though a priest and continuing to officiate as such, he became the most prominent leader of the advanced Hussite or Taborite forces during the latter part of the Hussite wars. He was not indeed the immediate successor of Ziéka as leader of the Taborites, as has been frequently stated, but he commanded the forces of Tabor when they obtained their great victories over the Germans and Romanists at Usti nad Labam (Aussig) in 1426 and Domailice (Tauss) in 1431. He also acted as leader of the Taborites during their frequent incursions into Hungary and Germany, particularly when in 1429 a vast Bohemian army invaded Saxony and the territory of Nuremberg. The Hussites, however, made no attempt permanently to conquer German territory, and on the 6th of February 1430 Prokop concluded at Kulmbach a treaty with Frederick of Brandenburg, burgrave of Nuremberg, by which the Hussites engaged themselves to leave Germany. When the Bohemians entered into negotiations with Sigismund and the Council of Basel and, after prolonged discussions, resolved to send an embassy to the council, Prokop the Great was the most prominent member of this embassy, which reached Basel on the 4th of January 1433. When the negotiations there for a time proved result less Prokop with the other envoys returned to Bohemia, where new internal troubles broke out. A Taborite army led by Prokop the Great besieged Plzen, which was then in the hands of the Romanists. The discipline in the Hussite camp had, however, slackened in the course of prolonged warfare, and the Taborites encamped before Plzeh revolted against Prokop, who therefore returned to Prague. Probably encouraged by these dissensions among the men of Tabor, the Bohemian nobility, both Romanist and utraquist, formed a league for the purpose of opposing democracy, which through the victories of Tabor had acquired great strength in the Bohemian towns. The struggle began at Prague. Aided by the nobles, the citizens of the old town took possession of the more democratic new town, which Prokop unsuccessfully attempted to defend. Prokop now called to his aid Prokop “ the Lesser, ” who had succeeded him in the command of the Taborite army before Plzefi. They jointly retreated eastward from Prague, and their forces, known as the army of the towns, met at Lipan, between Kourim and Kolin, the army of the nobles (May 30, 1434). The Taborites were decisively defeated, and Prokop the Great perished in this battle.

2. PROKOP “ the Lesser, ” or PROKUPEK (the Bohemian diminutive of the word Prokop), was one of the greatest Hussite generals. Little is known of his early life. He took part in all the later campaigns of Prokop the Great in Germany, and succeeded him as commander of the Taborite army that besieged Plzen. After the formation of the confederacy of the nobles he was recalled by Prokop the Great, with whom he shared the command of the army of the towns at the fateful battle of Lipan, in which he also perished.

See Count Lutzow, Bohemia: A Historical Sketch; Palacky, History of Bohemia; Toman, Husitske Valečnictvi (Hussite Warfare).

PROKOPOVICH, THEOFAN (1681–1736), Russian archbishop and statesman, one of the ablest coadjutors of Peter the Great, was sprung from a merchant family. He brilliantly distinguished himself at the Orthodox academy of Kiev, subsequently completing his education in Poland (for which purpose he turned Uniate), and at Rome in the College of the Propaganda. Primed with all the knowledge of the West, he returned home to seek his fortune, and, as the Orthodox monk, became one of the professors at, and subsequently rector of, the academy of Kiev. He entirely reformed the teaching of theology there, substituting the historical method of the German theologians for the antiquated Orthodox scholastic system. In 1709 Peter the Great, while passing through Kiev, was struck by the eloquence of Prokopovich in a sermon on “ the most glorious victory,” i.e. Poltava, and in 1716 summoned him to Petersburg. From henceforth it was Theofan's duty and pleasure to explain the new ideas and justify the most alarming innovations from the pulpit. So invaluable, indeed, did he become to the civil power, that, despite the determined opposition of the Russian clergy, who regarded “ the Light of Kiev ” as an interloper and semi-heretic, he was rapidly promoted, becoming, in 1718, bishop of Pskov, and finally, in 1724, archbishop of Novgorod. As the author of “ the spiritual regulation ” for the reform of the Russian Church, Theofan must, indeed, be regarded as the creator of “ the spiritual department ” superseding the patriarchate, and better known by its later name of “ the holy synod,” of which he was made the vice-president. Penetrated by the conviction that ignorance was the worst of the inveterate evils of old Russia, a pitiless enemy of superstition of every sort, a reformer by nature, overflowing with energy and resource, and with a singularly lucid mind armed at all points by a far reaching erudition, Prokopovich was the soul of the reforming party after the death of Peter the Great. To him also belongs the great merit of liberating Russian preaching from the fetters of Polish turgidity and affectation by introducing popular themes and a simple style into Orthodox pulpit eloquence.

See I. Chistovitch, Theofan Prokopooieh and his Times (Rus.; Petersburg, 1868); P. Morozov, Theophan Prokopooieh as a Writer (Rus.; Petersburg, 1880).

PROLEGOMENON (Gr. for “ that which is said beforehand,” προλέγειν, to speak, say before), a preface or introduction to a book, especially a preliminary introductory essay to a learned work, or a treatise which serves as a general survey or introduction to the study of some subject or as a special survey of the subject. The word is more often used in the plural.

 PROLETARIAT, or, a term borrowed from the French and used collectively of those classes of a political community who depend for their livelihood on their daily labour, the wage-earning, operative class as opposed to the capital owning class. It is of frequent use by those social reformers who base their theories on the supposed antagonism of capital and labour. The Latin proletarius, from which the word was formed, was the name given to the body of citizens possessed of no property and who therefore served the state with their children (proles, offspring). This division of the members of the state was traditionally ascribed to Servius Tullius.

 PROLOCUTOR, one who speaks for others (Lat. pro, for, and loqui, to speak); specifically the chairman of the lower house of convocation in the two provinces of the Church of England, who presides in that house and acts as representative and spokesman in the upper house. He is elected by the lower house, subject to the approval of the metropolitan. (See .)

PROLOGUE (from Gr. πρό, before, and λόγος, a word), a prefatory piece of writing, usually composed to introduce a drama. The Greeks use a word πρόλογος, which included the modern meaning of the prologue, but was of wider significance, embracing any kind of preface, like the Latin praefatio. In Attic Greek drama, a character in the play, very often a deity, stood forward or appeared from a machine before the action of the play began, and made from the empty stage such statements as it was necessary that the audience should hear, in order that they might appreciate the ensuing drama. It was the early Greek custom to dilate in great detail on everything that had led up to the play, the latter being itself, as a rule,