[f. TRI- + -arch in tetrarch: cf. Gr. τρίαρχος chief ruler, and next.]

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  1.  The ruler of one of three divisions of a country or territory.

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1886.  J. Bury, in Jrnl. Hellenic Stud., VII. 314. These three lords were called the terzieri (tierciers) of Negroponte. Hopf calls them Dreiherrn, and we may call them triarchs. Ibid., 321. William laid claim … to the north of Euboia, calling himself a triarch.

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  2.  In Fourier’s social organization: A ruler of the third (ascending) rank.

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1848.  Tait’s Mag., XV. 706. There will be duarchs for four phalanx, triarchs for 12, tetrarchs for 48, and so on until the douzarch reigns over a million.

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  Hence Triarchate, rare1. [cf. patriarchate], an association of three rulers.

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1881.  H. Hartshorne, 1931: A Glance at the 20th C., 15. Then, the triarchate; is it not surprising? Pope, Patriarch, and Primate of Canterbury! Roman, Greek, and Anglican, united at last! A dread of the last century ecclesiastics is fulfilled,—alas, too late; for the glory has departed from the tiara, the crozier, and the mitre altogether.

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