The Catholic Encyclopedia
(From the Latin tertiarius, the relative adjective of tertius, third).
Tertiaries, or what is known as "Third Orders", are those persons who live according to the Third Rule of religious orders, either outside of a monastery in the world, or in a religious community. The idea which forms the basis of this institute is in general this, that persons who on account of certain circumstances cannot enter a religious order, strictly so-called, may, nevertheless, as far as possible enjoy the advantages and privileges of religious orders. This is most clearly expressed in the Rule of the Third Order of St. Francis which, although not the oldest, has, nevertheless, become the model for the rule of almost all other Third Orders. Tertiaries are divided into Regular and Secular (see THIRD ORDERS).
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Obstat, Nihil. Lafort, Remy, Censor. Entry for 'Tertiaries'. The Catholic Encyclopedia. https://www.studylight.org/encyclopedias/eng/tce/t/tertiaries.html. Robert Appleton Company. New York. 1914.