The doctrine of the Trinity holds that God is trinue, existing as three independent 'Persons," Father, Son, and the Holy Spirit. Between them there is unity of divine essence, will, and purpose; the three Persons, however, are not to be commingled with one another as if there is no essential difference between them, or that they are thought of as merely different modes of existence (such as water exists in three states, solid, liquid, and gas). To make make discussion about this relationship of the Persons in the Trinity easier, theologians give this "necessary being-in-one-another" the term perichoresis, or in Latin equivalent, circumicession.
The term was popularized in the eighth century by John of Damascus who, in his De fide orthodoxa, said the three Persons of the Trinity 'are made one not so as to commingle, but so as to cleave to each other, and they have their being in each other [kai ten en allelais perichoresin] without any coalescence or commingling.'
Further Reading & Resources:
Myk Habets, "A Little Trinitarian Reflection," Evangel (2001): 80-82.
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Donald Macleod, "Doctrine of the Trinity," Scottish Bulletin of Evangelical Theology 3.1 (1985):11-21.
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