The following is based partially on H. A. Wolfson, The Philosophy of the Church Fathers, Volume One: Faith, Trinity, Incarnation (Harvard University Press, 1956), pp. 359-363.
Hippolytus: The Logos comes from the Father as water from a fountain.
Tertullian: The Father is to the Logos as fountain is to river. One substance assumes two forms.
Lactantius: The Father is an overflowing fountain, the Son a stream flowing from it.
Zeno of Verona: Father and Son are two seas filled with the same water which, though two, are yet one.
Vallicella of Arizona: Water occurs in three distinct states, the gaseous, the liquid, and the solid. One and and the same quantity of water can assume any of these three states. Distinctness of states is compatible with oneness of substance.
Of the water analogies, I like the last one best (!) despite its being as worthless as the others. All four involve an equivocation on ‘substance.’ The sense in which water is a substance is not the sense in which God is a substance. Water is a substance in the sense of a stuff; God is a substance in the sense of a hypostasis (that which stands under) or hypokeimenon (that which is placed under), or as I prefer to say, an individual. Note also that a quantity of H2O can be in the three states only successively not simultaneously whereas God is 'simultaneously' the three Persons.
Of course, there are better physical analogies, light for example, and also nonphysical analogies such as the soul (Augustine). Something on this later. My only point is that these water analogies do nothing to render the Trinity doctrine intelligible, hence no one should be convinced by them.
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