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Tertium comparationis
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Tertium comparationis

Tertium comparationis (Latin = the third [part] of the comparison) is the quality that two things which are being compared have in common. It is the point of comparison which prompted the author of the comparison in question to liken someone or something to someone or something else in the first place.

If a comparison visualizes an action, state, quality, object, or a person by means of a parallel which is drawn to a different entity, the two things which are being compared must necessarily not be identical. However, they must possess at least one quality in common. This common quality has traditionally been referred to as tertium comparationis.

The most common devices used to achieve this are metaphors and similes, especially, but by no means exclusively, in poetic language. In many cases one aspect of the comparison is implied rather than made explicit.

Examples

Objects of comparison: relationship between mother and child, relationship between necessity and invention
Tertium comparationis: source, where something derives from
Objects of comparison: treatment of blacks by US culture, treatment of women by the world culture
Tertium comparationis: inhumane treatment, subjugation, discrimination
Objects of comparison: rose; Diana, Princess of Wales
Tertium comparationis: beauty

If they [our two souls] be two, they are two so
As stiff twin compasses are two;
Thy soul, the fixed foot, makes no show
To move, but doth, if th'other do.
(John Donne: "A Valediction: Forbidding Mourning") (Read the whole poem.)

Objects of comparison: two souls; twin compasses
Tertium comparationis: a non-physical link between separate objects that causes action in one to result in action to the other.