Tertium comparationis 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 do not necessarily have to 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 metaphor

Metaphor

A metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...

s and simile

Simile

A simile is a figure of speech that directly compares two different things, usually by employing the words "like", "as". Even though both similes and metaphors are forms of comparison, similes indirectly compare the two ideas and allow them to remain distinct in spite of their similarities, whereas...

s, especially, but by no means exclusively, in poetic language

Poetry

Poetry is a form of literary art in which language is used for its aesthetic and evocative qualities in addition to, or in lieu of, its apparent meaning...

. In many cases one aspect of the comparison is implied rather than made explicit.

Examples

• Necessity is the mother of invention. (English proverb
  Proverb
  A proverb is a simple and concrete saying popularly known and repeated, which expresses a truth, based on common sense or the practical experience of humanity. They are often metaphorical. A proverb that describes a basic rule of conduct may also be known as a maxim...
  
  )

Objects of comparison: relationship between mother and child, relationship between necessity and invention

Tertium comparationis: source, where something derives from

• Woman is the nigger of the world. (John Lennon
  John Lennon
  John Winston Lennon, MBE was an English musician and singer-songwriter who rose to worldwide fame as one of the founding members of The Beatles, one of the most commercially successful and critically acclaimed acts in the history of popular music...
  
  )

Objects of comparison: treatment of blacks by US culture, treatment of women by global culture

Tertium comparationis: inhumane treatment, subjugation, discrimination

Discrimination

Discrimination is the prejudicial treatment of an individual based on their membership in a certain group or category. It involves the actual behaviors towards groups such as excluding or restricting members of one group from opportunities that are available to another group. The term began to be...

• Goodbye, England's rose. (Elton John
  Elton John
  Sir Elton Hercules John, CBE, Hon DMus is an English rock singer-songwriter, composer, pianist and occasional actor...
  
   on the death of Diana, Princess of Wales
  Diana, Princess of Wales
  Diana, Princess of Wales was the first wife of Charles, Prince of Wales, whom she married on 29 July 1981, and an international charity and fundraising figure, as well as a preeminent celebrity of the late 20th century...
  
  )

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

John Donne

John Donne 31 March 1631), English poet, satirist, lawyer, and priest, is now considered the preeminent representative of the metaphysical poets. His works are notable for their strong and sensual style and include sonnets, love poetry, religious poems, Latin translations, epigrams, elegies, songs,...

: "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.