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Corollary Meaning: Definition, Examples, and Translations

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corollary

[kəˈrɒl.ə.ri ]

Definition

Context #1 | Noun

mathematics, logic

A corollary is a statement that follows readily from a previous statement or proposition that has been proven. It is often considered an easy or obvious consequence that requires little additional proof because it is logically derived from established results. Corollaries provide insight and additional information about the original statement, and they are frequently used in mathematical and logical contexts. For example, if a theorem is proved, a corollary can be easily inferred from that theorem without extensive additional research.

Synonyms

consequence, implication, outcome, result.

Examples of usage

  • The triangle inequality is a corollary of the properties of absolute values.
  • From the theorem, we can derive a corollary that simplifies our calculations.
  • The corollary states that with the assumptions made, the following must also be true.

Translations

To see the translation, please select a language from the options available.

Interesting Facts

Mathematics

  • In mathematics, a corollary is a theorem that follows easily from a previous theorem, serving as a way to build on existing knowledge.
  • Famous corollaries often simplify complex ideas, making them easier to understand and apply.
  • An example includes the corollary that states if a triangle is right-angled, then the Pythagorean theorem applies.

Philosophy

  • In philosophical discussions, a corollary can be used to derive further implications or consequences from a primary argument.
  • This helps in constructing logical frameworks where one assertion leads to another, enriching the debate.
  • Philosophers like Aristotle often employed corollaries in their argumentation to illustrate points clearly and logically.

Psychology

  • In psychology, a corollary can be understood as the mental processes and subsequent behavior that result from a given thought or belief.
  • George Kelly's personal construct theory discusses corollaries as ways that individuals interpret experiences based on previous outcomes.
  • Corollary thinking emphasizes the connection between experiences and how they can lead to similar future reactions.

Legal Context

  • In law, a corollary may refer to principles that follow from established legal precedents to provide clarity in cases.
  • Lawyers often cite corollaries in reasoning to support their arguments, basing conclusions on what has been previously agreed upon.
  • Understanding legal corollaries helps in predicting outcomes in court based on past rulings.

Origin of 'corollary'

Main points about word origin

  • The word comes from the Latin 'corollarium', meaning 'a small crown', which suggests something that follows from or is added to what is already there.
  • First recorded use in English was in the 14th century, indicating a long history of the term in academic language.
  • Corollary originally referred to something that was 'added on', just like a decorative piece added to a crown.

The word 'corollary' originates from the Latin term 'corollarium', which means 'a garland' or 'a crown', derived from 'corolla', meaning 'little crown'. The etymology reflects the idea that a corollary is an addition to something already established, much like a garland that adorns a statue or a king's crown that signifies power. The term was adopted into English in the early 17th century, entering the vocabulary of mathematics and logic as a technical term for an inference drawn from an already proven theorem. Over time, it has retained its academic roots while also being used in broader contexts to refer to any result or consequence that follows logically from a preceding statement or event.

Word Frequency Rank

At position #12,991, this word is part of sophisticated English vocabulary. It's useful for academic or professional contexts where precise language is needed.