It is a proposition that does not need to be verified, since it is very easily deduced from what has been demonstrated. Almost always, the corollary immediately follows a theorem. An example of a corollary in the field of mathematics can be the following: Taking into account the theorem “In every triangle, the internal angles are equal to 180º”. Corollary A follows; 90º is the sum of its acute angles. Corollary B; In a triangle there can be no more than one right angle and no more than one obtuse angle.

what is corollary

The word refers to an affirmation corresponding to a previously proven fact, that is, it cannot be refuted since it has sufficient evidence to verify it automatically. This happens a lot in the area of ​​mathematics as in the case of a corollary theorem.

Similarly, it can also be applied in the field of logic, such as the case of the corollary of individuality, which expresses the fact that each individual builds their own reality based on lived experiences. From the etymological point of view it comes from the Latin corollarium, its meaning was ambiguous, both to refer to a small crown, and to express the act of giving a tip.

Synonym of corollary

Among the main words that can be used synonymously with the term are consequence, deduction, derivation and inference.

Antonym of corollary

On the other hand, contrary to the words that can be used as synonyms, the antonyms of the term could be the nouns origin and cause.

Corollary in mathematics

In the field of mathematics, it refers to an assertion that expresses what was previously demonstrated by means of a theorem, some examples of mathematical corollaries would be:

  • The corollary of Thales’ theorem: the theorem is basically based on the similarity or similarity between triangles, it establishes that any line that is located parallel to one side of a triangle forms with its other extensions another triangle similar to the original. Also known as corollaries of triangles.
  • Corollary of the Pythagorean theorem: this theorem states that “In a right triangle the square of the hypotenuse is equal to the sum of the squares of the legs”.

Among its main characteristics is the fact that they must be based on theories previously demonstrated with scientific evidence and also that they do not require tests or new evidence, since they are well founded on the basis of previous demonstrations.

Corollary in law

In the case of law, it is given a more logical perspective, it refers to establishing a fact or action carried out based on irrefutable antecedents, in this way by means of evidence it can be demonstrated, for example, the presence of a person in a particular place. and at an exact moment.

A more accurate example would be concluding a defendant’s presence at a robbery, having previously recorded video evidence of the person in the act.

Examples of corollaries

Corollary - Corollary Discharge

They are not only applied in mathematics and law, from a more logical point of view this can be applied even to society and to the field of psychology.

An example is the Kelly corollaries, which establishes 11 deductions related to the differences between the psychological processes of people in relation to their ability and way of anticipating possible events, they are the following:

  • Building
  • Individuality
  • Organization
  • Dichotomy
  • Choice
  • Ambit
  • Experience
  • Modulation
  • Fragmentation
  • communality
  • Sociability

Another example would be the theory of corollary discharge, this also has a focus on perception at the psychological level, it establishes that the perception of movements by people is governed by three fundamental factors and that they act synergistically at the moment of perception:

  1. The motor signal.
  2. The corollary discharge signal.
  3. The signal of the movement of the image.

Frequently Asked Questions about Corollary

What are corollaries?

They are statements or propositions based on theorems or previously demonstrated facts, they can be applied in areas such as mathematics, logic, psychology, among others.

What is a corollary in geometry?

It refers to statements related to statements already established about theorems, such as Pythagoras’s and Thale’s.

What is a mathematical corollary?

Proposition used to respond directly to some previously proven theorem, mainly used in the field of geometry.

What is the Roosevelt Corollary?

Adjustment applied to the well-known Monroe Doctrine by the President of the United States Theodore Roosevelt in the year 1904. Mainly related to avoiding the intervention of Europe in the countries of America, after the naval blockade of Venezuela, affirming that any action of this type would cause the reaction of the United States.

What is the corollary in law?

It refers to the fact of establishing an action carried out by a person at a certain time and place, previously having irrefutable evidence that places the accused at the scene.