What does cathetus mean?
A cathetus is one of the two sides of a right-angled triangle that meet at the right angle — in other words, either leg of the triangle as opposed to the hypotenuse, which lies opposite it. The term is common in European mathematical writing, where classical statements of the Pythagorean theorem speak of the square on the hypotenuse equalling the sum of the squares on the catheti, though many English-language texts simply say 'legs'. The word also has an older, historical sense in optics, denoting a perpendicular line dropped from an object to a refracting surface when tracing how images form. Derived ultimately from the Greek word for something 'set down' or perpendicular, it entered English through Latin in scholarly usage. Today it survives mainly in formal, technical, and educational contexts rather than everyday speech.
nounA straight line forming one of the two sides of a right-angled triangle that meet at the right angle; in other words, either of the legs of a right triangle, as distinct from the hypotenuse.
- Either of the two sides of a right-angled triangle that meet at the right angle (as opposed to the hypotenuse).
- (Historical, in optics) A perpendicular line dropped from an object point onto a refracting surface, used in constructing images formed by refraction.
"The area of a right triangle equals half the product of its two catheti."
"In the theorem, the square on the hypotenuse equals the sum of the squares on the two catheti."
"The student labelled each cathetus carefully before applying the tangent ratio."
The plural follows the Latin second-declension pattern; 'cathetuses' is nonstandard.
"Both catheti of the triangle were measured before computing its area."
Every right triangle you've ever drawn has two catheti — most people just call them 'legs' and never learn their proper name.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of cathetus
The word derives from the Greek 'kathetos' (κάθετος), meaning 'perpendicular' or 'let down, set down', from the verb 'kathienai' ('to let down'), built on the same Indo-European verbal root *dhē- that gives English 'thesis', 'theme', and 'hypothesis'. It passed into Latin as 'cathetus' and was adopted into English in scholarly and mathematical writing, with early attestations around the seventeenth century. Its plural, 'catheti', follows the Latin declension, reflecting the word's learned transmission through classical scholarship.
Related word forms
How cathetus is actually used
A formal, technical term used chiefly in geometry and mathematics education. In everyday English and even much modern mathematical writing, 'leg' is more common; 'cathetus' persists especially in continental European textbooks and in translations from Latin and Greek mathematical tradition. The plural is 'catheti', following its Latin form.
Easily confused with cathetus
A cathetus is a side of a right-angled triangle in geometry, while a catheter is a thin tube inserted into the body for medical purposes.