the.com/corollary
the truth that strolls in for free once the real proof does the work.
means A statement that follows naturally and easily from a proposition already proven, requiring little or no further argument.
from From Latin 'corollarium,' which first meant a little garland or a tip — a small wreath given as a gift or bonus. It comes from 'corolla,' a diminutive of 'corona,' meaning crown or garland. So a corollary was literally a small extra reward thrown in beyond what was owed — and that sense of 'something you get for free, on top' carried into logic and mathematics, where a corollary arrives as a bonus truth, paid for by the main proof.
- latin root
- corollarium meant a tip or garland given as bonus
- free gift
- named for the little wreath thrown in with payment
- euclid loved them
- Greek geometers tacked them onto big theorems
- no extra proof
- follows so obviously it needs almost none
- everyday use
- now means any natural consequence of something else
pythagorean theorem corollary — states that in a right triangle, if a² + b² = c², then the hypotenuse is the longest side