Theorema Pythagorae

Commotus geometricus approbatio theoremae Pythagorae

In Geometria Euclideana, theorema Pythagorae vel sententia Pythagorae dicit trianguli recti hypothenusam quadratam aequalem esse summae aliorum laterum quadratorum.

Enuntiatum theoremae est: in triangulum ABC rectum in B quod hypothenusa est AC, habemus AB² + BC² = AC².

Generaliter, si u et v duo orthogoni vectores in spatio hilbertiano sunt, tunc $\left\Vert u\right\Vert ^{2}+\left\Vert v\right\Vert ^{2}=\left\Vert u+v\right\Vert ^{2}$.