Euclides

https://farside.ph.utexas.edu/books/Euclid/Elements.pdf

The Geometry of Euclidean Space

Vectors in n-space

Cauchy–Bunyakovskii–Schwarz Inequality

Let $x,y$ be vectors in $R^n$. Then

$|x<y| \leq ||x||||y||$

Triangle Inequality

Let $x,y$ be vectors in $R^n$. Then

$||x+y|| \leq ||x||+||y||$

Next steps

Linear Algebra

Vector Calculus