Do any books or articles develop basic Euclidean geometry from the perspective of "inner product affine spaces"?

Question

Definitions.

• By a vector space, I simply mean an $\mathbb{R}$-module.

• By an affine space, I mean a vector space $X$ (the "translation space") together with a set $P$ (of "points"), together with an additively-denoted monoid action of $X$ on $P,$ such that for all points $p,q \in P$, there exists a unique vector $x \in X$ such that $q = x+p$.

• By an inner-product affine space, I mean an affine space $(X,P)$ together with an inner product structure on $X$.

• By the vectorial dimension of an affine space $(X,P),$ I mean the dimension of $X$.

• By a finite-dimensional affine space, I mean an affine space whose vectorial-dimension is finite.

• By a Euclidean space, I mean a finite-dimensional inner-product affine space.

• For each natural number $n$, write $\mathbb{E}_n$ for the unique $n$-dimensional Euclidean space, up to isomorphism.

Question. Do any books or articles develop basic Euclidean geometry (i.e. results about $\mathbb{E}_n$) from this perspective?

Answer 1

Perhaps you might like Audin's Geometry.

From the intro:

The first idea is to give a rigorous exposition, based on the definition of an affine space via linear algebra, but not hesitating to be elementary and down-to-earth. I have tried both to explain that linear algebra is useful for elementary geometry (after all, this is where it comes from) and to show “genuine” geometry: triangles, spheres, polyhedra, angles at the circumference, inversions, parabolas...

Chapter 1 is titled Affine Geometry, the next three chapters are about Euclidean geometry (generalities, in the plane, and in space), followed by projective geometry and then a few chapters on classical topics (conic sections, curves, surfaces).