It is shocking that young people should be addling their brains over mere logical subtleties in Euclid's Elements, trying to understand the proof of one obvious fact in terms of something equally .. obvious.

Shall I refuse my dinner because I do not fully understand the process of digestion?

Waves from moving sources: Adagio. Andante. Allegro moderato.

Euclid for children is barbarous.

If it is love that makes the world go round, it is self-induction that makes electromagnetic waves go round the world.

Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in spite of the abstract nature of its theory, involving quantities whose nature is entirely unknown at the present, is really and truly founded on the observations of real Newtonian forces, electric and magnetic respectively.

Mathematics is an experimental science, and definitions do not come first, but later on.