PCA and nature of solutions

Question

If we cal $X$ the matrix where each line is an observation, the book of Lebart & Co (https://horizon.documentation.ird.fr/exl-doc/pleins_textes/divers11-10/010007837.pdf) state that in PCA the "best" (such that the sum of squared distance projected observations on that space is maximized) vectorial space of dimension 2 contain the first factorial axis. The book dosn't prove this fact, have you an idea of the demonstration/intuition ? Thanks