Some elementary parts of the theory of elliptic functions can indeed be developed in this way. To those books listed by Alexey Ustinov I can add a large treatise by G. Haplphen, Traité des fonctions elliptiques et de leurs applications. (JFM 22.0447.01) in 3 volumes, published in 1886-1890.

He never misses a opportunity to give a geometric proof of some theorem, when available.

Some elementary parts of the theory of elliptic functions can indeed be developed in this way. To those books listed by Alexey Ustinov I can add a large treatise by G. Halphen, Traité des fonctions elliptiques et de leurs applications (JFM 22.0447.01), (BnF) in 3 volumes, published in 1886-1890.

He never misses a opportunity to give a geometric proof of some theorem, when available.