σκῐᾱμᾰχ-ία · skiamach-ia — LSJ
a fighting against a shadow: esp. a form of exercise with hands and feet, Ph. 1.153.
metaph., fighting with a shadow, mock-fight, ‘beating the air’, Cic. Fam. 11.14.1 (pl.), Plu. Garr. 2.514d, Eust. 663.16; title of satire by Varro, Non. p.190 L.—σκιομαχία is a later form, Gal. 6.146.