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... nomenque simul, quod possit equorum admonuisse, iubet deponere "qui"...

'equorum': my name, that could have warned/betrayed (me); 'equorum' goes with 'nomen'; deponere - nomen equorum = to lay down/ to do away with my name of horses : 'Hippolytus' is a greek word; hippos (greek) = horse