Lewis & Short

ăd-ĕquĭto, āvi, ātum, 1, v. n.

  1. I. To ride to or toward a place, to gallop up to.
    With ad: equites Ariovisti propius tumulum accedere et ad nostros adequitare, * Caes. B. G. 1, 46.
    With in: in primos ordines, Curt. 7, 4, 17.
    With the local adv. quo: quo tam ferociter adequitāsset, inde se fundi fugarique, Liv. 9, 22, 6.
    With dat.: portis, Liv. 22, 42, 5; so, portae Collinae, Plin. 15, 18, 20, § 76: vallo, Liv. 9, 22, 4: castris, Tac. A. 6, 34.
    With acc. of limit: adequitare Syracusas, Liv. 24, 31: perarmatos adequitare coepit, Curt. 4, 9, 14 (Vogel now reads here ad perarmatos).
  2. II. To ride near to or by: juxta aliquem, Suet. Cal. 25: vehiculo anteire aut circa adequitare, id. Aug. 64.