Lewis & Short

per-dŏcĕo, cui, ctum, 2, v. a., to teach or instruct thoroughly (rare but class.; syn. erudio): res difficilis ad perdocendum, Cic. Sest. 44, 96: aliquem, Plaut. Capt. 3, 5, 59: quanti istuc unum me coquitare perdoces? id. Ps. 3, 2, 85: si quid Apollo Utile mortales perdocet ore meo, Ov. R. Am. 490: homines, Lucr. 5, 1438: suam stultitiam, to betray, Quint. 1, 1, 8.
With object-clause: dignam Maeoniis Phaeacida condere chartis Cum te Pierides perdocuere tuae, Ov. P. 4, 12, 28.
Hence, perdoctus, a, um, P. a., very learned, very skilful (rare but class.), Plaut. Mil. 2, 2, 103; Ter. Heaut. 2, 3, 120: homo, Cic. Balb. 27, 60: genitor, Stat. S. 5, 3, 2: exitio, Lucr. 3, 473.
Adv.: perdoctē, very skilfully (ante-class.), Plaut. Most. 1, 3, 122.