κατά down (cp. κάτω), opposed to ἀνά. With the genitive (the genitive proper (of the goal) and the ablatival genitive) and the accusative. With the genitive, the motion is perpendicular; with the accusative, horizontal.

1. κατά with the Genitive

a. Local: down from, down toward, under: ἁλάμενοι κατὰ τῆς πέτρᾱς having leapt down from the rock X. A. 4.2.17, κατ᾽ ἄκρᾱς utterly, completely (down from the summit) P. L. 909b, ψῡχὴ κατὰ χθονὸς ᾤχετο his soul went down under the earth Ψ 100, μύρον κατὰ τῆς κεφαλῆς καταχέαντες having poured myrrh (down) over their heads P. R. 398a; rarely of rest: ὁ κατὰ γῆς the man under the earth X. C. 4.6.5.

b. Temporal (very rare): κατὰ παντὸς τοῦ αἰῶνος for all eternity Lyc. 7.

c. Other relations: against, as κατ᾽ ἐμαυτοῦ ἐρεῖν to speak against myself P. A. 37b; rarely in a favourable or neutral sense, as οἱ κατὰ Δημοσθένους ἔπαινοι the eulogies on Demosthenes Aes. 3.50, κατὰ πάντων λέγειν to speak with regard to all X. C. 1.2.16; by (with verbs of swearing), as ὀμνύντων τὸν ὅρκον κατὰ ἱερῶν τελείων let them swear the oath by (lit. down over) fullgrown victims T. 5.47.