To the opposite side.

Roget 708: against, versus, counter to, in conflict with, at cross purposes.    against the grain, against the current, against the stream, against the wind, against the tide; with a headwind; with the wind ahead, with the wind in one's teeth.    in spite, in despite, in defiance; in the way, in the teeth of, in the face of; across; athwart, overthwart^†; where the shoe pinches; in spite of one's teeth.    though etc. 30; even; quand meme [Fr.]; per contra.    ... show more

Transversely:
— The marble slabs were cut across.

synonyms: crossways, crosswise.