I just stumbled upon a linguistic problem I wasn't able to resolve via web search. Suppose we're given some geometric set $A$ and subset $B\subset A$. Isn't there a compact way of saying that there exists, say, a plane whose intersection with $A$ is equal to $B$ of the form "there exists a plane intersecting $A$ (preposition) $B$"?

AFAICT, the prepositions "at", "by" and "along" do not fit in general. Maybe I refuse to accept that there is no such construction in English because I'm just too used to the analogous Russian expression.

isB. $\endgroup$ – Vidit Nanda Feb 3 '14 at 4:31