Refers to a single edge, end, or side of something, often in contrast to the whole or the other parts.
I put the book on one end of the desk.
He lifted one edge of the paper.
one after another; systematically; thoroughly
Compound of 片 (かた, 'one side') and 端 (はし, 'edge/end'). The reading かたはし is a straightforward combination of the two components.