Stone which lies at the corner of twowalls and unites them; implies a sense of foundation in that the building would fall to ground without the cornerstone.
"This law is implicit in earlier work, but Lavoisier stated it explicitly and used it as the cornerstone of his science."
"Yoga and meditation were the cornerstone to the success of the stateranker."
To do something with less than the appropriate amount of care. Possibly from the practice of taking a short cut when running around a city block, effectively cuting off a corner of the route.
If they hadn't cut so manycorners when building that bridge, it probably wouldn't have fallen down.
1st guy: "you know the Pulp Fiction scene with SLJ, where hamburgers are mentioned as cornerstones?" (Jules Winnfield: "Hamburgers! The cornerstone of any nutritious breakfast.")
2nd guy "yeah"
1st guy: "well, they should make up a word called "cornerstoner""