1540s, of multiplication, from square (adj.) + -ly (2). From 1560s as "in a straightforward manner;" meaning "firmly, solidly" is from 1860.
the responsibility lies squarely with them
to face a problem squarely
looked him squarely in the eye
a squarely cut piece of paper
the bat met the ball squarely
hit the ball squarely
squalor
squamous
squander
square
squared
squarely
squash
squashy
squat
squatter
squaw