1 of keen and farsighted penetration and judgment, discerning
2 caused by or indicating acute discernment
Spencer’s lined face and sagacious wit expressed the history inherit to the President’s Chief of Staff and longtime friend, and he was nearly 10 years older than Brown when he first took on the role. (Ben Travers, 'A West Wing Special' Review: HBO Max Reunion Plays Handsomely to a Hidden Audience, IndieWire, October 2020)
As Silas himself says: 'People should just stay well clear of me if they have any sense'. Sagacious advice indeed. (Daniel Kilkelly, Hollyoaks star Jeff Rawle responds to Silas Blissett return, Yahoo News, October 2020)
He called a meeting of his colleagues, and laid before them a proposition which, it will be seen, was profoundly sagacious. (Jules Verne, From the Earth to the Moon)
You might expect the root of sagacious to be sage, which means 'wise' or 'wise man,' but that wouldn't be a wise assumption. Despite their similarities, the two words are not all that closely related. Sagacious traces back to sagire, a Latin verb meaning 'to perceive keenly.' It's also related to the Latin adjective sagus ('prophetic'), which is the ancestor of our verb seek. Etymologists believe that sage comes from a different Latin verb, sapere, which means 'to taste,' 'to have good taste,' or 'to be wise.'
Sagacious entered the English language around the beginning of the 17th century and, for some decades, referred to perceptiveness of sight, taste, and especially, smell. One of the first authors to use the word, Edward Topsell, wrote in 1607 of bees searching for something with “a most sagacious smelling-sence.” Sagacious has largely lost the sense (no pun intended) of being keen in sensory perception, and now almost exclusively means 'of keen judgment, discerning.” The upshot is that English has words for the state of possessing acute vision (such as far-sighted) and a fine sense of touch (such as sensitive), but lacks any adjectives describing an excellent sense of smell. (Merriam-Webster)