studio (n.)

early 12c., studien, "to strive toward, devote oneself to, cultivate" (virtue, vice, wisdom, art, etc., sometimes translating Latin occupare), from Old French estudiier "to study, apply oneself, show zeal for; examine" (13c., Modern French étudier).

This is from Medieval Latin studiare, from Latin studium "study, application," originally "eagerness," from studere "to be diligent," which is reconstructed to be from PIE *(s)teu- (1) "to push, stick, knock, beat" (see steep (adj.)). The notion appears to be "pressing forward, thrusting toward," hence "striving after."

Martha swanc and becarcade to geforðigene þan Hælende and his þeowen þa lichamlice behefðen. Seo studdede emb þa uterlice þing. ["Homily for the Feast of the Virgin Mary," c. 1125]

It is attested from c. 1300 specifically as "apply oneself to the acquisition of learning, pursue a formal course of study," also "read (a book or writings) intently or meditatively." It is from mid-14c. as "reflect, muse, think, ponder."

The broad meaning "seek to learn particulars of by observation" is from c. 1600; that of "regard attentively" is from 1660s. Related: Studied; studying.