normal: [17] Latin norma originally denoted a sort of set square used by carpenters, masons, etc for measuring right angles. It was extended metaphorically to a ‘rule, pattern, precept’, but English originally took over its derivative normālis as a mathematical term, in the fairly literal sense ‘perpendicular’. The more familiar modern sense ‘standard, usual’ did not emerge until the 19th century, at about the same time as normality, normalcy, and norm itself began to appear on the scene.
c. 1500, "typical, common;" 1640s, "standing at a right angle," from Late Latin normalis "in conformity with rule, normal," from Latin normalis "made according to a carpenter's square," from norma "rule, pattern," literally "carpenter's square" (see norm). Meaning "conforming to common standards, usual" is from 1828, but probably older than the record [Barnhart].
As a noun meaning "usual state or condition," from 1890. Sense of "normal person or thing" is from 1894. Normal school (1834) is from French école normale (1794), a republican foundation. The city of Normal, Illinois, U.S., was named 1857 for the normal school established there.