1590s, "having an angle or angles, pointy," from Latin angularis "having corners or angles," from angulus "angle, corner" (see angle (n.)). It is attested earlier in an astrological sense, "occupying a cardinal point of the zodiac" (late 14c.). Angulous "having many corners" is from mid-15c. Angular as "measured by an angle" is from 1670s, hence angular motion "motion of a body which moves around a fixed point."
1560s, "single number regarded as an undivided whole," alteration of unity on the basis of digit. Popularized in John Dee's English translation of Euclid, to express Greek monas (Dee says unity formerly was used in this sense). Meaning "single thing regarded as a member of a group" is attested from 1640s. Extended sense of "a quantity adopted as a standard of measure" is from 1738. Sense of "group of wards in a hospital" is attested from 1893.
"conglomerate rock of angular pieces," 1774, from Italian breccia, "marble of angular pieces," from a Germanic source akin to Old High German brecha "a breaking," from Proto-Germanic *brekan, from PIE root *bhreg- "to break." The same Germanic root is the source of Spanish brecha, French brèche "a breach."
"angular curvature of the spine," 1854 (in a translation from German, where it is attested by 1783), from Greek kyphos "crooked" + -osis.