Angle and History

The semi-square derives from the eightfold division of the circle, the same family that produces the square and the sesqui-quadrate by repeated halving, and its adoption is generally placed among the aspects formalised in the harmonic reform of the early seventeenth century led by Johannes Kepler in the Harmonices Mundi of 1619, even though the surviving record more confidently credits Kepler by name with the fivefold quintile family and the sesqui-quadrate than with the semi-square specifically, which may owe its regular use to the astrologers who extended his method in the generations after him. It is noted with the ordinary angle sign of geometry, an acute angle opened to the right, rather than with a dedicated astrological glyph, and unlike the sesqui-quadrate it was not given its own codepoint when aspect symbols were added to the Unicode Standard, so charting software renders it either with that borrowed angle character or with a font-specific mark that varies between publishers rather than one fixed sign recognised across the field. The semiquartile name, built the same way as the semi-sextile's dodecile, states its relationship to the square plainly, a quarter of the circle halved, and that transparency of naming has done more to keep the semi-square intelligible across different traditions than any settled glyph has.