‘A stalker who dressed a pillow “mannequin” in his ex’s nurse’s uniform, then sent her a picture, has been told he is “on the cusp” of jail,’ reported the Scottish edition of the Daily Star. ‘Sheriff Alastair Carmichael told Mark Glass: “I don’t think you understand just how serious this is. You are on the cusp of a custodial sentence.” ’ He’s not the only one on the cusp. Idris Elba is ‘on the cusp of landing the Holy Grail of film-star roles, James Bond,’ reported the Daily Telegraph in a splendidly mixed metaphor, as though the Holy Grail were a kind of giant marlin to land, and a marlin with cusps to boot.

A very nice reader of The Spectator wrote to me about the widespread efflorescence of cusps, but my husband threw out the letter with the potato peelings, both in the wrong bin of course. He’s right (the nice reader, not my husband). This month, supermarkets were on the cusp of recovery, a property developer was on the cusp of overseas expansion and England was on the cusp of qualification for Euro 2016.

I think of cusps as the points made by curved Gothic tracery, as indeed they are, but the word, taken from the Latin cuspis, ‘a point’, was first used in astrology. It is the ‘very entrance of any house, or first beginning’ as William Lilly explained it in 1647. The house is a sign of the zodiac. Halley the comet man used cusp of the horns of a crescent moon. It wasn’t till well after his death in 1742 that the word was taken up by geometers.

Geometric cusps may also be expressed algebraically, which confuses me. Two kinds of cusps are the keratoid cusp (which has concave branches on opposite sides of the common tangent) and the ramphoid cusp. The keratoid or horny cusp is the shape of a rose thorn. The ramphoid or beaky cusp is the shape of the upper beak of an eagle. It was only with Sir James Hall’s Essay on the origin and principles of Gothic architecture (1813) that cusp was first applied to the pointy ornament.

It seems to devalue language to use cusp merely to mean ‘edge’.