cusp

cusp \kuhsp\, noun:

1. a point or pointed end.
2. Anatomy, Zoology, Botany. a point, projection, or elevation, as on the crown of a tooth.
3. Also called spinode. Geometry. a point where two branches of a curve meet, end, and are tangent.
4. Architecture. a decorative device, used especially in Gothic architecture to vary the outlines of intradoses or to form architectural foils, consisting of a pair of curves tangent to the real or imaginary line defining the area decorated and meeting at a point within the area.
5. Astronomy. a point of a crescent, especially of the moon.
6. Astrology. a. the zodiacal degree that marks the beginning of a house or a sign. b. Informal. a person born on the first day of a sign.
7. a point that marks the beginning of a change: on the cusp of a new era.

From behind the cusp a figure had stepped out, entirely black, unfolding slowly, as though from a crouch.
-- David Herter, Ceres Storm, 2000

"I have put your father into it! There are the initial letters W. C. let into the cusp of the York rose, and the date, three years before the battle of Bosworth, over the chimneypiece."
-- Baron Edward Bulwer-Lytton, The Caxtons: A Family Picture, 1849

Cusp came to English in the late 1500s from the Latin cuspis meaning "a point."