Cusp

google

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late 16th century (in cusp (sense 3)): from Latin cuspis ‘point or apex’.

wiktionary

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From Latin cuspis(“a point, spear, pointed end”); first used in astrology.

etymonline

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cusp (n.)

1580s, in astrology, "first entrance of a house in the calculation of a nativity," from Latin cuspis "point, spear, pointed end, head," which is of unknown origin. Astronomical sense is from 1670s, "point or horn of a crescent." Anatomical sense of "a prominence on the crown of a tooth" is from 1839.