Tending to one point; approaching each other. Converging rays, those rays of light which proceed from different points of an object and tend toward a single point. A converging series, that in which the magnitude of the several terms gradually diminishes.
- Nuttall's Standard dictionary of the English language. By Nuttall, P.Austin. Published 1914. (participle, adjective) (p. pr. & a.) (present participle, adjective)

Usage examples:

When their witness to the past is supported by so many converging lines of evidence it becomes irresistible.
- The Story of Evolution by Joseph McCabe
Marion sat watching the two converging rows of flickering street lamps stretching away as far as she could see, and down the street before her she saw the lamps of Jack Elliot's coach gleaming in the darkness.
- With Edge Tools by Hobart Chatfield-Taylor
Yet it is to be doubted if this accurately represents the nature of her inner thoughts, for when she again turned towards Lao Ting the engaging frankness of her expression had imperceptibly deviated, as she continued: " In about nine and forty years, then, O impetuous one, our converging footsteps will doubtless again encounter upon this spot.
- Kai Lung's Golden Hours by Ernest Bramah Commentator: Hilaire Belloc