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There are finer divisions of angular measure. A degree is made up of 60 arcminutes, and each arcminute is divided into 60 arcseconds.
Volume 1, like Burnham's, begins with a roughly 100-page introduction to the astronomy that an amateur really needs to know: the celestial sphere and the sky's motions, the magnitude system, angular measures, and so on, along with lots about the various types of objects to be seen in amateur scopes.