Many early astronomy books included within them paper tools for practicing the theoretical knowledge they taught. Peter Apian's Astronomicum Caesareum or "Astronomy of the Caesars" (Item 1) is one of the most remarkable printed works from the sixteenth century. It includes 36 elaborately hand-colored woodcuts, 21 of which included woodcut volvelles, designed to help the reader identify planetary positions and alignments as well as other astronomical phenomena. The volvelle (Latin volvere, "to turn") is a paper disc capable of revolving on another paper surface or on multiply layered surfaces. On the page shown, there are in total five separate and movable layers. The weighted threads extending from the circles' centers allowed the user to calculate spatial positions and relations for particular times. The book was useful for making scientific calculations of astronomical phenomena within the Ptolomaic system, and also for making astrological calculations for the creation of horoscopes or the identification of propitious and unpropitious times.
Forty years after publication, this copy of Apian's book was given by the great Danish astronomer Tycho Brahe to a student, a gift recorded in Brahe's hand on the title page. By 1580, the diffusion of Copernicus' theories would have diminished the astronomical value of the book to those like Brahe. So the transaction between teacher and student, which must have been prompted by the book's extraordinary aesthetic beauty and monetary value, can also be seen as putting the book to one further use in consolidating this collegial friendship.