But popular science books posed some new challenges for both authors and readers. Since antiquity, teachers had held that scientific subjects were best learned through pictures and working models. Beginners needed to see, touch, and manipulate the objects of study. Teachers of astronomy and mathematics, for example, had long employed three-dimensional models and instruments in their classrooms. Anatomy instructors had used the bodies of humans and animals to illustrate their lessons. For this reason, many scientific, mathematical, and medical books were richly illustrated.

But for the reader to understand the intricate motions of the heavenly bodies, complex geometrical shapes, or the depths of the human body, a two-dimensional illustration might not do the trick. Movable paper parts did.

Authors of popular astronomy texts were among the first to utilize them. Astronomy in this period was geocentric; the sun, moon, and five visible planets were thought to move around the Earth. Each body’s overall motion combined several circular motions. To take the simplest example, the sun was thought to have two motions: It spun around the Earth from east to west every 24 hours, and it moved across the celestial sphere from west to east over the course of a year. Visualizing an object that is simultaneously rotating in two different directions at two different speeds around two different axes was (and is) no mean feat. Michael Crowe, a historian of astronomy, suggests imagining spinning a basketball on your finger while an ant crawls around the ball in the opposite direction. The motion of that ant is the combination of two circular motions. In the classroom, three-dimensional models of the cosmos (armillary spheres) helped students grasp these motions.

The authors of popular astronomy books used a simplified, paper-craft version: paper wheels called volvelles. These could be used to demonstrate the motions of heavenly bodies or to make calculations about those motions. Assembled from layers of paper circles that could be rotated by the reader, volvelles served the same function as armillary spheres in a more affordable, portable format.

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One of the most successful popular astronomy books of the 16th century was Peter Apian’s Cosmographia, a work that went through almost 40 editions in Latin, Dutch, French, and Spanish. Apian included five different volvelles in the book. One of these volvelles demonstrates the relationship between the moon and the sun and the phases of the moon.

The volvelle consists of two paper wheels connected with a small piece of string to a printed circle. The topmost wheel has a circular hole, revealing the lower wheel beneath. Both wheels can be rotated freely in either direction. The top wheel of the volvelle has an indicator with the moon on it. Spinning this wheel represents the moon’s west-to-east monthly circuit around the Earth. The lower wheel has an indicator with the sun on it. Spinning this wheel represents the sun’s yearly west-to-east motion. When the reader moves the two wheels, the phases of the moon appear in the hole cut out of the top wheel.