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Stereographic projections provide striking images: the heavens are displayed in two dimensions and constellations can be elaborately drawn. The engraved lines are impressive examples of the skill of instrument makers. But what can these images of stereographic projection tell us about how instruments were used?

The 'Doctrine of the Sphere'

Illustration from Apian's "Cosmographiae"
The principle of cosmography illustrated in Peter Apian's Cosmographiae. Note that the top image, the celestial sphere, is in fact a stereographic projection. Image © the Whipple Library.

One of the hardest tasks for the historian of scientific instruments is the identification of precisely how instruments were used. In the case of stereographic projections the argument has frequently been made that they were used to teach astronomy, and specifically to teach either the Ptolemaic or Copernican systems. Whilst this is a tempting assumption, it has very little support from accompanying texts.

However, there is another tradition of astronomical teaching - not so closely related to natural philosophy or modern astronomy - that explains how stereographic projections were used in teaching. This was the 'Doctrine of the Sphere' the contents of which were:

"... the Horizon, Meridian, Aequator, Zodiack, Ecliptick, Tropicks, Poles of the World ... representing the model of the Universe." (1)

This part of astronomy concerned the description of the universe, but not in terms familiar to us. Grand debates about planetary systems were not as important as the practical concerns of navigation and horology.

The Doctrine also explained how the astronomical coordinates and lines of celestial globes related to those shown on terrestrial globes - this subject was called 'cosmography'. The image from Peter Apian's Cosmographi shows the relationship with a striking 'projected' woodcut print.

Images as instruments

Images of stereographic projections can also deepen our understanding of the use of instruments in a more general way: the common distinction made between books and instruments, and the ownership of both, doesn't hold when we examine such texts as John Collins' 1658 book The Sector on a Quadrant. Here we find that the plates were intended to be cut out and pasted on wood or brass and to be used as fully functioning instruments.

This point has been made before, in reference to the presence of moving volvelles in a great many renaissance and early-modern books.(2) These volvelles, showing such things as the phases of the moon, are instruments - at least in terms of function, if not form. Because of the division of historical material into libraries and museums, and the modern separation of the two into separate categories of study, research on texts and instruments is often divided artificially. From Collin's text, among others, we can see that books on instruments were often bought and used as instruction manuals, while the plates were made into working instruments.

Read more: the Gunter quadrant.


  1. Anon, Letters and Poems in Honour of the Incomparable Princess, Margaret, Dutchess of Newcastle (London, 1676), p. 147.
  2. J. Bennett, 'Knowing and doing in the sixteenth century: what were instruments for?', British Journal for the History of Science 36.2 (2003).

Boris Jardine

Boris Jardine, 'Images of stereographic projections', Explore Whipple Collections, Whipple Museum of the History of Science, University of Cambridge, 2008

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