NOT all spheres are spherical. Not even among their material manifestations (and material spheres are not the only kind of spheres to be found in science) are all spheres spherical: they may also be flat – which is to say, they may be planispheres.
In its pure geometric form, a planisphere is just that: a sphere on a plane. Mathematically, the problem of representing a sphere on a plane is by no means trivial. A form of projection is required, in which the three dimensional surface is transformed into something capable of being represented in only two dimensions.
As few visitors can have failed to notice, the most abundant occurrence of planispheres in the Museum is not with maps of the earth, but with maps of the heavens, and in one form in particular: the astrolabe. A planispheric astrolabe is, essentially, a flat map of the celestial sphere. The mapping can be achieved in various ways, most commonly by a stereographic projection drawn for the location of the observer, but also by one of several alternative forms of universal projection.
The common stereographic projection is made from the south celestial pole onto the plane of the equator. A universal projection, on the other hand, is made from a point on the plane of the equator in the direction of the sun at the equinoxes onto the solstitial plane – the plane through the poles and the sun’s position at the summer and winter solstices.
The common stereographic projection and the universal projection each have their own virtues and limitations. In the common stereographic projection, circles on the celestial sphere are preserved as circles when projected, and the angles between them are maintained. The disadvantage of this projection is that it can be drawn for only one latitude at a time: in order to display star positions correctly at different latitudes, different projections must be made. The universal projection gets around this problem. As its name suggests, a single universal projection can be used at any latitude. The observed position of stars in the sky cannot, however, be read directly from a universal projection but must be calculated with the aid of rules and a pointing device.
The Museum owns the largest collection of astrolabes in the world, so it is not difficult to find specific instruments with which to illustrate these principles. The astrolabe chosen here is a particularly fine example from the collections nevertheless. It was made in Louvain in 1565, is 290 mm in diameter, and is finely worked throughout in gilt brass.
All the standard parts of an astrolabe can be seen on the front: a cutout ‘rete’, with pointers to mark the position of the principal stars, which rotates above a fixed latitude plate, consisting of a reference grid drawn in stereographic projection (the characteristic skewed ‘shuttlecock’ pattern). A rule with sights – the ‘alidade’ – is also included, to enable elevations of celestial bodies to be measured and other associated calculations to be performed. As well as the position of the stars, the rete is also marked with the ecliptic circle – the apparent path of the sun against the background of fixed stars over the course of a year.
The ecliptic is divided into and marked with the signs of the zodiac, which often comes as a surprise to many people, but is absolutely standard – astronomers have long referred to the sun by its position in the zodiac. This astrolabe does in fact have specifically astrological features: the planetary influences are given next to stars on the rete, and lines on the latitude plate mark the twelve astrological houses, used for casting horoscopes. But again, these are usual features and simply reflect the association of astronomy and astrology in the period.
The astrolabe comes from Louvain, but the question remains: who exactly made it? It is signed ‘Regnerus Arsenius Nepos Gemmæ Frisÿ fecit Louanÿ anno 1565’ – ‘Regnerus Arsenius the nephew of Gemma Frisius made this in Louvain in the year 1565’. The answer then would seem to be simple: Regnerus Arsenius made it. But this answer is not as straightforward as it seems. Who exactly was Regnerus Arsenius? Indeed, was Regnerus Arsenius at all?
That Gualterus is referred to in the singular should come as no surprise: there was after all only one of him, and he is referred to in the singular despite the fact that, as is accepted, Ferdinand was working with him. That Regnerus was a name in the family which Gualterus might choose to use on occasion is also possible, but what is arguably more likely is that a real Regnerus was using it as a first name on a permanent basis.
The reference by Guicciardini to a ‘Gautier Renier’ is the strongest evidence that exists. Were it not for other evidence it might be conclusive. But other evidence can be found, beyond the instruments signed ‘Regnerus’, that Gualterus and Regnerus were not the same person. The evidence comes from the accounts of Christopher Plantin, the Antwerp printer. Plantin bought instruments from the Arsenius workshop, meticulously recording his purchases in a ledger, including sums paid to Gualterus.