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Peter Paul Rubens frontispiece of Aguilon's bookIn the early years of the Society, many Jesuit superiors, Robert Bellarmine among them, wrote letters urging care in the teaching of mathematics and the training of mathematics teachers. In his time Clavius had these observations to make about the training of mathematics teachers and the formation of a mathematics society 350 years before the birth of the American Mathematical Society.
That the Society may be able always to have capable teachers of mathematics, a number of men fit and able to undertake such positions ought to be chosen and organized in a private academy for the study of the branches of mathematics. Otherwise it doesn't seem possible for these studies to survive, much less advance, in the Society.
A special school for mathematics was started in 1611 at Antwerp by François De Aguilon and produced Jesuit geometers such as Tacquet and de la Faille. It demonstrated how serious the Society was about geometry. The French Jesuits also developed another important school for Jesuit mathematicians which flourished for generations.
The Belgian Jesuit, François De Aguilon, S.J. was born in Brussels and died in Antwerp. The school he founded for mathematics was in Antwerp. Aguilon was first to use the word "stereographic" to describe the projections of Hipparcus. The first edition of his book, which went into several editions, was dedicated to the governor Inigo Borgia (a relative of Francis Borgia, S.J.).
Peter Paul Rubens designed the engravings for the illustrations of Aguilon's major work,
Opticorum libri sex philosophis juxta ac mathematicis utiles (Anvers, 1613),concerns geometrical optics, which in the Jesuit schools was taught under the heading of Geometry. He was given the task of organizing the teaching of geometry and science which would be useful for geography, navigation, architecture and the military arts. His plan was to synthesize the works of former geometers starting with Euclid and apply geometry to the three ways in which the eye perceives: directly, then by reflection and finally by refraction. Aguilon had planned to write books on catoptrics and dioptrics but his death interfered with the publication of the two later sections. His treatment of different kinds of projections, especially stereographic, was meant to aid architects, cosmographers, navigators and artists.
"Six Books of Optics, useful for philosophers and mathematicians alike",
Putti examining the eye of Cyclops Putti measuring the Colossus of Rhodes Putti learning of binocular vision Putti demonstrating the "horopter" Putti using the first photometer Putti illustrating steriographic projection
For centuries artists and architects sought formal laws of projection to place objects on a screen. Aguilon's Opticorum libri sex treated successfully projections and the errors in perception, and it was used by an architect Gérard Desargues, who in 1639 published a remarkable treatise on the conic sections, emphasizing the idea of projection. In Aguilon's text on geometrical optics are found elements of perspectivities as well as the sterographic projections of Ptolemy and Hipparcus.
Aguilon's Horopter CD assuming thatAguilon's book contained a number of original insights and contributions to the field of geometrical optics even though he was unaware of the optical theories established by Kepler in his Optics which had been published several years previously. Aguilon gave some early hints on perspective geometry which were later used by Desargues, the "Father of projective geometry". Aquilon was the first to use the term horopter, the line CD drawn through the focal point of both eyes and parallel to the line between the eyes. Binocular vision was not understood at this time. The puzzle centered on how two eyes are able to form one integral image since closing one, the other or neither give three different images?
the object is at F and the eyes at A and B
Constantijn Huygens read Aguilon's book at the age of 20, was enthralled by it. He later said that is was the best book he had ever read in geometrical optics, and thought that Aguilon should be compared to Plato, Eudoxus and Archimedes. In fact the title of Constantijn Huygens' first publication imitated Aguilon's title (omitting letters p and c): Otiorum Libri Sex (1625) and his son Christiaan Huygens many years later was still using Aguilon's book.
What is quite remarkable about this book is the fact that the illustrations at the beginning of each section are works of the greatest Flemish Baroque painter, Peter Paul Rubens. The frontispiece at the beginning of the book shows an eagle, referring to Aguilon's name and a variety of optical and geometrical images. On either side of the title stand Mercury holding the head of Argus with a hundred eyes, and Minerva holding a shield reflecting the head of Medusa. Then, at the beginning of each of six sections are Rubens' drawings describing Aguilon's experiments, one of which is the first known picture of a photometer. This is one of six experiments drawn by Rubens and shows how intensity of light varies with the square of distance from the source. The experiment was later taken up by Mersenne and another Jesuit, Claude de Chales, and eventually led to Bouguer's more famous photometer. It is evident, from the detail that he put into his drawings, how enthused Rubens was about the subject matter, perspective geometry and optical rules.
The evidence for collaboration is not confined to the words of Aguilon. Rubens himself has provided it in his own language: by his paintings. C. Parkhurst has shown how much Rubens' painting Juno and Argus is in agreement with Aguilon's theory of color and he concludes: Rubens' picture and d'Aguilon's text are important documents for the history of both science and art.
Michael Jaffe has called our attention to another earlier painting by Rubens, the Annunciation. The five elementary colors are displayed in the painting thus: White and blue in the Virgin's clothes; red in the drapery behind her; white and yellow in the Holy Spirit appearing as a dove with glory in the background; the composite colors in the clothing of Gabriel. Rubens is also said to have prepared a treatise on colors himself, therefore the reference to the explanation by painters at the end of Aguilon's discussion of colors seems to mean a reference even to a future book, the treatise of Rubens.
|Juno and Argus by Peter Paul Rubens|
following Aguilon's 3 primary colors, red, blue, yellow
| Annunciation by Peter Paul Rubens
illustrating Aguilon's theory of color
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