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(1546 to 1617)

And his Six books on Optics

## Peter Paul Rubens frontispiece of Aguilon's book

In 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 byFrançois De Aguilonand produced Jesuit geometers such asTacquetandde 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 Rubensdesigned the engravings for the illustrations of Aguilon's major work,

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. Opticorum libri sexphilosophis juxta ac mathematicis utiles (Anvers, 1613),

"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

Aguilon'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 lineCDassuming that

the object is at F and the eyes atAandBCDdrawn 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?

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' paintingJuno and Argusis 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, theAnnunciation. 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 Rubensfollowing Aguilon's 3 primary colors, red, blue, yellow | Annunciation by Peter Paul Rubens
illustrating Aguilon's theory of color |

Archivum Historicum Societatis Iesu ( AHSI ) Rome: Institutum Historicum

Bangert, William A History of the Society of Jesus. St. Louis: St. Louis Institute, 1972

Gillispie, Charles. C. ed., Dictionary of Scientific biography. 16 vols. New York: Charles Scribner and Sons, 1970

{Reference to Aguilon in the DSB is found in vol. 1 p81, and vol. 12 p74.}

Oldenburg, Henry ed. Philosophical Transactions of the Royal Society. vols. 1-30. London: 1665-1715

Reilly, Conor "A catalogue of Jesuitica in the Philosophical Transactions of the Royal Society of London" in A.H.S.I. vol. 27,1958, p. 339-362

Sommervogel, Carolus Bibliothèque de la compagnie de Jésus. 12 volumes. Bruxelles: Société Belge de Libraire, 1890-1960

{One entry for Aguilon are found in Sommervogel:

Opticorum libri sex (Antwerp, 1613)

Ziggelaar, August, S.J. Francois de Aguilon. Roma. IHSJ , 1983

François De Aguilon, S.J. - 1617: and his Six books on Optics

Roger Joseph Boscovich, S.J. - 1787: and his atomic theory

Christopher Clavius, S.J. - 1612: and his Gregorian Calendar

Honoré Fabri, S.J. - 1688: and his post-calculus geometry

Francesco M. Grimaldi, S.J. - 1663: and his diffraction of light

Paul Guldin, S.J. - 1643: applications of

Maximilian Hell, S.J. - 1792: and his Mesmerizing encounters

Athanasius Kircher, S.J. - 1680: The Master of a Hundred Arts

Francesco Lana-Terzi, S.J. - 1687: The Father of Aeronautics

Francis Line, S.J. - 1654: the hunted and elusive clock maker

Juan Molina, S.J. - 1829: The First Scientist of Chile

Jerôme Nadal, S.J. -1580: perspective art and composition of place

Ignace Pardies, S.J. - 1673: and his influence on Newton

Andrea Pozzo, S.J. - 1709: and his perspective geometry

Vincent Riccati, S.J. - 1775: and his hyperbolic functions

Matteo Ricci, S.J. - 1610: who brought scientific innovations to China

John Baptist Riccioli, S.J. - 167I: and his long-lived selenograph

Girolamo Saccheri, S.J. - 1733: and his solution to Euclid's blemish

Theorems of Saccheri, S.J. - 1733: and his non Euclidean Geometry

Christopher Scheiner, S.J. - 1650: sunspots and his equatorial mount

Gaspar Schott, S.J. - 1666: and the experiment at Magdeburg

Angelo Secchi, S.J. - 1878: the Father of Astrophysics

Joseph Stepling, S.J. - 1650: symbolic logic and his research academy

André Tacquet, S.J. - 1660: and his treatment of infinitesimals

Pierre Teilhard de Chardin, S. J. - 1955: and The Phenomenon of man

Ferdinand Verbiest, S.J. - 1688: an influential Jesuit scientist in China

Juan Bautista Villalpando, S.J. - 1608: and his version of Solomon's Temple

Gregory Saint Vincent, S.J. - 1667: and his polar coordinates

Nicolas Zucchi, S.J. - 1670: the renowned telescope maker

Post-Pombal Portugal opinion of Pre-Pombal Jesuit Scientists: a recent conference

Seismology, The Jesuit Science. a Jesuit history of geophysics

Visit the Jesuit Resource Page for even more links to things

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