François d'Aguilon (; also d'Aguillon or in Latin Franciscus Aguilonius) (4 January 1567 – 20 March 1617) was a

Jesuit The Society of Jesus (; abbreviation: S.J. or SJ), also known as the Jesuit Order or the Jesuits ( ; ), is a religious order (Catholic), religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rom ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

, and

architect An architect is a person who plans, designs, and oversees the construction of buildings. To practice architecture means to provide services in connection with the design of buildings and the space within the site surrounding the buildings that h ...

from the

Spanish Netherlands The Spanish Netherlands (; ; ; ) (historically in Spanish: , the name "Flanders" was used as a '' pars pro toto'') was the Habsburg Netherlands ruled by the Spanish branch of the Habsburgs from 1556 to 1714. They were a collection of States of t ...

. D'Aguilon was born in

Brussels Brussels, officially the Brussels-Capital Region, (All text and all but one graphic show the English name as Brussels-Capital Region.) is a Communities, regions and language areas of Belgium#Regions, region of Belgium comprising #Municipalit ...

; his father was a secretary to

Philip II of Spain Philip II (21 May 152713 September 1598), sometimes known in Spain as Philip the Prudent (), was King of Spain from 1556, King of Portugal from 1580, and King of Naples and List of Sicilian monarchs, Sicily from 1554 until his death in 1598. He ...

. He became a Jesuit in

Tournai Tournai ( , ; ; ; , sometimes Anglicisation (linguistics), anglicised in older sources as "Tournay") is a city and Municipalities in Belgium, municipality of Wallonia located in the Hainaut Province, Province of Hainaut, Belgium. It lies by ...

in 1586. In 1598 he moved to

Antwerp Antwerp (; ; ) is a City status in Belgium, city and a Municipalities of Belgium, municipality in the Flemish Region of Belgium. It is the capital and largest city of Antwerp Province, and the third-largest city in Belgium by area at , after ...

, where he helped plan the construction of the

Saint Carolus Borromeus church St. Charles Borromeo Church () is a Roman Catholic church in central Antwerp, Belgium, located on the Hendrik Conscienceplein. It was built in 1615–1621 as the Jesuit church of Antwerp, which was closed in 1773. It was rededicated in 1779 to Sai ...

. In 1611, he started a special school of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

in Antwerp, fulfilling a dream of

Christopher Clavius Christopher Clavius, (25 March 1538 – 6 February 1612) was a Jesuit German mathematician, head of mathematicians at the , and astronomer who was a member of the Vatican commission that accepted the proposed calendar invented by Aloysius ...

for a Jesuit mathematical school; in 1616, he was joined there by

Grégoire de Saint-Vincent Grégoire de Saint-Vincent () - in Latin : Gregorius a Sancto Vincentio, in Dutch : Gregorius van St-Vincent - (8 September 1584 Bruges – 5 June 1667 Ghent) was a Flemish Jesuit and mathematician. He is remembered for his work on quadrature of ...

. The notable geometers educated at this school included Jean-Charles della Faille,

André Tacquet André Tacquet (; 23 June 1612 Antwerp – 22 December 1660 Antwerp, also referred to by his Latinized name Andrea Tacquet) was a Brabantian mathematician and Jesuit priest. Tacquet adhered to the methods of the geometry of Euclid and the ...

, and Theodorus Moretus. RubensAguilonStereographic

His book, ''Opticorum Libri Sex philosophis juxta ac mathematicis utiles,'' or ''Six Books of Optics,'' is useful for philosophers and mathematicians. It was published by Balthasar I Moretus in Antwerp in 1613 and illustrated by the famous painter

Peter Paul Rubens Sir Peter Paul Rubens ( ; ; 28 June 1577 – 30 May 1640) was a Flemish painting, Flemish artist and diplomat. He is considered the most influential artist of the Flemish Baroque painting, Flemish Baroque tradition. Rubens' highly charged comp ...

. It included one of the first studies of

binocular vision Binocular vision is seeing with two eyes. The Field_of_view, field of view that can be surveyed with two eyes is greater than with one eye. To the extent that the visual fields of the two eyes overlap, #Depth, binocular depth can be perceived. Th ...

.. It also gave the names we now use to

stereographic projection In mathematics, a stereographic projection is a perspective transform, perspective projection of the sphere, through a specific point (geometry), point on the sphere (the ''pole'' or ''center of projection''), onto a plane (geometry), plane (th ...

and

orthographic projection Orthographic projection (also orthogonal projection and analemma) is a means of representing Three-dimensional space, three-dimensional objects in Plane (mathematics), two dimensions. Orthographic projection is a form of parallel projection in ...

, although the projections themselves were likely known to

Hipparchus Hipparchus (; , ; BC) was a Ancient Greek astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hippar ...

. This book inspired the works of Desargues and

Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...

. He died in

, aged 50.. Footnote 41
p. 38

Six Books of Optics

Francois d'Aguilon's ''Six Books of Optics'' concerns

geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light Wave propagation, propagation in terms of ''ray (optics), rays''. The ray in geometrical optics is an abstract object, abstraction useful for approximating the paths along ...

, which at the time in the Jesuit school was a subcategory of geometry. He taught

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

syntax In linguistics, syntax ( ) is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituenc ...

, and

theology Theology is the study of religious belief from a Religion, religious perspective, with a focus on the nature of divinity. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itse ...

while being charged with organizing the teaching of geometry and science which would be useful for geography, navigation, architecture and the military arts in Belgium. His superiors wanted him to synthesize the work of Euclid, Alhazen, Vitello, Roger Bacon and others. Although he died before completing the book, it still consists of six in-depth books, called ''Opticorum Libri Sex.''Bangert, William A History of the Society of Jesus. St. Louis: St. Louis Institute, 1972

Perception and the horopter

D'Aguilon extensively studied

, which he wanted to use a means to aid architects, cosmographers, navigators and artists. For centuries, artists and architects had sought formal laws of projection to place objects on a screen. Aguilon's ''Opticorum libri sex'' successfully treated projections and the errors in perception. D'Aguillon adopted Alhazen's theory that only light rays orthogonal to the cornea and lens surface are clearly registered.Gillispie, Charles. C. ed., Dictionary of Scientific biography. 16 vols. New York: Charles Scribner and Sons, 1970 Aguilon was the first to use the term

horopter In vision science, the horopter was originally defined in geometric terms as the Locus (geometry), locus of points in space that make the same angle at each eye with the Fixation (visual), fixation point, although more recently in studies of bino ...

, which is the line drawn through the

focal point Focal point may refer to: * Focus (optics) * Focus (geometry) * Conjugate points, also called focal points * Focal point (game theory) * Unicom Focal Point, a portfolio management software tool * Focal point review, a human resources process for e ...

of both eyes and parallel to the line between the eyes. In other words, it describes how only objects on the horopter are seen in their true location. He then built an instrument to measure the spacing of double images in the horopter as he saw fit. D'Aguilon expanded on the horopter by saying in his book: At first glance, it seems that Aguillon discovered the geometrical horopter more than 200 years before Prevost and Vieth and Muller. The horopter was then used by architect

Girard Desargues Girard Desargues (; 21 February 1591September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named i ...

, who in 1639 published a remarkable treatise on the conic sections, emphasizing the idea of projection.

Similarity to other theorists

In Aguilon's book there are elements of perspectivities as well as the stereographic projections of

Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...

and

. Unaware that

Johannes Kepler Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, Natural philosophy, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best know ...

had already published optical theories years before him, Aguilon decided to share his insights on geometric optics. At the age of 20, the Dutch poet Constantijn Huygens read Aguilon's and was enthralled by it. He later said that it was the best book he had ever read in geometrical optics, and he thought that Aguilon should be compared to

Plato Plato ( ; Greek language, Greek: , ; born BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...

, Eudoxus and

Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...

. In fact the title of Constantijn Huygens' first publication imitated Aguilon's title (omitting letters p and c): Otiorum Libri Sex (1625).

Accompanying art

In Aguilon's book the beginning of each section had works of the 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 stands 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.

References

External links

François De Aguilon, S.J. (1546 to 1617) And his Six books on Optics
Joseph MacDonnell, S.J., Fairfield University * BEIC digital library
François d'Aguilon, ''Opticorum libri'', Antwerpen, Jan Moretus widow & sons, 1613.
{{DEFAULTSORT:Aguilon, Francois D 1567 births 1617 deaths Mathematicians from the Spanish Netherlands Scientists from Antwerp Jesuits from the Spanish Netherlands Color scientists University of Douai alumni Jesuit scientists