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François d'Aguilon

January 01, 1970

François d'Aguilon (French pronunciation: [fʁɑ̃swa daɡilɔ̃]; also d'Aguillon or in Latin Franciscus Aguilonius) (4 January 1567 – 20 March 1617) was a Jesuit, mathematician, physicist, and architect from the Spanish Netherlands.

Opticorum libri sex, 1613

D'Aguilon was born in Brussels; his father was a secretary to Philip II of Spain.[1] He became a Jesuit in Tournai in 1586.[2] In 1598 he moved to Antwerp, where he helped plan the construction of the Saint Carolus Borromeus church.[1] In 1611, he started a special school of mathematics in Antwerp, fulfilling a dream of Christopher Clavius for a Jesuit mathematical school; in 1616, he was joined there by Grégoire de Saint-Vincent.[3] The notable geometers educated at this school included Jean-Charles della Faille,[4] André Tacquet,[5] and Theodorus Moretus.[4]

Illustration by Rubens for Opticorum Libri Sex demonstrating how the projection is computed.

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.[6] It included one of the first studies of binocular vision.[1][7] It also gave the names we now use to stereographic projection and orthographic projection, although the projections themselves were likely known to Hipparchus.[8][9][10] This book inspired the works of Desargues[11] and Christiaan Huygens.[12]

He died in Antwerp, aged 50.[2]

Six Books of Optics edit

Francois d'Aguilon's Six Books of Optics concerns geometrical optics, which at the time in the Jesuit school was a subcategory of geometry. He taught logic, syntax, and theology 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.[13] Although he died before completing the book, it still consists of six in-depth books, called Opticorum Libri Sex.[14]

Perception and the horopter edit

D'Aguilon extensively studied stereographic projection, 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.[15] Aguilon was the first to use the term horopter, which is the line drawn through the focal point 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:

If objects fall upon different rays it can happen that things at different distances can be seen at equal angles. If point C be directly opposite the eyes, A and B, with a circle drawn through the three points, A, B, and C.[14] By theorem 21 of Euclid's Third book, any other point D on its circumference which lies closer to the observer than C, will subend an angle ADB which will equal angle ACB. Therefore, objects at C and at D are judged equally far from the eye.[14] But this is false, because point C is farther away than D. Therefore a judgment of distance is false when based on the angles between converged axes, quod erat probandum.

At first glance, it seems that Aguillon discovered the geometrical horopter more than 200 years before Prevost and Vieth and Muller.[13] The horopter was then used by architect Girard Desargues, who in 1639 published a remarkable treatise on the conic sections, emphasizing the idea of projection.

Similarity to other theorists edit

In Aguilon's book there are elements of perspectivities as well as the stereographic projections of Ptolemy and Hipparchus. Unaware that Johannes Kepler 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, 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).[14]

Accompanying art edit

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[13] 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.

See also edit

References edit

  1. ^ a b c Neetens, A. (1997), "Franciscus Aguilonius (1567–1617)", Neuro-Ophthalmology, 18 (1): vii–xiii, doi:10.3109/01658109709044672.
  2. ^ a b Bosmans, Henri, S. J. (1902), "Deux lettres inédites de Grégoire de Saint-Vincent publiées avec des notes bibliographiques sur les œuvres de Grégoire de Saint-Vincent et les manuscrits de della Faille", Annales de la Société scientifique de Bruxelles (in French), 26: 23–40{{citation}}: CS1 maint: multiple names: authors list (link). Footnote 41, p. 38.
  3. ^ Smolarski, Dennis C. (2002), "Teaching mathematics in the seventeenth and twenty-first centuries", Mathematics Magazine, 75 (4): 256–262, doi:10.2307/3219160, JSTOR 3219160, MR 2074191.
  4. ^ a b Meskens, A. (1997), "The Jesuit mathematics school in Antwerp in the early seventeenth century", The Seventeenth Century, 12 (1): 11–22, doi:10.1080/0268117X.1997.10555421, In the few years the school was based in Antwerp it brought forth a first rate mathematician like Jan-Karel della Faille. ... Another important pupil of the school of mathematics was Theodore Moretus (1602–1667), son of Petrus and Henriette Plantin.
  5. ^ O'Connor, John J.; Robertson, Edmund F., "Andrea Tacquet", MacTutor History of Mathematics Archive, University of St Andrews
  6. ^ Held, Julius S. (1979), "Rubens and Aguilonius: New Points of Contact", The Art Bulletin, 61 (2): 257–264, doi:10.1080/00043079.1979.10787660, JSTOR 3049891.
  7. ^ Ziggelaar, August, S. J. (2012), "Theories of binocular vision after Aguilón", Strabismus, 20 (4): 185–193, doi:10.3109/09273972.2012.735524, PMID 23211145, S2CID 27056157{{citation}}: CS1 maint: multiple names: authors list (link).
  8. ^ Kreyszig, Erwin (1991), Differential Geometry, Toronto University Mathematical Expositions, vol. 11, Courier Dover Publications, p. 205, ISBN 9780486667218.
  9. ^ Olinthus, Gregory (1816), Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic Operations, Baldwin Cradock & Joy, p. 121.
  10. ^ Lombaerde, Piet (2008), Innovation and Experience in the Early Baroque in the Southern Netherlands: The Case of the Jesuit Church in Antwerp, Architectura moderna : architectural exchanges in Europe, 16th – 17th centuries, vol. 6, Brepols Pub, p. 66, ISBN 9782503523880.
  11. ^ Ormerod, David (1995), "The mastery of nature: aspects of art, science and humanism in the Renaissance (review)" (PDF), Parergon, 13 (1): 170–171, doi:10.1353/pgn.1995.0033, S2CID 145745735, (PDF) from the original on 14 November 2015, It required the combined brilliance of geometricians as diverse as Alberti, Leonardo, Dürer, De Caus, Aguilon, and Accolti to lay the groundwork, and the genius of Gerard Desargues to accomplish.
  12. ^ Ziggelaar, August, S. J. (2012), "The impact of the Opticorum Libri Sex", Strabismus, 20 (3): 133–138, doi:10.3109/09273972.2012.709577, PMID 22906385{{citation}}: CS1 maint: multiple names: authors list (link).
  13. ^ a b c "François de Aguilon, S.J."
  14. ^ a b c d Bangert, William A History of the Society of Jesus. St. Louis: St. Louis Institute, 1972
  15. ^ Gillispie, Charles. C. ed., Dictionary of Scientific biography. 16 vols. New York: Charles Scribner and Sons, 1970

Further reading edit

External links edit

 
Wikisource has the text of the 1911 Encyclopædia Britannica article "Aguillon, François D'".
  • 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.

January 01, 1970
françois, aguilon, french, pronunciation, fʁɑ, daɡilɔ, also, aguillon, latin, franciscus, aguilonius, january, 1567, march, 1617, jesuit, mathematician, physicist, architect, from, spanish, netherlands, opticorum, libri, 1613, aguilon, born, brussels, father, . Francois d Aguilon French pronunciation fʁɑ swa daɡilɔ also d Aguillon or in Latin Franciscus Aguilonius 4 January 1567 20 March 1617 was a Jesuit mathematician physicist and architect from the Spanish Netherlands Opticorum libri sex 1613 D Aguilon was born in Brussels his father was a secretary to Philip II of Spain 1 He became a Jesuit in Tournai in 1586 2 In 1598 he moved to Antwerp where he helped plan the construction of the Saint Carolus Borromeus church 1 In 1611 he started a special school of mathematics in Antwerp fulfilling a dream of Christopher Clavius for a Jesuit mathematical school in 1616 he was joined there by Gregoire de Saint Vincent 3 The notable geometers educated at this school included Jean Charles della Faille 4 Andre Tacquet 5 and Theodorus Moretus 4 Illustration by Rubens for Opticorum Libri Sex demonstrating how the projection is computed 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 6 It included one of the first studies of binocular vision 1 7 It also gave the names we now use to stereographic projection and orthographic projection although the projections themselves were likely known to Hipparchus 8 9 10 This book inspired the works of Desargues 11 and Christiaan Huygens 12 He died in Antwerp aged 50 2 Contents 1 Six Books of Optics 1 1 Perception and the horopter 1 2 Similarity to other theorists 1 3 Accompanying art 2 See also 3 References 4 Further reading 5 External linksSix Books of Optics editFrancois d Aguilon s Six Books of Optics concerns geometrical optics which at the time in the Jesuit school was a subcategory of geometry He taught logic syntax and theology 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 13 Although he died before completing the book it still consists of six in depth books called Opticorum Libri Sex 14 Perception and the horopter edit D Aguilon extensively studied stereographic projection 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 15 Aguilon was the first to use the term horopter which is the line drawn through the focal point 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 If objects fall upon different rays it can happen that things at different distances can be seen at equal angles If point C be directly opposite the eyes A and B with a circle drawn through the three points A B and C 14 By theorem 21 of Euclid s Third book any other point D on its circumference which lies closer to the observer than C will subend an angle ADB which will equal angle ACB Therefore objects at C and at D are judged equally far from the eye 14 But this is false because point C is farther away than D Therefore a judgment of distance is false when based on the angles between converged axes quod erat probandum At first glance it seems that Aguillon discovered the geometrical horopter more than 200 years before Prevost and Vieth and Muller 13 The horopter was then used by architect Girard Desargues who in 1639 published a remarkable treatise on the conic sections emphasizing the idea of projection Similarity to other theorists edit In Aguilon s book there are elements of perspectivities as well as the stereographic projections of Ptolemy and Hipparchus Unaware that Johannes Kepler 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 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 14 Accompanying art edit 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 13 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 See also editList of Catholic clergy scientistsReferences edit a b c Neetens A 1997 Franciscus Aguilonius 1567 1617 Neuro Ophthalmology 18 1 vii xiii doi 10 3109 01658109709044672 a b Bosmans Henri S J 1902 Deux lettres inedites de Gregoire de Saint Vincent publiees avec des notes bibliographiques sur les œuvres de Gregoire de Saint Vincent et les manuscrits de della Faille Annales de la Societe scientifique de Bruxelles in French 26 23 40 a href Template Citation html title Template Citation citation a CS1 maint multiple names authors list link Footnote 41 p 38 Smolarski Dennis C 2002 Teaching mathematics in the seventeenth and twenty first centuries Mathematics Magazine 75 4 256 262 doi 10 2307 3219160 JSTOR 3219160 MR 2074191 a b Meskens A 1997 The Jesuit mathematics school in Antwerp in the early seventeenth century The Seventeenth Century 12 1 11 22 doi 10 1080 0268117X 1997 10555421 In the few years the school was based in Antwerp it brought forth a first rate mathematician like Jan Karel della Faille Another important pupil of the school of mathematics was Theodore Moretus 1602 1667 son of Petrus and Henriette Plantin O Connor John J Robertson Edmund F Andrea Tacquet MacTutor History of Mathematics Archive University of St Andrews Held Julius S 1979 Rubens and Aguilonius New Points of Contact The Art Bulletin 61 2 257 264 doi 10 1080 00043079 1979 10787660 JSTOR 3049891 Ziggelaar August S J 2012 Theories of binocular vision after Aguilon Strabismus 20 4 185 193 doi 10 3109 09273972 2012 735524 PMID 23211145 S2CID 27056157 a href Template Citation html title Template Citation citation a CS1 maint multiple names authors list link Kreyszig Erwin 1991 Differential Geometry Toronto University Mathematical Expositions vol 11 Courier Dover Publications p 205 ISBN 9780486667218 Olinthus Gregory 1816 Elements of Plane and Spherical Trigonometry With Their Applications to Heights and Distances Projections of the Sphere Dialling Astronomy the Solution of Equations and Geodesic Operations Baldwin Cradock amp Joy p 121 Lombaerde Piet 2008 Innovation and Experience in the Early Baroque in the Southern Netherlands The Case of the Jesuit Church in Antwerp Architectura moderna architectural exchanges in Europe 16th 17th centuries vol 6 Brepols Pub p 66 ISBN 9782503523880 Ormerod David 1995 The mastery of nature aspects of art science and humanism in the Renaissance review PDF Parergon 13 1 170 171 doi 10 1353 pgn 1995 0033 S2CID 145745735 archived PDF from the original on 14 November 2015 It required the combined brilliance of geometricians as diverse as Alberti Leonardo Durer De Caus Aguilon and Accolti to lay the groundwork and the genius of Gerard Desargues to accomplish Ziggelaar August S J 2012 The impact of the Opticorum Libri Sex Strabismus 20 3 133 138 doi 10 3109 09273972 2012 709577 PMID 22906385 a href Template Citation html title Template Citation citation a CS1 maint multiple names authors list link a b c Francois de Aguilon S J a b c d 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 1970Further reading editMorere J E 1970 Aguilon Francois d Dictionary of Scientific Biography vol 1 New York Charles Scribner s Sons p 81 ISBN 0 684 10114 9 Ziggelaar August 1983 Francois de Aguilon S J 1567 1617 Scientist and Architect Bibliotheca Instituti Historici S I vol 44 Jesuit Historical Institute ISBN 9788870413441 External links edit nbsp Wikisource has the text of the 1911 Encyclopaedia Britannica article Aguillon Francois D Francois De Aguilon S J 1546 to 1617 And his Six books on Optics Joseph MacDonnell S J Fairfield University BEIC digital library Francois d Aguilon Opticorum libri Antwerpen Jan Moretus widow amp sons 1613 Retrieved from https en wikipedia org w index php title Francois d 27Aguilon amp oldid 1222627766, wikipedia, wiki, book, books, library,

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