1. 1998-1999 Faculty Exhibition research interests include philon of byzantium and the Hieronic Granaries of Morgantina. Philon Mechanikos of Byzantium http://www.art.msu.edu/facultyCatalog/page27a.html

Navigate by History of Art Professor Susan Bandes (Baroque) Paul Deussen (Ancient) Phylis Floyd (Modern, Contemporary) Kenneth Haltman (American) Anning Jing (Asian) William Kilbourne Jr (Architechure, Design) Stuart Lingo (Renaissance) Marsha Macdowell (Folk Art) Susan Madigan (Medieval) Raymond Silverman (African) Lindo Stanford (American Architechure) Paul Deussen My research interests include Philon of Byzantium and the Hieronic Granaries of Morgantina. Philon Mechanikos of Byzantium was an engineer and architectural theoretician in the third century B.C. His writings have survived, in part, though the manuscripts are corrupt and filled with serious lacunae. Philon's main extant treatises deal with siegecraft and military fortifications. There are clear indications that his prescripts were followed in building the Syracusan defenses, generally attributed to Archimedes. In an excursus, Philon explains ways to construct granaries and storage facilities for victuals, although his text is particularly obscure. However, the third-century granaries of Morgantina, excavated over the past decades and which I am at present preparing for publication, provide explanations and thus illuminate the text (while normally it is the written evidence which is ancillary to archaeology).

2. Trebuchet: Defense Against The Catapult Defense Against Catapult There are three types fortifications field fortifications, continuous barriers and castles. From O'Connor. philon of byzantium. Before describing the contents of Philon's masterpiece Mechanics let us give some http://web.grinnell.edu/techstudies/vick/cat_def.html

Defense Against Catapult Castles There are three types fortifications: field fortifications, continuous barriers and castles. Field fortifications were the simplest: "Originally such fortifications may have been derived from hunting, where various devices were used since prehistoric times to trap animals and to limit their movements..."[ Van Creveld 25 ] Field fortifications were mostly temporary structures, and did not withstand attacks any better than one might expect of hasty works. Continuous barriers, such as Hadrian's Wall and the Great Wall of China were stronger but required far more resources. "It [required] managerial and organizational skills and resources, and the ability to put thousands and even tens of thousands of men to work in a purposeful, coordinated fashion while simultaneously keeping them fed, clothed, housed, and policed... It was a question of pouring sweat in order to save blood. "[ Van Creveld 26-7 ] Niether of these types of fortification were effective against artillery, which led to the creation of the third type of fortification, the castle. Rather than trying to protect an entire region, it was far more reasonable to concentrate defenses on a single point. "However great the superiority that an invader enjoyed in the field, and however numerous his victories in battle, a country was not really occupied until its fortresses had been reduced."[ Van Creveld 28 Figure 1.

3. Philon's Line philon of byzantium , sometimes called Philo, was a lessor known scientist/mathematician living around 280 BC. http://www.pballew.net/Philo.html

Philon's Line Philon of Byzantium , sometimes called Philo, was a lessor known scientist/mathematician living around 280 BC.  One of his projects in geomery was the ancient problem of making a cube with twice the volume of a given cube.  In trying to solve the problem, he encountered and solved the following problem: Given an angle BAC and a point X, interior to the angle, find the shortest line segment through X reaching from ray AC to ray AB.  (see figure) Philon's discovery was that the shortest segment occurred when the distance from the point X to one ray was equal to the distance from the other ray to the foot (G in the figure) of the perpendicular  to the segment from A .    Philon's only surviving work is his treatise on mechanics.  It appears that he travelled throughout the Eastern Mediterranean studying the construction of catapults.  He may have been a militrary advisor of some sort.  He is mentioned in the writings of Heron of Alexandria.  You can find more about his life at the St Andrews University web site.

4. Tempo the second century B.C, the Greek author philon of byzantium wrote down a list of the seven most magnificent monuments http://www.ifrance.com/le-kiosque-des-mots/bmausoleum.htm

A mausoleum Mausoleion or the Portuguese Whereas the word Mausoleo spread to Spain and Italy, in Russia Lenin is resting in his Mavzoley Biographies Next word Other Items

5. Seven Wonders Of The Ancient World Greek engineer and mathematician named philon of byzantium, yet many scholars and historians believe that Philon had not http://www.allaboutturkey.com/7wonders.htm

The Seven Ancient Wonders of the World What Makes These Wonders So Wonderful? These Wonders of the World originate from history, before the birth of Christ, during the Greek era. (second century B.C). These were built during a period of time that extended more than two thousand years: from the ancient kingdoms of Egypt and Babylaon to the Golden Age of Classical Greece. A Greek poet named Antipater (also known as Antipatros) created a list of seven marvelous structures, later to be known as the Seven Wonders of the World. This list was created by him as a tribute to the ancient world's acheivements, a summary of mankind's outstanding accomplishments in creation. Antipater, however, was not alone in compiling lists of these great works. Only one other nearly complete list of Wonders of the World has existed through the years. This was found in a book said to have been written by a famous Greek engineer and mathematician named Philon of Byzantium , yet many scholars and historians believe that Philon had not written the book - they believe that a man had written it after Philon's death and had signed it under Philon's name to gain recognition. In these two lists consistency was dominant in several of these Wonders of the World, yet an only six were originally on these lists. The final Wonder of the World - The Lighthouse of Alexandria - was added to the list in the sixth century B.C. What about the other Wonders of the World?

6. Philon philon of byzantium. Born about 280 BC in Byzantium (Turkey) Died about 220BC. Only a few references to philon of byzantium exist in the literature. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Philon.html

Philon of Byzantium Born: about 280 BC in Byzantium (Turkey) Died: about 220 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Only a few references to Philon of Byzantium exist in the literature. He is mentioned by Vitruvius who was a Roman architect and engineer. Vitruvius (1st century BC) was the author of the famous treatise De architectura (On Architecture) and in this work he gives a list of twelve inventors of machines which include Archytas (second in the list), Archimedes (third in the list), Ctesibius (fourth in the list), and Philon of Byzantium (sixth in the list). Heron of Alexandria mentions a work by Philon On automatic theatres which in fact forms part of his Mechanics treatise. Eutocius also mentions Philon and cites a work by him on the duplication of the cube and this material is again contained in his Mechanics treatise. Perhaps the most information about Philon's life, and this is very little indeed, comes from the only work of his which has survived (at least major parts have survived) Mechanics.

7. Philon Biography of Philon (280BC220BC) philon of byzantium. Born about 280 BC in Byzantium (Turkey) http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Philon.html

Philon of Byzantium Born: about 280 BC in Byzantium (Turkey) Died: about 220 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Only a few references to Philon of Byzantium exist in the literature. He is mentioned by Vitruvius who was a Roman architect and engineer. Vitruvius (1st century BC) was the author of the famous treatise De architectura (On Architecture) and in this work he gives a list of twelve inventors of machines which include Archytas (second in the list), Archimedes (third in the list), Ctesibius (fourth in the list), and Philon of Byzantium (sixth in the list). Heron of Alexandria mentions a work by Philon On automatic theatres which in fact forms part of his Mechanics treatise. Eutocius also mentions Philon and cites a work by him on the duplication of the cube and this material is again contained in his Mechanics treatise. Perhaps the most information about Philon's life, and this is very little indeed, comes from the only work of his which has survived (at least major parts have survived) Mechanics.

8. Greek Mathematics Index Hypatia Hypsicles Leucippus Marinus of Neapolis Menaechmus Menelaus Nicomachus NicomedesOenopides of Chios Pappus Perseus philon of byzantium Plato Porphyry http://www-gap.dcs.st-and.ac.uk/~history/Indexes/Greeks.html

History Topics: Index of Ancient Greek mathematics Articles about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy ... Greek number systems Various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name below to go to that biography. Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers Al-Haytham Johann Bernoulli Cusa James Gregory ... Search Form JOC/EFR August 2001 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Greeks.html

9. Alexandria Museum of automata, York (England). philon of byzantium worked on pneumatics,clepsydras, automata, incredible instruments, and war machines. http://miralabwww.unige.ch/subpages/automates/antiquite/alexandria.htm

Automata of Alexandria The Alexandrian School inherited from a long tradition dating back to the 6th century BC with Thales, Pythagorus and Euclid, who provided inspiration for the illustrious mechanists. Of the above, Ctesibius is generally considered to be the founder of the Mechanical School in Alexandria. He explored new areas, carried out research into wind instruments and the basic principles of mechanics, such as the elasticity of air, the incompressibility of water, and transmission and reduction ratio mechanisms. He is attributed with the invention of the suction and force pump and the hydraulic organ. Museum of automata, York (England) Philon of Byzantium worked on pneumatics, clepsydras, automata, incredible instruments, and war machines. His research into the nature of air, how it interacts with water and vacuum, the equilibrium of liquids in communicating vessels, and siphons, led him to create some extraordinary objects with neither screws nor springs, just levers and skillfully drilled tubes. Fountain with figure and animal by Philon of Byzantium. This was activated by water.

10. The Philon Line The line is name after philon of byzantium, an ancient Greek engineer. http://cgm.cs.mcgill.ca/~godfried/research/philon.html

"Well begun is half done." - Aristotle This page is still under construction. Philon of Byzantium (circa 100 A.D.) worked on trying to duplicate the cube (construct a cube with volume equal to twice the volume of a given cube) using only a straight edge and compass. Since he could not find a direct solution he kept searching for problems that were equivalent in the sense that one could construct the solution to one problem from the solution to the other by means of the straight edge and compass. Constructing the Philon line (as it is now known) is one such equivalent problem that he discovered. He could not find a solution to the Philon line problem either. During the past 2000 years many of the giants of computing science, including Newton, tried to solve Philon's problem with straight edge and compass without success. It was only one hundred years ago, using algebra, that this was shown to be impossible. History and various solutions to the problem of doubling the cube. Research Interests Homepage

11. Siege Engine Prototypes The repeating catapult designed by Dionysius and the wedge framecatapulta developed by philon of byzantium are included here. http://198.144.2.125/Siege/SiegePrototypes/Prototypes.htm

This page was made in answer to several requests for diagrams featuring prototype siege engines of which at least one was constructed and tested by ancient engineers. The repeating catapult designed by Dionysius and the "wedge" frame catapulta developed by Philon of Byzantium are included here. The bronze spring catapulta and pneumatic powered catapulta designed by the famous Greek engineer Ctesibius are not depicted here since there is no evidence that they were ever constructed, though the innovative mechanical ideas introduced by these machines shows a great deal of ingenuity on the part of Ctesbius. The images below were taken from Eric William Marsden's GREEK & ROMAN ARTILLLERY. I highly recommend this work. It is the finest book on siege engines that I know of. The Repeating Catapulta of Dionysius Dionysius of Alexandria constructed this advanced form of catapulta with the engineers working in Rhodes, who were already famous for production of siege engines. Philon of Byzantium claims that the machine did not shoot as far as standard single-shot catapultae of the day. There is no evidence that this machine ever entered mass production, most probably because of the high cost and complexity. It remains an oddity in ancient engineering that demonstrates the astounding level of mechanical technology of its day. The Wedge Catapulta of Philon Concept Siege Artillery

12. No. 308: The Last Wonder Of The World The Last of the 7 Wonders of the World, The Great Pyramid The 2ndcentury BC Hellenistic engineer philon of byzantium wrote a tract called De Septem Orbis Spectaculis http://www.uh.edu/admin/engines/epi308.htm

No. 308: THE LAST WONDER OF THE WORLD by John H. Lienhard Click here for audio of Episode 308. Today, we look at the first and last wonder of the world. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. W e use the words "Eighth Wonder of the World" to name each new engineering marvel that comes down the road bridges, ships, and rockets. Maybe it's time to look back at the original Wonders. The 2nd-century BC Hellenistic engineer Philon of Byzantium wrote a tract called De Septem Orbis Spectaculis , literally, Of the Seven Spectacles of the World . He listed: The Lighthouse at Alexandria The Hanging Gardens of Babylon The Colossus of Rhodes The Statue of Zeus at Olympia The Temple of Artemis at Ephesus The Tomb of Mausolus at Halicarnassus The Great Pyramid of Cheops So the Seven Wonders of the Ancient World are correctly those and those alone. They were marvels, of course. The great 150-foot bronze Colossus standing astride the jetties of Rhodes must have been daunting indeed. Yet Philon's list did by no means include the definitive great works for all time. They were the seven grandest works that he could identify in 150 BC. The Colossus lasted only 56 years before it was brought down by an earthquake. All Philon actually saw of it was bronze rubble.

13. Ballista Project walls. This ballista is based on texts left to us by Heron of Alexandriaand philon of byzantium, both engineers of great skill. It http://198.144.2.125/Siege/Photos.htm

Ballista Test Firing 4/17/99 The day had finally arrived! The ballista crew assembled at Anoka High School soccer field to try out the ballista for the first time. Th e f irst shot was done with the slider and sling drawn back only about halfway, just in case the shock of firing did any damage. The first shot went well, so the next shot was made a t 45 degrees for maximum range and power. Unfortunately, the piece of wood that stops the slider from sliding backwards when the trigger was released broke off when the slider struck it. The second shot flew 430 feet (134 yards). Also, some minor damage occurred to the engine. The hemp cord seizing the left loop of the sling to form the eye br oke. No big deal there. We noticed a piece of wood flying off to the left when the trigger was pulled, which also shows up in the photo to the left. As it turned out, the wood piece was the small piece of wood that was glued to the back of the left arm to prev e n t the arm from sliding inward in the cord bundle from the tension of the sling when it mov ed to the brace (undrawn) position. The glue joint obviously wasn't

14. The Philoís Line the point for the given angle. The line is name after philon of byzantium,an ancient Greek engineer. This problem was devised by http://www.cs.mcgill.ca/~cs507/projects/1998/simonpie/

The Philon's Line The Transversal "AB" drawn through a given point "P" within a given angle "RCS" so that the sides of the angle intercept on the transversal a segment of minimum length has become known as the Philo Line (or Philon Line) of the point for the given angle. The line is name after Philon of Byzantium , an ancient Greek engineer. This problem was devised by Philo as a reduction to the duplication of the cube problem, and because of this link to this famous problem, it has excited interest over the ages. Initial proposition of the Philo line. Unimodality of the Philo line. Caracterisation of the Philo line. References [1] Howard Eves, Scripta Mathematica , vol.26, 1959, pp. 141-148 [2] Sir Thomas L. Heath, A Manual of Greek Mathematics , Oxford University Press, 1963, pp.262-264 [3] B. Bhattacharya and G. Toussaint, Computing Shortest Transversals , Computing, vol. 46, 1991, pp 93-119 [4] Coxeter and Van de Craats, Philon Lines In Non-Euclidean Planes , Journal of Geometry, vol. 48, 1993, pp 26-55 [5] David Hounshell, Grolier Electronic Publishing, 1995.

15. Siege Engine Prototypes This page was made in answer to several requests for diagrams featuring prototype siege engines of which at least one was constructed and tested by ancient engineers. catapult designed by Dionysius and the "wedge" frame catapulta developed by philon of byzantium are included here. http://www.stormthewalls.dhs.org/Siege/SiegePrototypes/Prototypes.htm

This page was made in answer to several requests for diagrams featuring prototype siege engines of which at least one was constructed and tested by ancient engineers. The repeating catapult designed by Dionysius and the "wedge" frame catapulta developed by Philon of Byzantium are included here. The bronze spring catapulta and pneumatic powered catapulta designed by the famous Greek engineer Ctesibius are not depicted here since there is no evidence that they were ever constructed, though the innovative mechanical ideas introduced by these machines shows a great deal of ingenuity on the part of Ctesbius. The images below were taken from Eric William Marsden's GREEK & ROMAN ARTILLLERY. I highly recommend this work. It is the finest book on siege engines that I know of. The Repeating Catapulta of Dionysius Dionysius of Alexandria constructed this advanced form of catapulta with the engineers working in Rhodes, who were already famous for production of siege engines. Philon of Byzantium claims that the machine did not shoot as far as standard single-shot catapultae of the day. There is no evidence that this machine ever entered mass production, most probably because of the high cost and complexity. It remains an oddity in ancient engineering that demonstrates the astounding level of mechanical technology of its day. The Wedge Catapulta of Philon Concept Siege Artillery

16. The Philon Line philon of byzantium (circa 100 AD) worked on trying to duplicate the cube (constructa cube with volume equal to twice the volume of a given cube) using only a http://www-cgrl.cs.mcgill.ca/~godfried/research/philon.html

"Well begun is half done." - Aristotle This page is still under construction. Philon of Byzantium (circa 100 A.D.) worked on trying to duplicate the cube (construct a cube with volume equal to twice the volume of a given cube) using only a straight edge and compass. Since he could not find a direct solution he kept searching for problems that were equivalent in the sense that one could construct the solution to one problem from the solution to the other by means of the straight edge and compass. Constructing the Philon line (as it is now known) is one such equivalent problem that he discovered. He could not find a solution to the Philon line problem either. During the past 2000 years many of the giants of computing science, including Newton, tried to solve Philon's problem with straight edge and compass without success. It was only one hundred years ago, using algebra, that this was shown to be impossible. History and various solutions to the problem of doubling the cube. Research Interests Homepage

17. Research Interests Mainly in computational geometry, eg, mobility of objects in space, degeneracies, quadrangulations, Category Science Math Geometry Computational Geometry...... Rhythm Rhythm Generation. History of Computing The Collapsing Compass(Euclid of Alexandria) The Philon Line (philon of byzantium). http://www-cgrl.cs.mcgill.ca/~godfried/research.html

"Everything should be made as simple as possible but not simpler." - Albert Einstein "Simplicity is embarrasing when you have to work for months to achieve it." - Kary Mullis Computational Geometry: Proofs and Refutations in Geometry Mobility of Objects in Space (Robotics, Linkages, Polymer Physics and Protein Folding) Visualization Avoiding Algorithm-Induced Degeneracies Quadrangulations in Mesh Generation Geometric Tomography ... Convexity Theory and Unimodality Computer Vision and Pattern Recognition: Document Analysis Detecting Structure in Dot Patterns Nearest Neighbor Classification (Prototype Selection in Instance-Based Learning) Shape Hulls Computational Rhythm: Combinatorial and Phylogenetic Analysis of Rhythms Rhythm Segmentation The Complexity of Rhythm Rhythm Generation History of Computing: The Collapsing Compass (Euclid of Alexandria) The Philon Line (Philon of Byzantium) Homepage

18. Faculty And Staff Professor Ancient Art Ph.D. Princeton University statement My research interestsinclude philon of byzantium and the Hieronic Granaries of Morgantina. http://www.msu.edu/~art/faculty/history/deussen_m.html

Paul Deussen Professor Ancient Art Ph.D. Princeton University statement My research interests include Philon of Byzantium and the Hieronic Granaries of Morgantina. Philon Mechanikos of Byzantium was an engineer and architectural theoretician in the third century B.C. His writings have survived, in part, though the manuscripts are corrupt and filled with serious lacunae. Philon's main extant treatises deal with siegecraft and military fortifications. There are clear indications that his prescripts were followed in building the Syracusan defenses, generally associated with Archimedes. In an excursus, Philon explains ways to construct granaries and storage facilities for victuals, although here his text is particularly obscure. However, the third-century granaries of Morgantina, excavated over the past decades and which I am at present preparing for publication, provide explanations and thus illuminate the text (while normally it is the written evidence which is ancillary to archaeology).

19. Trebuchet: Bibliography STAAC. Downloaded April 2000. http//www.nzp.com/0603onager.html O'Connor, JJand Robertson, EF philon of byzantium. History of Mathematics. April 1999. http://web.grinnell.edu/techstudies/vick/bibliography.html

Bibliography Contamine, Phillipe. War in the Middle Ages . Translated by Michael Jones. New York: Basil Blackwell Inc., 1985 Van Creveld, Martin L. Technology and War . New York: Macmillan, Inc., 1989 Marsden, E. W. Greek and Roman Artillery . London: Oxford University Press, 1969 Montross, Lynn. War Through the Ages Rowlett, Russ. "Volume T." How Many? A Dictionary of Units of Measurement Rowlett, Russ. "Volume M." How Many? A Dictionary of Units of Measurement Catapult History "Biffa." Les Amis de Larressingle - The city of Medieval Machines Dawson, David. "The English Medieval Castle." The Development of the English Castle "Roman Catapults: The Onager." The Catapult Museum Online O'Connor, J. J. and Robertson, E. F. "Philon of Byzantium." History of Mathematics Miners, Russell. "Historic Trebuchet Illustrations Part 2." Grey Company Trebuchet Page To the Index

20. Antipater Of Sidon - Wikipedia He and the mathematician and engineer philon of byzantium (born about 280 BC in Byzantium,present Turkey) are known as the most famous observers of the Seven http://www.wikipedia.org/wiki/Antipater_of_Sidon

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Antipater of Sidon From Wikipedia, the free encyclopedia. Antipater of Sidon 2nd century BC ) is an ancient Greek writer and poet. He is best known for his list of Seven Wonders of the World . He and the mathematician and engineer Philon of Byzantium (born about 280 BC in Byzantium , present Turkey ) are known as the most famous observers of the Seven Wonders. Edit this page Discuss this page Older versions What links here ... Recent changes It was last modified 05:06 Aug 23, 2002. All text is available under the terms of the GNU Free Documentation License Main Page Recent changes Random page ... Bug reports

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