1. Philon's Line 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. Philon's discovery was that the shortest segment occurred when the distance from 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.

2. Faculty And Staff Paul Deussen. Professor. Ancient Art. Ph.D. Princeton University. statement. My research interests include philon of byzantium and the Hieronic Granaries of Morgantina. http://www.art.msu.edu/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).

3. 1998-1999 Faculty Exhibition research interests include philon of byzantium and the Hieronic Granaries of Morgantina. Philon Mechanikos of Byzantium was an engineer 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).

4. Wonders Of The World The best known are those of Antipater of Sidon, one mathematician named philon of byzantium. Included on the list in its http://www.only4ukids.com/knowledge/worldwonders/index.shtml

Wonders of the world Knowledge main Bigbang Computer Earth ... Send Greetings The vast world is full of wonders. We call them the wonders. For, they are the sights that appear amazing because of their uniqueness on different aspects. Many are the overwhelming gifts of Nature. While some have been created exclusively by man. And when we talk about the Seven Wonders of the world, things which flash on our eyes from the pages of history are all man-made pieces of wonders. In fact, these wonders can be regarded as some architectural and sculptural milestones of the ancient Mediterranean and Middle East, as listed by various observers. The best known are those of Antipater of Sidon, one mathematician named Philon of Byzantium. Included on the list in its eventual form were the following: Pyramids of Giza; Hanging Gardens of Babylon; Mausoleum of Halicarnassus; Temple of Artemis; Pharos of Alexandria; Statue of Zeus; Colossus of Rhodes. Each of them is indeed an amazing feat and creativity and was created in the ancient period when technology was still at its infancy. And each of them is a piece of

5. Seven Wonders Of The Ancient World mathematician named philon of byzantium, yet many scholars and historians believe that Philon had not written had written it after Philon's death and had signed it under Philon's http://www.allaboutturkey.com/7wonders.htm

SEVEN WONDERS OF THE ANCIENT 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 Babylon 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 achievements, 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 (1 st 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. Search Results For Archimedes of machines which include Archytas (second in the list), Archimedes (third in thelist), Ctesibius (fourth in the list), and philon of byzantium (sixth in the http://www-gap.dcs.st-and.ac.uk/~history/Search/historysearch.cgi?SUGGESTION=Arc

8. Alexandria Museum of automata, York (England). philon of byzantium worked on pneumatics,clepsydras, automata, incredible instruments, and war machines. http://www.miralab.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.

9. No. 308: The Last Wonder Of The World The 2ndcentury BC Hellenistic engineer philon of byzantium wrote a tract called the jetties of Rhodes must have been daunting indeed. Yet Philon's list did by no means include 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.

10. 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

11. 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. designed by Dionysius and the "wedge" frame catapulta developed by philon of byzantium are included here The Wedge Catapulta of Philon. philon of byzantium, who wrote about siege http://www.stormthewalls.dhs.org/Siege/SiegePrototypes/Prototypes.htm

12. 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

13. Manuscripts Catalogue philon of byzantium, 2 entries. (Poliorcetici Graeci.) Athenaei, De Machinis. Graece.Bitonis, De Constrvctione Bellicarvm Machinarvm et Catapvltarvm. Graece. http://special.lib.gla.ac.uk/manuscripts/search/resultsn.cfm?NID=15829&RID=

14. New 7 Wonders - Origin In 200 B.C., philon of byzantium proposed a list of human civilization's most masterful We have adopted Philon's ancient concept not to replace these 'Seven Wonders of the World http://www.new7wonder.com/ancient.php

Project Vote Candidates Origin ... Statistics 578 DAYS LEFT TO VOTE The Ancient 7 Wonders Of The World In 200 B.C., Philon of Byzantium proposed a list of human civilization's most masterful architectural accomplishments, which are still known today as the 'Seven Wonders of the World' - The Hanging Gardens of Babylon, the Colossus of Rhodes, the Mausoleum at Halicarnassus, the Temple of Artemis, the Lighthouse of Alexandria, the Statue of Zeus, and the Great Pyramid at Giza, Egypt. However, these sites are buildings and sculptures that belong exclusively to the Ancient World. All of them were constructed more than 2000 years ago, and it is only one, the Pyramid of Khufu, that still exists today. We have adopted Philon's ancient concept not to replace these 'Seven Wonders of the World' but to take the decision making process out of the hands of an individual and place it into the hands of the world's citizens. A global consultation is to determine which of the architectural constructions shall be recognised as the New 7 Wonders of the World. The Lighthouse of Alexandria The Temple of Artemis The Statue of Zeus The Colossus of Rhodes ... Pyramids of Egypt Become a Patron Become a patron of New 7 Wonders and help to support the vote.

15. Ballista Construction marble temple. Heron of Alexandria and philon of byzantium both stress that the appearance of siege the ultimate torsion power. philon of byzantium and Heron of Alexandria both http://www.stormthewalls.dhs.org/Siege/ConstructionPics.htm

16. Ancient Greek Artillery Technology: Catapults (Heron, Philon, Biton and Vitruvius are the main sources of informationabout ancient Catapults). philon of byzantium c. (280220) BC. http://www.mlahanas.de/Greeks/war/CatapultTypes.htm

Ancient Greek Artillery Technology The word Catapult comes from the Greek words kata and peltes Kata means downward and peltes describes a small shield ). Catapult means therefore shield piercer. Catapults were first invented about 400 BC in the Greek town Syracus under Dionysios I (ca. 430-367 BC). The Greek engineers first constructed a comparatively small machine, the gastraphetes (belly-bow), a version of a crossbow. The gastraphetes is a large bow mounted on a case, one end of which rested on the belly of the person using it. When the demands of war required a faster, stronger weapon, the device was enlarged, and a winch pull-back system and base were added. Technology of Catapults ( belopoietic from belos (arrow or it is better to say a bolt) and poiw make) was a key part of ancient mechanics, a branch of mathematics that also included fortification building, statics, and pneumatics. Later, weapons fired by torsion bars powered by horsehair and ox tendon (the Greeks called this material neuron ) springs could fire arrows, stones, and pots of burning pitch along a parabolic arc. Some of these machines were quite large and heavy and this were thus mounted on wheels to improve tactical mobility and deployment. The production method is not known.

17. Colossus Of Rhodes It was said to have caused a shortage of bronze throughout the ancient world duringits construction although philon of byzantium says that 15 tons of bronze http://www.mlahanas.de/Greeks/Colossus.htm

The Colossus of Rhodes And so you shall; ascend, therefore, in imagination with me to the Moon, and consider the situation and appearance of the earth from thence: suppose it to seem, as it did to me, much less than the moon, insomuch, that when I first looked down, I could not find the high mountains, and the great sea; and, if it had not been for the Rhodian Colossus, and the tower of Pharos, should not have known where the earth stood. Lucian of Samosata Astronauts are supposed to be able to see the Great Wall in China. Also the first Greek Astronaut Mennipus on his trip to the moon tried to see if the Colossus of Rhodes is visible. To you, O Sun, the people of Dorian Rhodes set up this bronze statue reaching to Olympus when they had pacified the waves of war and crowned their city with the spoils taken from the enemy. Not only over the seas but also on land did they kindle the lovely torch of freedom. Dedicatory inscription of the Colossus of Rhodes The Colossus of Rhodes ( Salvador Dali ) Technology in the Greek island of Rhodes was advanced around the period of Alexander the Great. The island was known for its technology of

18. Greek Index Marinus of Neapolis. Menaechmus. Menelaus. Nicomachus. Nicomedes. Oenopides of Chios. Pappus. Perseus. philon of byzantium. Plato http://stm21645-01.k12.fsu.edu/Greek_Index.htm

Index of Greek mathematicians Below are various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name to go to that biography. Some History Topics about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy 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'Haitam Johann Bernoulli Cusa Franco of Liège James Gregory Lambert Leonardo Lindemann ... Search Suggestions JOC/EFR April 1999 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Greek_index.html

19. Trebuchet: Defense Against The Catapult off with minimal damage.Marsden 143. From O Connor. philon of byzantium.Before describing the contents of Philon s masterpiece 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.

20. 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

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