Tuesday, 29 November 2011

Alexander the Great

ALEXANDER THE GREAT:

Alexander III the Great, the King of Macedonia and conqueror of the Persian Empire is considered one of the greatest military geniuses of all times. He was inspiration for later conquerors such as Hannibal the Carthaginian, the Romans Pompey and Caesar, and Napoleon.  Alexander was born in 356 BC in Pella, the ancient capital of Macedonia. He was son of Philip II, King of Macedonia, and Olympias, the princess of neighboring Epirus. He spent his childhood watching his father transforming Macedonia into a great military power, winning victory after victory on the battlefields throughout the Balkans.  When he was 13, Philip hired the Greek philosopher Aristotle to be Alexander’s personal tutor.  During the next three years Aristotle gave Alexander a training in rhetoric and literature and stimulated his interest in science, medicine, and philosophy, all of which became of importance in Alexander’s later life.  In 340, when Philip assembled a large Macedonian army and invaded Thrace, he left his 16 years old son with the power to rule Macedonia in his absence as regent, which shows that even at such young age Alexander was recognized as quite capable.  But as the Macedonian army advanced deep into Thrace, the Thracian tribe of Maedi bordering north-eastern Macedonia rebelled and posed a danger to the country.  Alexander assembled an army, led it against the rebels, and with swift action defeated the Maedi, captured their stronghold, and renamed it after himself to Alexandropolis. 


Two years later in 338 BC, Philip gave his son a commanding post among the senior generals as the Macedonian army invaded Greece. At the Battle of Chaeronea the Greeks were defeated and Alexander displayed his bravery by destroying the elite Greek force, the Theban Secret Band. Some ancient historians recorded that the Macedonians won the battle thanks to his bravery.


The Family Split and the Assassination of Philip II


But not too long after the defeat of the Greeks at Chaeronea, the royal family split apart when Philip married Cleopatra, a Macedonian girl of high nobility. At the wedding banquet, Cleopatra's uncle, general Attalus, made a remark about Philip fathering a ‘legitimate’ heir, i.e., one that was of pure Macedonian blood. Alexander threw his cup at the man, blasting him for calling him 'bastard child’. Philip stood up, drew his sward, and charged at Alexander, only to trip and fall on his face in his drunken stupor at which Alexander shouted:

"Here is the man who was making ready to cross from Europe to Asia, and who cannot even cross from one table to another without losing his balance."

He then took his mother and fled the country to Epirus. Although allowed to return later, Alexander remained isolated and insecure at the Macedonian court.  In the spring of 336 BC, with Philip’s Persian invasion already set in motion, the king was assassinated by a young Macedonian noble Pausanias, during the wedding ceremony in Aegae, the old capital of Macedonia.  Why Pausanias killed the Macedonian king is a question that puzzled both ancient and modern historians. There is a claim that Pausanias was driven into committing the murder because he was denied justice by the king when he sought his support in punishing the Cleopatra's uncle Attalus for earlier mistreatment. But there are also reports that that both Olympias and Alexander were responsible for the assassination, by driving the young men into committing the act. That might explain why Pausanias was instantly put to death by Alexander's close friends as he attempted to flee the scene, instead of being captured alive and tried before the Macedonian assembly.  Philip, the great Macedonian conqueror was dead, the men who liberated his own country and brought if from the edge of the abyss into a world power. His dream of conquering the Persian Empire now lays on his successor, his son king Alexander III. 

Suppression of the Thracian, Illyrian, and Greek Rebellions

Once he ascended on the Macedonian throne, Alexander quickly disposed of all of his domestic enemies by ordering their execution.  But soon he had to act outside Macedonia.  Philip’s death caused series of rebellions among the conquered nations and the Illyrians, Thracians, and Greeks saw a chance for independence.  Alexander acted swiftly.  He forced his way into Greece despite the roads leading to the country being blocked by the Thessalians.  As soon as he restored Macedonian rule in northern Greece, he marched into southern Greece.  His speed surprised the Greeks and by the end of the summer 336 BC they had no other choice but to acknowledge his authority.
Believing the Greece would remain calm, Alexander returned to Macedonian, marched east into Thrace, and campaigned as far as the Danube river.  He defeated the Thracians and Tribalians in series of battles and drove the rebels beyond the river. Then he marched back across Macedonia and on his return crushed in a single week the threatening Illyrians, before they could receive additional reinforcements.


But now in Greece, upon rumors of his death, a major revolt broke out that engulfed the whole nation.  Enraged, Alexander marched south covering 240 miles in two weeks appearing before the walls of Thebes with large Macedonian army.  He let the Greeks know that it was not too late for them to change their minds, but the Thebans confident in their position called for all the Greeks who wished to set Greece free to join them against the Macedonians.  They were not aware that the Athenians and the Peloponnesians, stunned by the speed of the Macedonian king, quickly reconsidered their options and were now awaiting the outcome of the battle before they make their next move.


Alexander's general Perdiccas attacked the gates, broke into the city, and Alexander moved with the rest of the army behind him to prevent the Thebans from cutting him off.  The Macedonians stormed the city, killing everyone in sight, women and children included.  6,000 Thebans citizens died and 30,000 more were sold as slaves. The city where Alexander's father was kept as hostage for three years, was plundered, sacked, burned, and razed to the ground, just like Philip acted with Methone, Olynthus, and the rest of the Greek cities in Chalcidice.  Only the temples and the house of the poet Pindar were spared from distraction. This was example to the rest of Greece and Athens and the other Greek city-states quickly rethought their quest for freedom.  Greece remained under Macedonian rule.


The Battle of Granicus


With the conquered territories firmly in Macedonian control, Alexander completed the final preparations for the invasion of Asia.  The 22 year-old king appointed Philip's experienced general Antipater as regent in his absence to preside over the affairs of Macedonia and Greece, left him a significant force of 13,500 Macedonian soldiers to watch Greece, Thrace, Illyria, and protect Macedonia, and set out for the Hellespont (modern Dardanelles) in the spring of 334 BC. 






As his ship approached the Asia Minor's coast, he threw his spear from abroad and stuck it in the ground. He stepped onto the shore, pulled the weapon from the soil, and declared that the whole of Asia would be won by the Macedonian spear.   






In the army there were 25,000 Macedonians, 7,600 Greeks, and 7,000 Thracians and Illyrians, but the chief officers were all Macedonians, and Macedonians also commanded the foreign troops.  Alexander's second in command was Philip's general Parmenio, the other important commanders being Perdiccas, Craterus, Coenus, Meleager, Antigonus, and Parmenio's son Philotas. The army soon encountered the forces of King Darius III. There were 40,000 Persians and Greeks (20,000 each) waiting for them at the crossing of the river Granicus, near the ancient city of Troy.  These Greeks had joined the Persians in the years following the defeat of the Greek army by Philip II at Chaeronea.  It is important to note the number of Greeks on the both sides. The Greeks in the Macedonian train were mobilized by the Macedonians, and historians Peter Green and Ulrich Wilcken speak of them as hostages that would ensure the good behavior of their countrymen left behind in Greece under the watch of Antipater's Macedonian garrisons.  Not surprisingly, the Greeks in Alexander's army played insignificant role in the upcoming battles, only to be discharged when convenient. But far greater number of Greeks joined the Persians brushing away the memory of the Persian invasion of Greece some 150 years ago. The ancient Greek historian Arrian cited the "old racial rivalry between the Greeks and Macedonians" that led to this hatred on both sides. 


The Macedonians defeated the Persians and put them to flight and although the Greeks held their ground and fiercely fought, the battle ended in Macedonian victory.  Almost the entire Greek force was annihilated. 18,000 Greeks perished on the banks of Granicus and the 2,000 survivors were sent to forced labor in Macedonia. The Macedonians lost only 120 men according to tradition.


The Campaigns in Asia Minor


Alexander then led the army south across Asia Minor.  Ironically, it is not the Persians but the Greek coastal cities which gave the greatest resistance to the Macedonians.  The Greek commander Memnon and his men considerably slow down the advance of Alexander and many Macedonians died during the long and difficult sieges of the Greek cities of Halicarnassus, Miletus, Mylasa.  But at the end the Macedonian army defeated the enemy and conquered the coast of Asia Minor. Alexander then turned northward to central Asia Minor, to the city of Gordium. 


  


Gordium was a home of the famous so-called Gordian Knot. Alexander knew the legend that said that the man who could untie the ancient knot was destined to rule the entire world. To that date nobody had succeeded in raveling the knot. But the young Macedonian king simply slashed it with his sword and unraveling its ends. 


The Battle of Issus


In the autumn of 333 BC, the Macedonian army's encountered the Persian forces under the command of King Darius III himself at a mountain pass at Issus in northwestern Syria. 30,000 Greeks again formed a sizable addition to the Darius' army as elite fighters and were positioned directly against the Macedonian phalanx. Describing the atmosphere before a battle, the Roman historian Curtius explained how Alexander raised the morale of the Macedonians, Greeks, Illyrians, and Thracians in his army, one at the time:


"Riding to the front line he (Alexander the Great) named the soldiers and they responded from spot to spot where they were lined up. The Macedonians, who had won so many battles in Europe and set off to invade Asia ... got encouragement from him - he reminded them of their permanent values. They were the world's liberators and one day they would pass the frontiers set by Hercules and Father Liber. They would subdue all races on Earth. Bactria and India would become Macedonian provinces. Getting closer to the Greeks, he reminded them that those were the people (the Persians on the other side) who provoked war with Greece, ... those were the people that burned their temples and cities ... As the Illyrians and Thracians lived mainly from plunder, he told them to look at the enemy line glittering in gold ..." (Q. Curtius Rufus 3.10.4-10) 


   


Darius's army greatly outnumbered the Macedonians, but the Battle of Issus ended in a big victory for Alexander. Ten's of thousands of Persians, Greeks, and other Asiatic soldiers were killed and king Darius fled in panic before the Macedonian phalanx, abandoning his mother, wife, and children behind.  Alexander treated them with the respect out of consideration for their royalty.


The Sieges of Tyre and Gaza


The victory at Issus opened the road for Syria and Phoenicia.  In early 332, Alexander sent general Parmenio to occupy the Syrian cities and himself marched down the Phoenician coast where he received the surrender of all major cities except the island city of Tyre which refused to grant him access to sacrifice at the temple of the native Phoenician god Melcart.  A very difficult seven-month siege of the city followed.  In an enormous effort, the Macedonians begun building a mole that would connect the island-city with the coast.  Tons of rocks and wood were poured into the water strip separating the island from the coast but its construction and the attacks from the city walls cost Alexander many of his bravest Macedonians.  Although seriously tempted to lift the siege and continue marching on Egypt, Alexander did not abandon the project and continued the siege, surrounding the island with ships and blasting the city walls with catapults.  When the walls finally gave in, the Macedonians poured their anger over the city defenders - 7,000 people were killed, 30,000 were sold as slaves.  Alexander entered the temple of Melcart, and had his sacrifice.  


During the seven-month siege of Tyre, Alexander received a letter from Darius offering a truce with a gift of several western provinces of the Persian Empire, but he refused to make peace unless he could have the whole empire.  He continued marching south toward Egypt but was again held up by resistance at Gaza.  The Macedonians put the city under a siege which lasted two months, after which the scenario of Tyre was repeated.  With the fall of Gaza, the whole Eastern Mediterranean coast was now secured and firmly in the hands of the Macedonians. 


The mainland Greeks had hoped that the Persian navy and the Greek commander Memnon would land in Greece and help them launch a rebellion against Antipater's Macedonians, transfer the war into Macedonia itself, and cut off Alexander in Asia, but the sealing of the coast prevented this from happening.  Memnon fell sick and died while attempting to regain the lost Greek city of Miletus on the Asia Minor coast, and the Persian plan to transfer the war into Europe well apart.


Alexander in Egypt


Alexander entered Egypt in the beginning of 331 BC. The Persian satrap surrendered and the Macedonians were welcomed by the Egyptians as liberators for they had despised living under Persian rule for almost two centuries.  Here Alexander ordered that a city be designed and founded in his name at the mouth of river Nile, as trading and military Macedonian outpost, the first of many to come. He never lived to see it built, but Alexandria will become a major economic and cultural center in the Mediterranean world not only during the Macedonian rule in Egypt but centuries after.


In the spring of 331 Alexander made a pilgrimage to the great temple and oracle of Amon-Ra, the Egyptian god of the sun, whom the Greeks and Macedonians identified with Zeus Ammon. The earlier Egyptian pharaohs were believed to be sons of Amon-Ra and Alexander as new ruler of Egypt wanted the god to acknowledge him as his son. He decided to make the dangerous trip across the desert to visit the oracle at the temple of the god. According to the legend, on the way he was blessed with abundant rain, and guided across the desert by ravens. At the temple, he was welcomed by the priests and spoke to the oracle. The priest told him that he was a son of Zeus Ammon, destined to rule the world, and this must have confirmed in him his belief of divine origin.  Alexander remained in Egypt until the middle of 331, and then returned to Tyre before facing Darius. 


The Battle of Gaugamela


At Tyre, Alexander received reinforcements from Europe, reorganized his forces, and started for Babylon. He conquered the lands between rivers Tigris and Euphrates and found the Persian army at the plains of Gaugamela, near modern Irbil in Iraq, which according to the exaggerated accounts of antiquity was said to number a million men. The Macedonians spotted the lights from the Persian campfires and encouraged Alexander to lead his attack under cover of darkness. But he refused to take advantage of the situation because he wanted to defeat Darius in an equally matched battle so that the Persian king would never again dare to raise an army against him.






The two armies met on the battlefield the next morning, October 1, 331 BC.  On the Persian side were numerous Asiatic nations - Bactrians, Indians, Medians, Sogdians, even Albanians from the Caucasus, the ancestors of the modern Albanians who many centuries later migrated to Europe and are now northern neighbors to the modern Greeks and western neighbors to the modern Macedonians.  The survivors of the 50,000 Greeks which Darius had on his side at the beginning of the war were also among the Persian ranks. 


   


At the beginning of the battle the Persian forces split and separated the two Macedonians wings. The wing of general Parmenio appeared to be backing down, but Alexander's cavalry rode straight after Darius and forced again his flight like he did at Issus. Darius fled to Ecbatana in Media, and Alexander occupied Babylon, the imperial capital Susa, and the Persian capital Persepolis, and was henceforth proclaimed king of Asia. Four months later, the Macedonians burned the royal palace in Persepolis, completing the end of the ancient Persian Empire.


Suppression of the Greek Rebellion, Discharge of the Greeks, and the Death of Darius


Meanwhile in Greece, the Greeks under the leadership of Sparta rose to a rebellion against the Macedonian occupation. Antipater was in Thrace at the time and the Greeks took the opportunity to push back the Macedonian forces.  But their initial victory did not last for long as Antipater returned with a large army, defeated the rebels, and regained Greece.  5,300 Greeks, including the Spartan king Agis were killed, while the Macedonians lost 3,500 men.


In Asia, the news of the beginning of the Greek rebellion had Alexander so deeply worried, that he immediately sent money to Antipater to counter it.  And when he learned that the Greeks were defeated, he proclaimed the end of the "Hellenic Crusade" and discharged all-Greek forces in his army. He no longer needed these hostages and potential troublemakers. 






Alexander continued his pursuit of Darius for hundreds of miles from Persepolis. When he finally caught up to him, he found the Persian king dead in his coach.  He was assassinated by Bessus, the satrap of Bactria which now proclaimed himself "King of the Kings", assuming the title of the Persian kings. Alexander gave Darius a royal funeral and set out for Bactria after his murderer.


The Trial of Philotas and the Murder of Parmenio


To win the support of the Persian aristocracy Alexander appointed many Persians as provincial governors in his new empire.  He adopted the Persian dress for ceremonies, gave orders for Persians to be enlisted in the army, and encouraged the Macedonians to marry Persian women.   


But the Macedonians were unhappy with Alexander's Orientalization for they were proud of their Macedonian customs, culture, and language.  His increasingly Oriental behavior eventually led to conflict with the Macedonian nobles and some Greeks in the train. In 330 BC series of allegations were brought up against some of Alexander's officers concerning a plot to murder him. Alexander tortured and executed the accused leader of the conspiracy, Parmenio's son Philotas, the commander of the cavalry. Several other officers were also executed according to Macedonian law, in order to eliminate the alleged attempt on Alexander's life. During the trial of Philotas Alexander raised the question of the use of the ancient Macedonian language. He spoke:


"'The Macedonians are about to pass judgment upon you; I wish to know whether you will use their native tongue in addressing them.' Philotas replied: 'Besides the Macedonians there are many present who, I think, will more easily understand what I shall say if I use the same language which you have employed.' Than said the king: 'Do you not see how Philotas loathes even the language of his fatherland? For he alone disdains to learn it. But let him by all means speak in whatever way he desires, provided that you remember that he holds out customs in as much abhorrence as our language.'" (Quintus Curtius Rufus 6.9.34-36)


The trial of Philotas took place in Asia before a multiethnic public, which has accepted Greek as their common language. Alexander spoke Macedonian with his conationals, but used Greek in addressing the Greeks and the Asians, as Greek was widely taken as international language in ancient times.  Like Carthaginian, Illyrian, and Thracian, ancient Macedonian was not recorded in writing. However, on the bases of about hundred glosses, Macedonian words noted and explained by Greek writers, some place names from Macedonia, and names of individuals, most scholars believe that ancient Macedonian was a separate Indo-European language. Evidence from phonology indicates that the ancient Macedonian language was distinct from ancient Greek and closer to the Thracian and Illyrian languages. Some modern writers have erroneously concluded that the Macedonians spoke Greek based on few Greek inscriptions discovered in Macedonia, but that is by no means a proof that the Macedonian was not a distinct language.  Greek inscriptions were also found in Thrace and Illyria, the Thracians even inscribed their coins and vessels in Greek, and we know that both the Illyrians and the Thracians were not Greeks who had distinct languages.


After Philotas was executed according to the Macedonian custom, Alexander ordered next the execution of Philotas' father, general Parmenio.  But the death of the old general did not sit well with every Macedonian in the army.  Parmenio was a veteran, proven solder of Philip's guard, a men who played a major part in leading the Macedonian armies and rising the country to a world power. In fact Philip II had often remarked how proud he was to have Parmenio as his general.  


The Murder of Cleitus and the execution of Callisthenes


Alexander next killed Cleitus, another Macedonian noble, in a drunken brawl. Heavy drinking was a cherished tradition at the Macedonian court and that day Cleitus publicly denounced the king before the present for the murders of Parmenio and Philotas. He went further by ridiculing Alexander for claiming to be "son of Ammon" and for denouncing his own father Philip II.  Alexander lost his temper, snatched the spear from the bodyguard standing near, and ran Cleitus through with it. Although he mourned his friend excessively and nearly committed suicide when he realized what he had done, all of Alexander's associates thereafter feared his paranoia and dangerous temper.


He next demanded that Europeans, just like the Asians, follow the Oriental etiquette of prostrating themselves before the king - which he knew was regarded as an act of worship by the Greeks. But resistance put by Macedonian officers and by the Greek historian Callisthenes, the nephew of Aristotle who had joined the expedition, defeated the attempt. Callisthenes was soon executed on a charge of conspiracy, and we can only imagine how Aristotle received the news of his death.  The two were already estranged for a long time before Callisthenes’ execution, as Alexander's letters to his former tutor carried unfriendly contents.


The Macedonians spent two hard years in Bactria fighting a guerilla war against the followers of Bessus and the Sogdian ruler Spitamenes.  Finally, Bessus was caught and executed for the murder of his king Darius III, and Spitamenes was killed by his own wife which was tired of running away. Bactria and Sogdiana, the most eastern provinces of the Persian Empire came under Macedonian control.  It is here that Alexander fell in love with and married the beautiful Sogdian princess Roxane.


The March on India


In the spring of 327 BC, Alexander and his army marched into India invading Punjab. The greatest of Alexander's battles in India was at the river Hydaspes, against king Porus, one of the most powerful Indian rulers. In the summer of 326 BC, Alexander's army crossed the heavily defended river during a violent thunderstorm to meet Porus' forces. The Indians were defeated in a fierce battle, even though they fought with elephants, which the Macedonians had never seen before. Porus was captured and like the other local rulers he had defeated, Alexander allowed him to continue to govern his territory. 


In this battle Alexander's horse Bucephalus was wounded and died. Alexander had ridden Bucephalus into every one of his battles in Europe and Asia, so when it died he was grief-stricken.  He founded a city which he named Buckephalia, in his horse's name.


The army continued advancing as far as the river Hydaspes but at this point the Macedonians refused to go farther as reports were coming of far more larger and dangerous armies ahead equipped with many elephants and chariots. General Coenus spoke on army's behalf to the king.  Reluctantly, Alexander agreed to stop here.  Not too long afterwards Coenus died and the army buried him with the highest honors.


It was agreed that the army travel down south the rivers Hydaspes and Indus so that they might reach the Ocean on the southern edge of the world and from there head westward toward Persia. 1,000 ships were constructed and while the navy sailed the rivers, the army rode down along the rivers banks, stopping to attack and subdue the Indian villages along the way. 






One of the villages in which the army stopped belonged to the Malli, who were said to be one of the most warlike of the Indian tribes. Alexander was severally wounded in this attack when an arrow pierced his breastplate and his ribcage.  The Macedonians rescued him in a narrow escape from the village. Still the Malli surrendered as Alexander became to recover from the grave wound.  The travel down the river resumed and the Macedonian army reached the mouth of the Indus in the summer of 325 BC. Then it turned westward to Persia.






But the return was a disaster.  The army was marching through the notorious Gerdosian desert during the middle of the summer. By the time Alexander reached Susa thousands had died of heat and exhaustion. 


Alexander's Death


In the spring of 324, Alexander held a great victory celebration at Susa. He and 80 of his close associates married Persian noblewomen. In addition, he legitimized previous so-called marriages between soldiers and native women and gave them rich wedding gifts, no doubt to encourage such unions.


Little later, at Opis he proclaimed the discharge of 10,000 Macedonian veterans to be sent home to Macedonia with general Craterus.  Craterus' orders were to replace Antipater and Antipater’s to bring new reinforcements in Asia. But the army mutinied hearing this. Enraged Alexander pointed the main ringleaders to his bodyguards to be punished and then gave his famous speech where he reminded the Macedonians that without him and his father Philip, they would have still been leaving in fear of the nations surrounding Macedonia, instead of ruling the world.  After this the Macedonians were reconciled with their king and 10,000 of them set out for Europe, leaving their children of Asian women with Alexander. In the same time 30,000 Persian youth already trained in Macedonian manner were recruited in the army.  Alexander prayed for unity between Macedonians and Persians and by breeding a new army of mixed blood he hoped to create a core of a new royal army which would be attached only to him. 


But Alexander will never see this happen.  Shortly before beginning of the planned Arabian campaign, he contracted a high fever after attending a private party at his friend's Medius of Larisa.  As soon as he drank from the cup he “shrieked aloud as if smitten by a violent blow”. The fever became stronger with each following day to the point that he was unable to move and speak.  The Macedonians were allowed to file past their leader for the last time before he finally succumbed to the illness on June 7, 323 BC in the Macedonian month of Daesius. Alexander the Great, the Macedonian king and the great conqueror of Persian Empire, died at the age of 33 without designating a successor to the Macedonian Empire. 






After Alexander


After his death, nearly all the noble Susa marriages dissolved, which shows that the Macedonians despised the idea. There never came to unity between Macedonians and Persians and there wasn't even a unity among the Macedonians.  Alexander's death opened the anarchic age of the Successors and a bloody Macedonian civil war for power followed. 


As soon as the news of Alexander's death were known, the Greeks rebelled yet again and so begun the Lamian War.  The Macedonians were defeated and expelled from Greece, but then Antipater received reinforcements from Craterus who brought to Macedonia the 10,000 veterans discharged at Opis.  Antipater and Craterus jointly marched into Greece, defeated the Greek army at Crannon in Thessaly and brought the war to an end. Greece will remain under Macedonian rule for the next one and a half century.  


In Asia the Macedonian commanders who served Alexander fought each other for power.  Perdiccas and Meleager were murdered, Antigonus rose to control most of Asia, but his growth of power brought the other Macedonian generals in coalition against him.  He was killed in battle and the Macedonian Empire split into four main kingdoms - the one of Seleucus (Asia), Ptolemy (Egypt), Lysimachus (Thrace), and Antipater's son Cassander (Macedonia, including Greece).


The rise of Rome put an end to Macedonian kingdoms. Macedonia and Greece were conquered in 167/145 BC, Seleucid Asia by 65 BC, and Cleopatra VII, the last Macedonian descendent of Ptolemy committed suicide in 30 BC, after which Egypt was added to the Roman Empire. 


With the split of the Roman Empire into Western and Eastern (Byzantium), the Macedonians came to play a major role in Byzantium.  The period of rule of the Macedonian dynasty which ruled the Eastern Roman Empire from 867 to 1056 is known as the "Golden Age" of the Empire.  The Eastern Roman Empire fell in the 15th century and Macedonia, Greece, and the whole southern Balkans came under the rule of the Turkish Empire.


Greece gained its independence at the beginning of the 19th century with the help of the Western European powers, while Macedonia which continued to be occupied by foreign powers, gained independence in 1991, but only over 37% of its historical ethnic territory. With the Balkan Wars of 1912/13 Macedonia was occupied by the armies of its neighbors - 51% of it's territory came under, and still is under the rule of Greece, while the remaining 12% are still occupied by Bulgaria. Both Greece and Bulgaria had been condemned numerous times for the oppression of their large Macedonian minorities which they had stripped off basic human rights, ever since the partition of the country.  (bibliography Ancient Greek and Roman Historians and Modern Historians)
ALEXANDER THE GREAT
ALEXANDER THE GREAT
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ALEXANDER THE GREAT
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ALEXANDER THE GREAT
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Alexander the Great
Alexander the Great

Aristotle

SCIENTIST ARISTOTLE:

he Greek philosopher and scientist Aristotle created the scientific method, the process used for scientific investigation. His influence served as the basis for much of the science and philosophy of Hellenistic (Ancient Greek) and Roman times, and even affected science and philosophy thousands of years later.


Early life


Aristotle was born in the small Greek town of Stagiros (later Stagira) in the northern Greek district of Chalcidice. His father, Nicomachus, was a physician who had important social connections. Aristotle's interest in science was surely inspired by his father's work, although Aristotle did not display a particularly keen interest in medicine. The events of his early life are not clear. It is possible that his father served at the Macedonian court (the political leaders of Macedonia, an ancient empire) as physician to Amyntas II (died c. 370 B.C.E. ) and that Aristotle spent part of his youth there.


At the age of seventeen Aristotle went to Athens, Greece, and joined Plato's (c. 428–c. 348 B.C.E. ) circle at the Academy, a school for philosophers. There he remained for twenty years. Although his respect and admiration for Plato was always great, differences developed which ultimately caused a break in their relationship. Upon Plato's death Aristotle left for Assos in Mysia (in Asia Minor, today known as Turkey), where he and Xenocrates (c. 396–c. 314 B.C.E. ) joined a small circle of Platonists (followers of Plato) who had already settled there under Hermias, the ruler of Atarneus. Aristotle married the niece of Hermias, a woman named Pythias, who was killed by the Persians some time thereafter.


In 342 B.C.E. Aristotle made his way to the court of Philip of Macedon (c. 382–c. 336 B.C.E. ). There Aristotle became tutor to Alexander (c. 356–c. 323 B.C.E. ), who would become master of the whole Persian Empire as Alexander the Great. Little information remains regarding the specific contents of Alexander's education at the hands of Aristotle, but it would be interesting to know what political advice Aristotle gave to the young Alexander. The only indication of such advice is found in the fragment of a letter in which the philosopher tells Alexander that he ought to be the leader of the Greeks but the master of the barbarians (foreigners).


Peripatetic School


Aristotle returned to Athens around 335 B.C.E. Under the protection of Antipater (c. 397–c. 319 B.C.E. ), Alexander's representative in Athens, Aristotle established a philosophical school of his own, the Lyceum, located near a shrine of Apollo Lyceus. Also known as the Peripatetic School, the school took its name from its colonnaded walk (a walk with a series of columns on either side). The lectures were divided into morning and afternoon sessions. The more difficult ones were given in the morning, and the easier and more popular ones were given in the afternoon. Aristotle himself led the school until the death of Alexander in 323 B.C.E. , when he left Athens, fearing for his safety because of his close association with the Macedonians. He went to Chalcis, Greece, where he died the following year of intestinal problems. His will, preserved in the writings of Diogenes Laertius (third century C.E. ), provided for his daughter, Pythias, and his son, Nicomachus, as well as for his slaves.


His writings


Aristotle produced a large number of writings, but few have survived. His earliest writings, consisting for the most part of dialogues (writings in the form of conversation), were produced under the influence of Plato and the Academy. Most of these are lost, although the titles are known from the writings




Aristotle.
of Diogenes Laertius and from others. Among these important works are Rhetoric, Eudemus (On the Soul), On Philosophy, Alexander, Sophistes, On Justice, Wealth, On Prayer, and On Education. They were a wide variety of works written for the public, and they dealt with popular philosophical themes. The dialogues of Plato were undoubtedly the inspiration for some of them, although the fall out between Plato and Aristotle reveals itself to a certain extent in these works, too.
A second group of writings is made up of collections of scientific and historical material, among the most important of which is the surviving fragment of the Constitution of the Athenians. This formed part of the large collection of Constitutions, which Aristotle and his students collected and studied for the purpose of analyzing various political theories. The discovery of the Constitution of the Athenians in Egypt in 1890 shed new light on the nature of the Athenian democracy (a government of elected officials) of Aristotle's time. It also revealed the difference in quality between the historical and scientific works of Aristotle and those that followed.


Theophrastus (c. 372–c. 287 B.C.E. ) had kept Aristotle's manuscripts after the master's death in 322 B.C.E. When Theophrastus died Aristotle's works were hidden away and not brought to light again until the beginning of the first century B.C.E. They were then taken to Rome and edited by Andronicus (first century B.C.E. ). The texts that survive today come from Andronicus's revisions and probably do not represent works that Aristotle himself prepared for publication. From the time of his death until the rediscovery of these writings, Aristotle was best known for the works that today are known as the lost writings.


Philosophical and scientific systems


The writings that did survive, however, are sufficient to show the quality of Aristotle's achievement. The Topics and the Analytics deal with logic (the study of reasoning) and dialectic (a method of argument) and reveal Aristotle's contributions to the development of debate. His view of nature is set forth in the Physics and the Metaphysics, which mark the most serious difference between Aristotelianism and Platonism: that all investigation must begin with what the senses record and must move only from that point to thought. As a result of this process of intellectualizing, God, who for Plato represents beauty and goodness, is for Aristotle the highest form of being and is completely lacking in materiality. Aristotle's God neither created nor controls the universe, although the universe is affected by this God. Man is the only creature capable of thought even remotely resembling that of God, so man's highest goal is to reason abstractly, like God, and he is more truly human to the extent that he achieves that goal.


Aristotle's work was often misunderstood in later times. The scientific and philosophical systems set forth in his writings are not conclusions that must be taken as the final answer, but rather experimental positions arrived at through careful observation and analysis. During the slow intellectual climate of the Roman Empire, which ruled over much of Europe for hundreds of years after Aristotle died, and the totally unscientific Christian Middle Ages (476–1453), Aristotle's views on nature and science were taken as a complete system. As a result, his influence was enormous but not for any reason that would have pleased him.


Aristotle shares with his master, Plato, the role of stimulating human thought. Plato had a more direct influence on the development of that great spiritual movement in late antiquity (years before the Middle Ages), and Aristotle had a greater effect on science. Antiquity produced no greater minds than those of Plato and Aristotle. The intellectual history of the West would be extremely different without them.
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Plato

SCIENTIST PLATO:

Before giving details of Plato's life we will take a few moments to discuss how definite the details are which we give below. The details are mostly given by Plato himself in letters which seem, on the face of it, to make them certain. However, it is disputed whether Plato did indeed write the letters so there are three possible interpretations. Firstly that Plato wrote the letters and therefore the details are accurate. Secondly that although not written by Plato, the letters were written by someone who knew him or at least had access to accurate information on his life. The third possibility, which unfortunately cannot be ruled out, is that they were written by someone as pure fiction.


Next we should comment on the name 'Plato'. In [13] Rowe writes:-


It was claimed that Plato's real name was Aristocles, and that 'Plato' was a nickname (roughly 'the broad') derived either from the width of his shoulders, the results of training for wrestling, or from the breadth of his style, or from the size of his forehead.


Plato was the youngest son of Ariston and Perictione who both came from famous wealthy families who had lived in Athens for generations. While Plato was a young man his father died and his mother remarried, her second husband being Pyrilampes. It was mostly in Pyrilampes' house that Plato was brought up. Aristotle writes that when Plato was a young man he studied under Cratylus who was a student of Heracleitus, famed for his cosmology which is based on fire being the basic material of the universe. It almost certain that Plato became friends with Socrates when he was young, for Plato's mother's brother Charmides was a close friend of Socrates.


The Peloponnesian War was fought between Athens and Sparta between 431 BC and 404 BC. Plato was in military service from 409 BC to 404 BC but at this time he wanted a political career rather than a military one. At the end of the war he joined the oligarchy of the Thirty Tyrants in Athens set up in 404 BC, one of whose leaders being his mother's brother Charmides, but their violent acts meant that Plato quickly left.


In 403 BC there was a restoration of democracy at Athens and Plato had great hopes that he would be able to enter politics again. However, the excesses of Athenian political life seem to have persuaded him to give up political ambitions. In particular, the execution of Socrates in 399 BC had a profound effect on him and he decided that he would have nothing further to do with politics in Athens.


Plato left Athens after Socrates had been executed and travelled in Egypt, Sicily and Italy. In Egypt he learnt of a water clock and later introduced it into Greece. In Italy he learned of the work of Pythagoras and came to appreciate the value of mathematics. This was an event of great importance since from the ideas Plato gained from the disciples of Pythagoras, he formed his idea [6]:-


... that the reality which scientific thought is seeking must be expressible in mathematical terms, mathematics being the most precise and definite kind of thinking of which we are capable. The significance of this idea for the development of science from the first beginnings to the present day has been immense.


Again there was a period of war and again Plato entered military service. It was claimed by later writers on Plato's life that he was decorated for bravery in battle during this period of his life. It is also thought that he began to write his dialogues at this time.


Plato returned to Athens and founded his Academy in Athens, in about 387 BC. It was on land which had belonged to a man called Academos, and this is where the name "Academy" came from. The Academy was an institution devoted to research and instruction in philosophy and the sciences, and Plato presided over it from 387 BC until his death in 347 BC.


His reasons for setting up the Academy were connected with his earlier ventures into politics. He had been bitterly disappointed with the standards displayed by those in public office and he hoped to train young men who would become statesmen. However, having given them the values that Plato believed in, Plato thought that these men would be able to improve the political leadership of the cities of Greece.


Only two further episodes in Plato's life are recorded. He went to Syracuse in 367 BC following the death of Dionysius I who had ruled the city. Dion, the brother-in-law of Dionysius I, persuaded Plato to come to Syracuse to tutor Dionysius II, the new ruler. Plato did not expect the plan to succeed but because both Dion and Archytas of Tarentum believed in the plan then Plato agreed. Their plan was that if Dionysius II was trained in science and philosophy he would be able to prevent Carthage invading Sicily. However, Dionysius II was jealous of Dion who he forced out of Syracuse and the plan, as Plato had expected, fell apart.


Plato returned to Athens, but visited Syracuse again in 361 BC hoping to be able to bring the rivals together. He remained in Syracuse for part of 360 BC but did not achieve a political solution to the rivalry. Dion attacked Syracuse in a coup in 357, gained control, but was murdered in 354.


Field writes in [6] that Plato's life:-


... makes it clear that the popular conception of Plato as an aloof unworldly scholar, spinning theories in his study remote from practical life, is singularly wide of the mark. On the contrary, he was a man of the world, an experienced soldier, widely travelled, with close contacts with many of the leading men of affairs, both in his own city and elsewhere.


Plato's main contributions are in philosophy, mathematics and science. However, it is not as easy as one might expect to discover Plato's philosophical views. The reason for this is that Plato wrote no systematic treatise giving his views, rather he wrote a number of dialogues (about 30) which are written in the form of conversations. Firstly we should comment on what superb pieces of literature these dialogues are [6]:-


They show the mastery of language, the power of indicating character, the sense of a situation, and the keen eye for both its tragic and its comic aspects, which set Plato among the greatest writers of the world. He uses these gifts to the full in inculcating the lessons he wants to teach.


In letters written by Plato he makes it clear that he understands that it will be difficult to work out his philosophical theory from the dialogues but he claims that the reader will only understand it after long thought, discussion and questioning. The dialogues do not contain Plato as a character so he does not declare that anything asserted in them are his own views. The characters are historic with Socrates usually the protagonist so it is not clear how much these characters express views with which they themselves would have put forward. It is thought that, at least in the early dialogues, the character of Socrates expresses views that Socrates actually held.


Through these dialogues, Plato contributed to the theory of art, in particular dance, music, poetry, architecture, and drama. He discussed a whole range of philosophical topics including ethics, metaphysics where topics such as immortality, man, mind, and Realism are discussed.


He discussed the philosophy of mathematics, political philosophy where topics such as censorship are discussed, and religious philosophy where topics such as atheism, dualism and pantheism are considered. In discussing epistemology he looked at ideas such as a priori knowledge and Rationalism. In his theory of Forms, Plato rejected the changeable, deceptive world that we are aware of through our senses proposing instead his world of ideas which were constant and true.


Let us illustrate Plato's theory of Forms with one of his mathematical examples. Plato considers mathematical objects as perfect forms. For example a line is an object having length but no breadth. No matter how thin we make a line in the world of our senses, it will not be this perfect mathematical form, for it will always have breadth. In the Phaedo Plato talks of objects in the real world trying to be like their perfect forms. By this he is thinking of thinner and thinner lines which are tending in the limit to the mathematical concept of a line but, of course, never reaching it. Another example from the Phaedo is given in [6]:-


The instance taken there is the mathemtical relation of equality, and the contrast is drawn between the absolute equality we think of in mathematics and the rough, approximate equality which is what we have to be content with in dealing with objects with our senses.


Again in the Republic Plato talks of geometrical diagrams as imperfect imitations of the perfect mathematical objects which they represent.


Plato's contributions to the theories of education are shown by the way that he ran the Academy and his idea of what constitutes an educated person. He also contributed to logic and legal philosophy, including rhetoric.


Although Plato made no important mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely important in the development of the subject. Over the door of the Academy was written:-


Let no one unversed in geometry enter here.


Plato concentrated on the idea of 'proof' and insisted on accurate definitions and clear hypotheses. This laid the foundations for Euclid's systematic approach to mathematics. In [2] his contributions to mathematics through his students are summarised:-


All of the most important mathematical work of the 4th century was done by friends or pupils of Plato. The first students of conic sections, and possibly Theaetetus, the creator of solid geometry, were members of the Academy. Eudoxus of Cnidus - author of the doctrine of proportion expounded in Euclid's "Elements", inventor of the method of finding the areas and volumes of curvilinear figures by exhaustion, and propounder of the astronomical scheme of concentric spheres adopted and altered by Aristotle - removed his school from Cyzicus to Athens for the purpose of cooperating with Plato; and during one of Plato's absences he seems to have acted as the head of the Academy. Archytas, the inventor of mechanical science, was a friend and correspondent of Plato.


In mathematics Plato's name is attached to the Platonic solids. In the Timaeus there is a mathematical construction of the elements (earth, fire, air, and water), in which the cube, tetrahedron, octahedron, and icosahedron are given as the shapes of the atoms of earth, fire, air, and water. The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.


Plato's beliefs as regards the universe were that the stars, planets, Sun and Moon move round the Earth in crystalline spheres. The sphere of the Moon was closest to the Earth, then the sphere of the Sun, then Mercury, Venus, Mars, Jupiter, Saturn and furthest away was the sphere of the stars. He believed that the Moon shines by reflected sunlight.


Perhaps the best overview of Plato's views can be gained from examining what he thought that a proper course of education should consist. Here is his course of study [2]:-


... the exact sciences - arithmetic, plane and solid geometry, astronomy, and harmonics - would first be studied for ten years to familiarise the mind with relations that can only be apprehended by thought. Five years would then be given to the still severer study of 'dialectic'. Dialectic is the art of conversation, of question and answer; and according to Plato, dialectical skill is the ability to pose and answer questions about the essences of things. The dialectician replaces hypotheses with secure knowledge, and his aim is to ground all science, all knowledge, on some 'unhypothetical first principle'.


Plato's Academy flourished until 529 AD when it was closed down by the Christian Emperor Justinian who claimed it was a pagan establishment. Having survived for 900 years it is the longest surviving university known.
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Hippocrates of Cos

SCIENTIST HIPPOCRATES OF COS:

he ancient Greek physician Hippocrates is called the father of medicine. He changed the course of Greek medicine with his certainty that disease was not caused by gods or spirits but was the result of natural action.


Early life


Hippocrates was born on the Aegean island of Cos, just off the Ionian coast near Halicarnassus (island of Greece) during the end of the fifth century B.C.E. He is called Hippocrates Asclepiades, "descendant of (the doctor-god) Asclepios," but it is uncertain whether this descent was by family or merely by his becoming attached to the medical profession. Legend likewise places him in the family line of the hero Hercules.


Son of Heracleides and Praxithea, Hippocrates's family's wealth permitted him to have a good educational beginning as a child. After nine years of physical education, reading, writing, spelling, music, singing, and poetry, he went to a secondary school, where he spent two years and had very thorough athletic training. It is likely that he went on to study medicine under his father in a form of apprenticeship (arrangement to learn a trade through work experience). This involved following his father and another doctor, Herodicos, from patient to patient and observing their treatment. It is believed that his training included traveling to the Greek mainland and possibly to Egypt and Libya to study medical practices.


Adult talents


Hippocrates is credited with healing many, including the king of Macedonia whom he examined and helped to recover from tuberculosis (disease of the lungs). His commitment to healing was put to the test when he battled the plague (a bacteria-caused disease that spreads quickly and can cause death) for three years in Athens (430–427 B.C.E. ). It is also clear that the height of his career was during the Peloponnesian War (431–404 B.C.E. ).


His teaching was as well-remembered as his healing. A symbol of the many students he encouraged is the "Tree of Hippocrates," which shows students sitting under a tree listening to him. In time he apprenticed his own sons, Thessalus and Draco, in the practice of medicine. The teacher and doctor role combined well in 400 B.C.E. , when he founded a school of medicine in Cos.


Hippocratic Corpus


The body of writing attributed to Hippocrates, the Hippocratic Corpus, is a collection of roughly seventy works—the oldest surviving complete medical books. In ancient times some works in the Hippocratic Corpus, the first known edition of which are from the time of the emperor Hadrian (reigned C.E. 117–138), were recognized as having been written by persons other than Hippocrates. Modern scholars have no knowledge of his writing style to prove which of the works Hippocrates wrote. Nowhere in the Hippocratic Corpus is the entire Hippocratic set of guidelines found. Each subject was written with a particular reader in mind. Some books are directed toward the physician, some for the pharmacist, some for the professional physician, and some are directed more at the layman (person who is not an expert in the field).


In Hippocrates's time doctors wrote treatises (written arguments) for the educated public, who in turn discussed medical problems with their doctors. The aim of these books was to teach the layman how to judge a physician—not to advise on self-treatment or even first aid in order to avoid seeing a doctor.


These medical treatises made up the Hippocratic Corpus. Modern readers can see that experimentation played its role in the Hippocratic view of medicine, because the individual approach to disease is nothing more than experimentation. It is obvious, too, that firsthand experience played a part, since throughout the Corpus the plant ingredients of remedies are described by taste and odor. There are also instances of very basic laboratory-type experiments. The Sacred Disease, one treatise of the Hippocratic Corpus, describes dissections (the act of being separated into pieces) of animals, the results of which permitted comparisons to the human body to be drawn. Further, in their attempts to describe the body, the Hippocratics made use of external (outside) observation only. In On Ancient Medicine the internal organs are described as they can be seen or felt externally. It is most unlikely that dissection of the human body was practiced in the fifth century B.C.E.


Hippocrates favored the use of diet and exercise as cures but realized that some people, unable to follow such directions, would need medicine. His writings teach that physical handling could cure some physical troubles, like a dislocated hip, by the doctor moving it back into place. In A Short History of Medicine E. A. Ackerknecht summed it up: "For better or worse Hippocrates observed sick people, not diseases." This attitude is a timely solution to those who formerly insisted on the coldly scientific approach of the Hippocratic physician, who seemed to be so callous toward his patient.


Little is known of Hippocrates's death other than a range of date possibilities. Different sources give dates of either 374 B.C.E. , the earliest date, or 350 B.C.E. , the latest date. What lives on in modern medicine is his commitment to the treatment of disease.
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Hippocrates of Cos (The Father of Medicine)
HIPPOCRATES IN OLYMPIA

Democritus of Abdera

SCIENTIST  DEMOCRITUS OF ABDERA:
Democritus of Abdera is best known for his atomic theory but he was also an excellent geometer. Very little is known of his life but we know that Leucippus was his teacher.

Democritus certainly visited Athens when he was a young man, principally to visit Anaxagoras, but Democritus complained how little he was known there. He said, according to Diogenes Laertius writing in the second century AD [5]:-

I came to Athens and no one knew me.

Democritus was disappointed by his trip to Athens because Anaxagoras, then an old man, had refused to see him.

As Brumbaugh points out in [3]:-

How different he would find the trip today, where the main approach to the city from the northeast runs past the impressive "Democritus Nuclear Research Laboratory".

Certainly Democritus made many journeys other than the one to Athens. Russell in [9] writes:-

He travelled widely in southern and eastern lands in search of knowledge, he perhaps spent a considerable time in Egypt, and he certainly visited Persia. He then returned to Abdera, where he remained.

Democritus himself wrote (but some historians dispute that the quote is authentic) (see [5]):-

Of all my contemporaries I have covered the most ground in my travels, making the most exhaustive inquiries the while; I have seen the most climates and countries and listened to the greatest number of learned men.

His travels certainly took him to Egypt and Persia, as Russell suggests, but he almost certainly also travelled to Babylon, and some claim he travelled to India and Ethiopia. Certainly he was a man of great learning. As Heath writes in [7]:-

... there was no subject to which he did not notably contribute, from mathematics and physics on the one hand to ethics and poetics on the other; he even went by the name of 'wisdom'.

Although little is known of his life, quite a lot is known of his physics and philosophy. There are two main sources for our knowledge of his of physical and philosophical theories. Firstly Aristotle discusses Democritus's ideas thoroughly because he strongly disagreed with his ideas of atomism. The second source is in the work of Epicurus but, in contrast to Aristotle, Epicurus is a strong believer in Democritus's atomic theory. This work of Epicurus is preserved by Diogenes Laertius in his second century AD book [5].

Certainly Democritus was not the first to propose an atomic theory. His teacher Leucippus had proposed an atomic system, as had Anaxagoras of Clazomenae. In fact traces of an atomic theory go back further than this, perhaps to the Pythagorean notion of the regular solids playing a fundamental role in the makeup of the universe. However Democritus produced a much more elaborate and systematic view of the physical world than had any of his predecessors. His view is summarised in [2]:-

Democritus asserted that space, or the Void, had an equal right with reality, or Being, to be considered existent. He conceived of the Void as a vacuum, an infinite space in which moved an infinite number of atoms that made up Being (i.e. the physical world). These atoms are eternal and invisible; absolutely small, so small that their size cannot be diminished (hence the name atomon, or "indivisible"); absolutely full and incompressible, as they are without pores and entirely fill the space they occupy; and homogeneous, differing only in shape, arrangement, position, and magnitude.

With this as a basis to the physical world, Democritus could explain all changes in the world as changes in motion of the atoms, or changes in the way that they were packed together. This was a remarkable theory which attempted to explain the whole of physics based on a small number of ideas and also brought mathematics into a fundamental physical role since the whole of the structure proposed by Democritus was quantitative and subject to mathematical laws. Another fundamental idea in Democritus's theory is that nature behaves like a machine, it is nothing more than a highly complex mechanism.

There are then questions for Democritus to answer. Where do qualities such as warmth, colour, and taste fit into the atomic theory? To Democritus atoms differ only in quantity, and all qualitative differences are only apparent and result from impressions of an observer caused by differing configurations of atoms. The properties of warmth, colour, taste are only by convention - the only things that actually exist are atoms and the Void.

Democritus's philosophy contains an early form of the conservation of energy. In his theory atoms are eternal and so is motion. Democritus explained the origin of the universe through atoms moving randomly and colliding to form larger bodies and worlds. There was no place in his theory for divine intervention. Instead he postulated a world which had always existed, and would always exist, and was filled with atoms moving randomly. Vortex motions occurred due to collisions of the atoms and in resulting vortex motion created differentiation of the atoms into different levels due only to their differing mass. This was not a world which came about through the design or purpose of some supernatural being, but rather it was a world which came about through necessity, that is from the nature of the atoms themselves.

Democritus built an ethical theory on top of his atomist philosophy. His system was purely deterministic so he could not admit freedom of choice to individuals. To Democritus freedom of choice was an illusion since we are unaware of all the causes for a decision. Democritus believed that [3]:-

... the soul will either be disturbed, so that its motion affects the body in a violent way, or it will be at rest in which case it regulates thoughts and actions harmoniously. Freedom from disturbance is the condition that causes human happiness, and this is the ethical goal.

Democritus describes the ultimate good, which he identifies with cheerfulness, as:-

... a state in which the soul lives peacefully and tranquilly, undisturbed by fear or superstition or any other feeling.

He wanted to remove the belief in gods which were, he believed, only introduced to explain phenomena for which no scientific explanation was then available.

Very little is known for certainty about Democritus's contributions to mathematics. As stated in the Oxford Classical Dictionary :-

Little is known (although much is written) about the mathematics of Democritus.

We do know that Democritus wrote many mathematical works. Diogenes Laertius (see [5]) lists his works and gives Thrasyllus as the source of this information. He wrote On numbers, On geometry, On tangencies, On mappings, On irrationals but none of these works survive. However we do know a little from other references. Heath [7] writes:-

In the Method of Archimedes, happily discovered in 1906, we are told that Democritus was the first to state the important propositions that the volume of a cone is one third of that of a cylinder having the same base and equal height, and that the volume of a pyramid is one third of that of a prism having the same base and equal height; that is to say, Democritus enunciated these propositions some fifty years or more before they were first scientifically proved by Eudoxus.

There is another intriguing piece of information about Democritus which is given by Plutarch in his Common notions against the Stoics where he reports on a dilemma proposed by Democritus as reported by the Stoic Chrysippus (see [7], [10] or [11]).

If a cone were cut by a plane parallel to the base [by which he means a plane indefinitely close to the base], what must we think of the surfaces forming the sections? Are they equal or unequal? For, if they are unequal, they will make the cone irregular as having many indentations, like steps, and unevennesses; but, if they are equal, the sections will be equal, and the cone will appear to have the property of the cylinder and to be made up of equal, not unequal, circles, which is very absurd.

There are important ideas in this dilemma. Firstly notice, as Heath points out in [7], that Democritus has the idea of a solid being the sum of infinitely many parallel planes and he may have used this idea to find the volumes of the cone and pyramid as reported by Archimedes. This idea of Democritus may have led Archimedes later to apply the same idea to great effect. This idea would eventually lead to theories of integration.

There is much discussion in [7], [8], [10] and [11] as to whether Democritus distinguished between the geometrical continuum and the physical discrete of his atomic system. Heath points out that if Democritus carried over his atomic theory to geometrical lines then there is no dilemma for him since his cone is indeed stepped with atom sized steps. Heath certainly believed that to Democritus lines were infinitely divisible. Others, see for example [10], have come to the opposite conclusion, believing that Democritus made contributions to problems of applied mathematics but, because of his atomic theory, he could not deal with the infinitesimal questions arising.
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