Chapter Three:
Alexandria
In the year 356 BCE, in the city of Pella, between the Aegean and Adriatic Seas in southeastern Europe, Queen Olympias, the daughter of King Neoptolemus of Epirus, gave birth to a son. Her husband, King Philip II, had conquered the Greek peninsula through decades of warfare with the powerful city‑states of Thebes and Athens, buying off enemies who would be bought, crushing and enslaving those who would not. Philip's son, called after his uncle, the King's brother, bore the name many men in his family shared and passed down. He would be educated in warfare, and grow with his familial disposition for violence, conquest and power. The name given the boy was Alexander. His father's kingdom was Macedon.
Then, just as now, the scions of the ruling elite attended the best schools, and at the age of 13 Alexander arrived at Athens and embarked on three years of study with Aristotle at Plato's famous Academy. With Aristotle, Alexander explored philosophy, science and medicine. But Alexander's real education had little to do with scrolls, much to do with swords.
In 340 BCE when Alexander was 16 his father attacked Byzantium and left his son at the head of his kingdom in his absence. Alexander—at an age most American boys are just learning to drive—seized the opportunity to attack the Maedi in Thrace. He defeated them.
Within four years, a series of military victories and the murder of his father by a begrudged Macedonian nobleman elevated Alexander to the throne. Across the Dardanelles to the east, in the vast and mighty Persian Empire, Alexander saw not a threat but a prize: wealth and victories which would secure his power and guarantee the support of the army. In 334 BCE, at the age of 22, Alexander left Macedon in the charge of his father's trusted deputy Antipater and led an army across the straights into Asia Minor and Persian territory. The following year he conquered that province, then Cappadocia, Syria and Phoenecia, slaughtering the men he met on the field of battle, and making slaves of their wives and children in the subjugated cities.
In November 332 BCE Alexander and his army arrived in Egypt, where the Egyptians, who shed few tears at the vanquishment of their Persian masters, welcomed them as liberators. Alexander paid proper respect and made sacrifice to their gods and became pharaoh with the blessings of the Egyptian priests.
That winter Alexander traveled along the Mediterranean coast west of the Nile, on his way to the Oasis of Siwa to consult an oracle to glean how favorable the heavens would be before resuming his campaign east against the Persians. On the way he came across a neck of land between the sea and the freshwater lake of Mareotis. Close offshore lay the island of Pharos with an excellent harbor. With access to the port, fresh drinking water, and the hinterlands joined to the coast by the Nile, Alexander recognized it as a promising site and chose it to be his capital in Egypt. Greek architect Dinocrates designed the city, with Alexander, the military genius, choosing the locations for the foundations of the city's defensive walls. On April 7, 331 BCE the capital was dedicated, and named Alexandria to honor its founding king.
Ancient Alexandria became an unparalleled wonder: New York, London, Oxford, Cambridge and Miami Beach rolled into one. In the two centuries after its founding it grew to one of the largest cities in the world—attracting immigrants and tourists from around the Mediterranean—and a center of learning never before seen on the planet. In the harbor on Pharos a lighthouse was constructed which is renowned as one of the Seven Wonders of the ancient world. In Alexandria a great library, known as the Mouseion, became the center of systematic study and science unmatched for over a thousand years. In it resided the greatest scholars, not just of that time, but to that point ever known in the West. There Dionysius of Thrace first defined the parts of speech. There Herophilus discovered that thought occurred in the brain rather than the heart. There Heron invented the steam engine and wrote the first book on robotics. There Eratosthenes discovered the circumference of the Earth, and Archimedes laid the foundations for calculus.
The brightness of these stars of science however dimmed beside the fame of another Alexandrian mathematician, a man of wit, and occasional sarcasm, renowned as a patient teacher and a kind man. This unpretentious soul would be credited with creating, in addition to several other less influential titles, a written work which had a staggering impact on the world, an impact reverberating yet today. Eventually readership of this collection would rival that of the Bible, and would be credited with stimulating the scientific interest of some notable young eggheads named Kepler, Newton and Einstein. The book was called the Elements, and the mathematician Euclid.
Euclid is known to have authored at least ten books on science. Of these, the Elements is his masterpiece and the source of his enduring legacy. It's a 13 volume collection of Greek mathematics and geometry, covering the full range of those topics, from proportions to prime numbers, plane geometry to regular solids.
To an extent the Elements was an editorial job. Euclid compiled the massive collection from numerous earlier sources. Portions of the Elements can be recognized as drawn from books by Hippocrates of Chios, who preceded Euclid by 200 years, and Theudius, who 100 years before Euclid wrote the textbook on the geometry probably used by Aristotle and which may have subsequently been used to teach Alexander. The hand of Theaetetus, a student of Pythagoras, can be seen beneath books X and XIII of the Elements; Eudoxus, a professor at the Alexandria school, can be seen behind books V and XII.
It was the format of Elements however—undisputedly Euclid's original work—which made it superior. Each volume began with a set of postulates and theorems, which were then followed by proofs. Prior to Euclid each mathematical school in the ancient world had its own textbook with its own set of postulates, not all built on a solid foundation of reason. Euclid's method spelled out each problem clearly, then proved it, then moved on to the next, in a standardized, methodical way. Euclid's exhaustively rendered Elements proved a far superior text and quickly pushed the older books on geometry aside.
Very, very little information exists about Euclid and his life. No one knows the exact year or place of his birth, but inferences have been made from the few sources there are, though those are separated from the facts they report by several centuries and must thus be read with a touch of skepticism.
The Greek philosopher Proclus lived in Constantinople 800 years after Euclid. In the midst of a description of several students of Plato he digressed to record:
"Euclid... put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy, for Archimedes, who came immediately after the first [Ptolemy] makes mention of Euclid: and further they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements [sic], and he answered that there was no royal road to geometry. He [Euclid] is then younger than the pupils of Plato, but older than Eratosthenes and Archimedes, for the latter were contemporary with one another, as Eratosthenes somewhere says."
This information from Proclus allows scholars to deduce the time in which Euclid lived and worked from the known dates of the lives of Plato, Archimedes and Eratosthenes, as well as those of the reign of the first Ptolemy, the first Macedonian king of Egypt who succeeded Alexander, thus placing Euclid's life sometime around 300 BCE. If, as Proclus says, Euclid was in fact a student of Plato, it would suggest that he acquired his scholarly training as one of the earliest students at the Academy in Athens.
Scholars are able to locate Euclid in Alexandria and surmise that he taught and was founder of a school there based upon information from another Alexandrian mathematician named Pappus, who lived in that city 600 years after Euclid. While writing of a student of mathematics named Apollonius, who traveled to Alexandria to study mathematics among Euclid's students around 200 BCE, Pappus remarked: "'[Apollonius] spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought." Pappus also wrote of Euclid directly, commenting on his "scrupulous fairness and his exemplary kindliness towards all who could advance the mathematical science to however small an extent... [he] being moreover in no wise contentious and, though exact, yet no braggart..."
The final bit of folklore about Euclid survives in the collection of Johannes Stobaeus, a Greek of the 5th century CE, who assembled an anthology of classical writings for his son to study in which are preserved excerpts from many earlier Greek texts which are now otherwise lost. Along with a reiteration of Proclus' tale of Euclid's contention that there was "no royal road to geometry," Stobaeus' anecdote is the other most famous story about Euclid, and the two are often quoted together as evidence of Euclid's sense of humor. "[S]omeone who had just begun to read geometry with Euclid," Stobaeus wrote, "when he had learnt the first theorem, asked Euclid, 'But what shall I get by learning these things?' Euclid called his slave and said, 'Give him threepence, since he must make gain out of what he learns.'"
Elements was revised by later Greek authors and eventually translated into Arabic. The collection weathered the Dark Ages of Europe in the libraries of the Islamic empires of the Middle East. English scholar Adelard of Bath made the first known Latin translation in 1120 after obtaining a copy of an Arabic version in Spain. The first printed collection of the Elements appeared in 1482 and more than 1,000 editions have appeared since. Sir Henry Billingsley of Oxford University in England made the first translation of the Elements into English in 1570.
For over 2,000 years Euclid's Elements has been the ur‑source for the study of geometry, and the practice of its daughter arts of engineering, architecture, construction and survey.
What, then, does all this have to do with a narrow, swampy plain and the highlands above it on the shores of a glacial lake almost seven thousand miles and more than two millennia distant from Euclid and Alexandria and the world of the ancient Greeks? When the constituent players all came together on the bluff above the mouth of the Cuyahoga River in the fall of 1796 it all made perfect sense, and it constituted an astute tribute to the Classical mathematician who survived the centuries through his work. But that story, for the moment, will wait.
The information in Chapter Three is drawn from the following sources:
"Alexandria, Egypt." University of South Florida Department of Civil and Environmental Engineering website. http://ce.eng.usf.edu/pharos/Alexandria/index.html
Golba, Paul. "Euclid." Seaton Hall University website. www.shu.edu/html/teaching/math/reals/ history/euclid.html
Heath, Thomas L., editor. The Thirteen Books of Euclid's Elements. Dover Publications, 1956. Volumes 11, 12 & 13.
O'Connor, J.J. and Robertson, E.F. "Euclid of Alexandria." University of St. Andrew's Scotland School of
Mathematics and Statistics website. www-groups.dcs.st-andrews.ac.uk/~history/ Mathematics/Euclid.html
Sagan, Carl. Cosmos. Ballentine. 1980.