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The Greeks: Lost Civilizations

The Greeks: Lost Civilizations

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Matyszak’s book is full of engaging historical narration, clearly reflecting deep knowledge of various regions and time periods. Even so, he boils the complexities down so that general readers can comprehend the historical and political circumstances. As such, I highly recommend this volume to general audiences and public libraries.

Unlike most histories of ancient Greece, Philip Matyszak's book primarily focuses on Greek history which occurred outside of the Greek mainland. His story begins by describing Greek ideas, individuals, and politics before Alexander the Great, emphasizing how Greeks were spread throughout the ancient Mediterranean. The second chapter describes Alexander's movement from Macedonia, through Mesopotamia, and to India, illuminating how the demeanor of Alexander and others shifted in the duration of his campaign and the various people groups against whom he fought. With Alexander's death as a turning point, Chapter Three describes the complex succession of power that resulted in the Seleucid, Macedonian, and Ptolemaic empires. Here, Matyszak highlights how Greek discoveries and scholars were spread throughout the Hellenistic world, from Mesopotamia to Spain.

In Chapter Four, he offers a general overview of the political and military history of the Seleucid Empire, especially emphasizing how they sought to incorporate various people groups via Hellenistic ideology. Chapter Five focuses east of the Seleucid Empire, towards the Macedonian and Ptolemaic empires, in particular how the Ptolemies established Egypt, especially Alexandria, as a center for the Greek world. Chapter Six, then, describes the fall of these empires.

Chapter Seven outlines how Greek culture impacted Roman architecture, philosophy, language, and the rise of Christianity in the 1st century CE. Chapter Eight points to the Byzantine Empire as the last major stronghold of the Greek world, only to be destroyed in the 15th century CE by the Ottoman Turks. For Matyszak, this symbolized the end of the Greek world. Punctuating the legacy of the Greek world, the Epilogue identifies various ways in which the Greeks impacted and continually impact the world. He suggests, “the Greek legacy has become an integral part of a Western-based culture” (190).

The Greeks is especially unique in that it primarily emphasizes the role that Greeks played outside of Greece proper.

Overall, Matyszak's book is full of engaging historical narration, clearly reflecting deep knowledge of the complex history of various regions and time periods. Even so, he boils the complexities down so that the audience, namely general readers, can comprehend the historical and political circumstances. Moreover, The Greeks is especially unique in that it primarily emphasizes the role that Greeks played outside of Greece proper, clearly illuminating how widespread Greek populations were throughout the ancient world.

With regard to criticism, two issues stand out. First, he could have provided more depth concerning the role of Greeks in Mesopotamia. Though it is not a flaw, The Greeks would be enriched by the inclusion of how Greeks are presented in cuneiform texts from the periods discussed in the book. Second, though Greece undoubtedly influenced the modern West significantly, he pushes the conclusion too far by commenting that “In a sense, today we are all Greek” (190). While Greek ideas did influence the West significantly, we should be careful not to marginalize other cultures throughout history who impacted the West.

Seeing that Matyszak is a teacher at the Institute of Continuing Education with the University of Cambridge, his voice in presenting history is a welcome addition to books oriented towards general audiences, Matyszak being both an informed and engaging author. As such, I highly recommend The Greeks: Lost Civilizations to general audiences and public libraries.


  • Barrett, A. A. "Reviewed Work(s): The Sons of Caesar: Imperial Rome's First Dynasty by Philip Matyszak." The Historian, Vol. 70, No. 4 (2008), pp. 838-839.
  • Coro P. "KislÄ«mu Day 10, Year 31, Seleucus and Antiochus the Kings." Greek Elements in Babylonian Sources, edited by Antonetti, C. and Biagi, P. Oxbow, 2017
  • Grayson, A. K. Assyrian and Babylonian Chronicles. Eisenbrauns, 2000.
  • Moore, R. "Reviewed Work: The Enemies of Rome: From Hannibal to Attila the Hun by Philip Matyszak." The Classical Outlook, Vol. 82, No. 4 (2005), p. 162.
  • Sherwin-White, S. M. "Ritual for a Seleucid King at Babylon?." The Journal of Hellenic Studies, Vol. 103 (1983), pp. 156-159.

10 Civilizations That Disappeared Under Mysterious Circumstances

For almost as long as we've had civilization, we've lost it. There are records going back hundreds of years of explorers discovering huge temples encrusted with jungle, or giant pits full of treasure that were once grand palaces. Why did people abandon these once-thriving cities, agricultural centers, and trade routes? Often, the answer is unknown. Here are ten great civilizations whose demise remains a mystery.

1. The Maya
The Maya are perhaps the classic example of a civilization that was completely lost, its great monuments, cities and roads swallowed up by the central American jungles, and its peoples scattered to small villages. Though the languages and traditions of the Maya still survive up to the present day, the civilization's peak was during the first millennium AD, when their greatest architectural feats and massive agricultural projects covered a vast region in the Yucatán — today, an area stretching from Mexico to Guatemala and Belize. One of the largest Mesoamerican civilizations, the Maya made extensive use of writing, math, an elaborate calendar, and sophisticated engineering to build their pyramids and terraced farms. Though it's often said that the Maya civilization began a mysterious decline in roughly the year 900, a great deal of evidence points to climate change in the Yucatán combined with internecine warfare , which resulted in famine and abandonment of the city centers.

What really destroyed the Maya civilization?

One of the biggest debates in archaeology is what destroyed the extensive, highly-advanced Maya…

2. Indus Valley Civilization
One of the great civilizations of the ancient world is called simply the Indus or Harappan civilization. Thousands of years ago, it may have boasted up to 5 million people, almost 10 percent of the world's population, spread over a region that encompassed parts of today's India, Pakistan, Iran and Afghanistan. But its grand walkways (with sophisticated roadside drainage), metallurgy shops, and massive, multistory, brick hives of houses were abandoned over 3,000 years ago. It's likely that this ancient civilization, like the Maya, suffered from gradual changes in rainfall patterns that made it difficult for its peoples to raise enough food for their massive population.

Climate change ended one of the great ancient civilizations

The Indus or Harappan Civilization was one of the greatest societies in the ancient world.…

3. Easter Island
The people of Eastern Island represent another classic "lost" civilization, famed in part for its enigmatic, enormous stone statues of human heads (called Moai) lined up along the island's coastline. How did this thriving Polynesian civilization disappear after centuries of monument-building and navigating hundreds of miles of ocean waters to go from island to island? Jared Diamond sums up what many scientists now believe in his book Collapse, which is that the Easter Islanders were incredibly sophisticated, but their methods weren't sustainable. During the time they settled Easter Island, possibly between 700-1200 AD, they used up all the island's trees and agricultural resources, and then had to move on.

4. Catalhöyük
Often called the world's oldest city, Catalhöyük was part of a large city-building and agricultural civilization thriving between 9,000-7,000 years ago in what is today south-central Turkey. What's interesting about Catalhöyük is its structure, which is quite unlike most other cities since. It contained no roads as we know them, and was instead built sort of like a hive, with houses built next to each other and entered through holes in the roofs. It's believed that people farmed everything from wheat to almonds outside the city walls, and got to their homes via ladders and sidewalks that traversed their roofs. Often, these people decorated the entrances to their homes with bull skulls, and buried the bones of their honored dead beneath the packed dirt of their floors. The civilization was pre-Iron Age and pre-literate, but they nevertheless left behind ample evidence of a sophisticated society, full of art and and public ritual, that was possibly 10,000 strong at many points in its 2,000 year existence. Why did people eventually abandon the city? It is unknown.

Ancient graves suggest that family didn't really matter 9,000 years ago

Çatalhöyük is one of the world's most ancient settlements, founded in what is now Turkey around…

5. Cahokia
Long before Europeans made it to North America, the so-called Mississippians had build a great city surrounded by huge earthen pyramids and a Stonehenge-like structure made of wood to track the movements of the stars. Called Cahokia today, you can still see its remains in Illinois . At its height between 600-1400 AD, the city sprawled across 6 square miles, and contained almost a hundred earthen mounds as well as an enormous grand plaza at its center. Its population might have been as much as 40,000 people, some of whom would have lived in outlying villages. The people of this great city, the biggest so far north in Mesoamerica, were brilliant artists, architects, and farmers, creating incredible art with shells, copper, and stone. They even diverted a branch of the local Mississippi and Illinois rivers to suit their needs for irrigation. It's not entirely certain what led people to abandon the city starting in the 1200s, but some archaeologists say the city had always had problems with disease and famine (it had no sanitary system to speak of), and that people left for greener (and healthier) pastures elsewhere on the Mississippi River.

6. Göbekli Tepe
One of the most mysterious human structures ever discovered, Göbekli Tepe was probably built in 10,000 BCE, and is located in today's southern Turkey. A series of nested, circular walls and steles, or monoliths, carved evocatively with animals, the place probably served as a temple for nomadic tribes in the area. It was not a permanent residence, though it's possible a few priests lived there all year. It is the first permanent human-built structure that we have ever found, and probably represented the pinnacle of the local Mesopotamian civilization of its era. What were people worshiping there? When did they come? Were they there to do something other than worship? We may never know, but archaeologists are working hard to find out.

The mysterious remains of one of the world's first organized religions

Homo sapiens may have had religion since the dawn of our evolution, but building vast monuments to

7. Angkor
Most people have heard of the magnificent temple Angkor Wat in Cambodia. But it was only one small part of a massive urban civilization during the Khmer Empire called Angkor. The city flourished during the late middle ages, from 1000-1200 AD, and may have supported up to a million people. There are a lot of good reasons why Angkor may have fallen, ranging from war to natural disaster. Now most of it lies beneath the jungle. A marvel of architecture and Hindu culture, the city is mysterious mostly because we still aren't certain how many people lived there. Given all the roads and canals connecting its many regions, some archaeologists believe it may have been the biggest urban site in the world at its height.

8. The Turquoise Mountain
Though not every crumbling monument represents a lost civilization, some of them do. Such is the case with the Minaret of Jam , a gorgeous architectural feat built in the 1100s as part of a city in Afghanistan, where archaeological remains suggest that it was a cosmopolitan area where many religions, including Jews, Christians, and Muslims, lived together harmoniously for hundreds of years. It's possible that the incredible minaret was part of the lost medieval capital of Afghanistan, called Turquoise Mountain.

9. Niya
Now a desolate spot in the Taklamakan Desert of Xinjiang province in China, 1600 years ago Niya was a thriving city in an oasis along the famous Silk Road. For the past two centuries, archaeologists have uncovered countless treasures in the dusty, shattered remains of what was once a graceful town full of wooden houses and temples. In a sense, Niya is a relic of the lost civilization of the early Silk Road, a trade route that linked China with Central Asia, Africa, and Europe. Many groups traveled the Silk Road , from wealthy merchants and religious pilgrims to scholars and scientists, exchanging ideas and creating a complex, enlightened culture everywhere the 4,000 mile Silk Road passed. The route underwent many changes, but its importance as a trade route waned as the Mongol Empire collapsed in the 1300s. Traders afterwards preferred sea routes for trade with China.

Forgotten Places: Books About Lost Cities & Lost Civilizations

In Four Lost Cities, acclaimed science journalist Annalee Newitz takes readers on an entertaining and mind-bending adventure into the deep history of urban life. Investigating across the centuries and around the world, Newitz explores the rise and fall of four ancient cities. Four Lost Cities is a journey into the forgotten past, but, foreseeing a future in which the majority of people on Earth will be living in cities, it may also reveal something of our own fate.

The films and books abound, particularly in fiction: a group of explorers hack their way through a jungle in search of a mysterious lost city and its trove of treasure. But through a maze of traps, illness, surprises, suspense, romance, adventure, and villains, they end up withdrawing, the secrets and the treasure lost, the rush of discovery fresh in the hearts of our protagonists.

While that classic action movie is fun, there are real-world stories too: lost cities and lost civilizations rumored, discovered, and uncovered. The world of archaeology has experienced true moments like this, whether it be explorers disappearing under mysterious circumstances or a few adventurers making an archaeological discovery that shifts history altogether.

Unfortunately, the world of adventure and exploration writing seems to often fall to white authors, often men, and I was largely unable to find nonfiction books on lost cities and lost civilizations by women, gender-nonconforming writers, and authors of color. If you find any such titles, please let me know. I am particularly invested in finding such books, as these lost places and mysteries are most often set in places where the majority of the population is non-white, and in places that have been colonized or &ldquodiscovered&rdquo by white men. There are many books out there, too, that feature imperialist or racist outlooks &mdash and even books that have been partially recanted because the author realized it wasn&rsquot their story to tell. I am looking forward with anticipation to the growth of this genre into a more interesting, complex, diverse genre.

Below are eight books about lost cities and lost civilizations that are exciting, that will charge your wanderlust, that will make you want to explore, discover, and dig deeper into the histories you may know little about.

The Lost City of the Monkey God by Douglas Preston

Legends of the White City had swirled ever since the day the brutal invader Cortés arrived in Honduras. Indigenous people told stories of a city to which people fled to escape the Spanish invaders &mdash but warned that anyone who found it would die. In 1940, journalist Theodore Morde claimed to have found it, but died by suicide several years later without ever substantiating the claim. In 2012, author Preston would join a group of scientists on a quest to find the city, and this book chronicles the story of their journey, their discoveries, and the disease that struck them shortly after returning from their journey. It&rsquos a suspenseful true story that features drama and adventure.

Unruly Places: Lost Spaces, Secret Cities, and Other Inscrutable Geographies by Alastair Bonnett

People tend to think that there&rsquos nothing unexplored now, thanks to the internet and its corners. But Bonnett bursts that bubble in a spectacular, fantastical way, by guiding us through unexpected places &mdash from Sealand, the gun platform off the English coast that a British citizen claimed as a nation, to Sandy Island, a place that was on maps until just recently despite never existing, to moving villages, no man&rsquos lands, and enclaves that push at our understanding of borders and the undiscovered.

The Lost City of Z: A Tale of Deadly Obsession in the Amazon by David Grann

In 1925, an explorer named Percy Fawcett went to the Amazon to try and find an ancient lost history after spending years making the case that an ancient civilization he called Z existed. But then his expedition vanished. It created an obsession for many, all of whom wanted to find the civilization or find out what happened to Fawcett, and all failed. Grann digs into that series of stories and tales, picking apart the evidence Fawcett had gathered, and then decides to go himself. His journey, and the way he looks into the psychology and impact of the journey on the people who have attempted it, is fascinating and entertaining.

Gods, Graves, and Scholars: The Story of Archaeology by C.W. Ceram, Translated by Sophie Wilkins and E.B. Garside

Ceram&rsquos book is a dramatic narrative that paints the picture of archaeology and the way man searches for his past &mdash he digs into a lot of discoveries, from the first glimpse of Tutankhamen&rsquos tomb, to the remains of Troy, to the discoveries of Chichen Itza, the Mayan pyramids, the Rosetta stone, and more. While it&rsquos nonfiction, it has a distinctive adventurous feel. Reviewers mention that it&rsquos an outdated text in many ways &mdash between updated information and a western-centered outlook. But for many, it serves as a fantastic and accessible introduction to archaeology and discovery of early great civilizations.

Rivers of Power: How a Natural Force Raised Kingdoms, Destroyed Civilizations, and Shapes Our World by Laurence C. Smith

This one is a little different than the others on this list, but I think it evokes the same rich feeling of exploration, wonder, and mystery. Smith looks at the underappreciated but undeniable link between rivers and civilization &mdash their influence on our lives and how they&rsquove been shaped, their influence on borders, war, religion &mdash as well as the stress test of flooding, the controversy of dam-building. It&rsquos a fascinating book of environmental history that shines a light on the mysterious forces that can make and break civilizations, both early and modern.

Pleasure of Ruins by Robin Macaulay

This travelogue written in the 1950s is a love letter to famous sites that Macaulay visited in their decaying state. She writes about allowing them to remain how they are, without the efforts of &ldquorestoration,&rdquo and captures beautiful photos of these ruins alongside quotes from poets and authors who loved them, as Macaulay adds her own notes, observations, and historic facts and lessons. It&rsquos more of an exploratory, creative work than most of the books on this list: Macaulay wants to get at something about what it means to explore ruins, to see them, to wander among them, and what ruins mean to us as people.

Forgotten Peoples of the Ancient World by Philip Matyszak

Obviously &ldquoforgotten&rdquo is a stretch, to some degree, as this book is pitched towards western audiences. Nevertheless, this book is an introduction to the diversity of ancient peoples focused in the Mediterranean and in the Tigris and Euphrates Valley. Matyszak is right that people remember and learn in their history classes about the Egyptians, Babylonians, Hebrews, Greeks, Romans, and other such classic empires &mdash but Matyszak introduces readers to the Akkadians, the Hephthalites, the Hyksos, and other &ldquolost peoples&rdquo who existed in those areas from 3000 BCE to 550 CE. The book includes illustrated artifacts and artworks as well, and reminds readers that the empires we learn about aren&rsquot the only ones that existed and thrived.

Jungle of Stone: The Extraordinary Journey of the American Explorer Who Discovered the Lost Civilization of the Mayans by William Carlsen

In 1839, adventurers John Lloyd Stephens and Frederick Catherwood decided to pursue rumors of extraordinary ruins in the jungles of Central America. Carlsen charts what they endured as they uncovered and documented the remains of the ancient Mayans and the book they wrote and illustrated about the experience, notable not only because of their discoveries, but because they seemed to grasp the significance of finding such a sophisticated ancient civilization outside of the western world &mdash the Mayans were already constructing their pyramids when classical Greece was flowering. Carlsen brings the often forgotten archaeologists and authors into the spotlight.

Ancient Rome – History

History of Ancient Rome begins in a small village in central Italy this unassuming village would grow into a small metropolis, conquer and control all of Italy, southern Europe, the Middle East, and Egypt, and find itself, by the start of AD time, the most powerful and largest empire in the world. They managed what no other people had managed before: the ruled the entire world under a single administration for a considerable amount of time. This imperial rule, which extended from Great Britain to Egypt, from Spain to Mesopotamia, was a period of remarkable peace. The Romans – citizens of ancient Rome, would look to their empire as the instrument that brought law and justice to the rest of the world in some sense, the relative peace and stability they brought to the world did support this view.

They were, however, a military state, and they ruled over this vast territory by maintaining a strong military presence in subject countries. An immensely practical people, the Romans devoted much of their brilliance to military strategy and technology, administration, and law, all in support of the vast world government that they built.

Ancient Rome, however, was responsible for more than just military and administrative genius. Culturally, the Romans had a slight inferiority complex in regards to the Greeks, who had begun their city-states only a few centuries before the rise of the Roman republic. The Romans, however, derived much of their culture from the Greeks: art, architecture, philosophy, and even religion. However, the Romans changed much of this culture, adapting it to their own particular world view and practical needs. It is this changed Greek culture, which we call Graeco-Roman culture, that was handed down to the European civilizations in late antiquity and the Renaissance.

People have lived in Italy for a long time, because Italy is a fairly fertile area, but the time when Rome was powerful did not begin until after the greatest power of Egypt and Greece.

History of Ancient Rome is usually divided into three main periods: before the rise of Rome, the Roman Republic, and the Roman Empire. The Empire is usually divided up according to who was emperor.

The Top Ten Most Important Ancient Documents Lost to History

From Rome’s holiest texts to a Chinese manuscript that wouldn’t have fit inside a shipping container, here’s our top ten list of the most important ancient documents that no longer exist:

Sibylline Books
Roman leaders consulted these oracular sayings during political crises for perhaps 900 years. The originals burned in 83 B.C. Their replacements were allegedly destroyed by a 5th-century Roman general who feared that invading Visigoths would use them.

Sappho’s Poems
In the 6th century B.C. she composed 10,000 lines of poetry, filling nine volumes. Fewer than 70 complete lines exist. But those have made Lesbos’ most famous daughter (as classicist Daniel Mendelsohn has called her) a revered lyric poet of erotic love.

Aeschylus’ Achilleis
The famed Greek dramatist’s (c. 525-456 B.C.) tragic trilogy is thought to have reframed the Trojan War as a reckoning with contemporary Athenian democracy. An estimated total of more than 80 of his works are lost to history. Seven plays survive.

Mayan Codices​
Out of perhaps thousands of bark-cloth books recording Mayan history, culture and religion—written in hieroglyphics as early as the 9th century—fewer than five texts survive. The rest were burned by conquistadors and Catholic monks in the 16th century.

This collection of beloved Indian animal fables, written as early as 100 B.C., is known to us from early translations in Pahlavi (now lost), Syriac and Arabic—the original Sanskrit source vanished. A Hebrew translation was the basis for a popular version in medieval Europe.

Zoroastrian Avesta
The holy book of ancient Persia’s quasi-monotheistic creed survives as a sprawling collection of fragments—an estimated one-quarter of the original text. The last complete manuscripts may have burned when Alexander the Great conquered Persepolis in 330 B.C.

Confucius’ Sixth Classic
We still have the “Five Classics” traditionally ascribed to the Chinese philosopher, covering poetry, rhetoric, ancient rites, history and divination. The sixth, on music, may have disappeared in the 3rd-century-B.C. “Burning of Books and Burying of Scholars.”

Yongle Encyclopedia
More than 2,000 scholars contributed to this 11,000-volume Ming dynasty text on subjects ranging from agriculture to art, theology and natural sciences. Half of 800 remaining volumes burned in the Boxer Rebellion of 1900 3 percent of the original text survives.

Ibn Al-Haytham’s Treatises
The Iraq-born medieval mathematician, astronomer and physicist, whose work on optics (in a Latin translation of the Arabic) and the scientific method influenced thinkers in Europe, wrote more than 200 works. Only 55 survive in any language.

Book of the Chronicles of the Kings of Israel 
The Hebrew Bible refers to some 20 works that no longer exist. The frequently cited “Chronicles” was a detailed early Iron Age history from which numerous other biblical narratives may have been drawn.

(Harry Campbell)

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The Greeks: Lost Civilizations - History

The Origins of Greek Mathematics

  • The most impressive of all civilizations,
  • The most influential in Western culture,
  • The most decisive in founding mathematics as we know it.
  • The best estimate is that the Greek civilization dates back to 2800 B.C. -- just about the time of the construction of the great pyramids in Egypt. The Greeks settled in Asia Minor, possibly their original home, in the area of modern Greece, and in southern Italy, Sicily, Crete, Rhodes, Delos, and North Africa.
  • About 775 B.C. they changed from a hieroglyphic writing to the Phoenician alphabet. This allowed them to become more literate, or at least more facile in their ability to express conceptual thought.
  • The ancient Greek civilization lasted until about 600 B.C.
  • The Egyptian and Babylonian influence was greatest in Miletus, a city of Ionia in Asia Minor and the birthplace of Greek philosophy, mathematics and science.
  • From the viewpoint of its mathematics, it is best to distinguish between the two periods: the classical period from about 600 B.C. to 300 B.C. and the Alexandrian or Hellenistic period from 300 B.C. to 300 A.D. Indeed, from about 350 B.C. the center of mathematics moved from Athens to Alexandria (in Egypt), the city built by Alexander the Great (358 -323 B.C.). It remained the center of mathematics for a millennium until the library was sacked by the Muslims in about 700 A.D.

The Sources of Greek Mathematics

In actual fact, our direct knowledge of Greek mathematics is less reliable than that of the older Egyptian and Babylonian mathematics, because none of the original manuscripts are extant.

  • Byzantine Greek codices (manuscript books) written 500-1500 years after the Greek works were composed.
  • Arabic translations of Greek works and Latin translations of the Arabic versions. (Were there changes to the originals?)
  • Moreover, we do not know even if these works were made from the originals. For example, Heron made a number of changes in Euclid's Elements , adding new cases, providing different proofs and converses. Likewise for Theon of Alexandria (400 A. D.).
  • Eudemus ( century B.C.), a member of Aristotle's school wrote histories of arithmetic, geometry and astronomy (lost),
  • Theophrastus (c. 372-c. 287 B.C.) wrote a history of physics (lost).
  • Pappus (late cent A.D.) wrote the Mathematical Collection , an account of classical mathematics from Euclid to Ptolemy (extant).
  • Pappus wrote Treasury of Analysis , a collection of the Greek works themselves (lost).
  • Proclus (A.D. 410-485) wrote the Commentary , treating Book I of Euclid and contains quotations due to Eudemus (extant).
  • various fragments of others.

The Major Schools of Greek Mathematics

    The Ionian School was founded by Thales (c. 643- c. 546 B.C.). Students included Anaximander (c. 610-c. 547 B.C.) and Anaximenes (c. 550-c. 480 B.C.). Thales is sometimes credited with having given the first deductive proofs.

  • The importance of the Ionian School for philosophy and the philosophy of science is however without dispute.
  1. Philosophy.
  2. The study of proportion.
  3. The study of plane and solid geometry.
  4. Number theory.
  5. The theory of proof.
  6. The discovery of incommensurables.

Zeno's Paradoxes Zeno constructed his paradoxes to illustrate that current notions of motion are unclear, that whether one viewed time or space as continuous or discrete, there are contradictions. They are

Dichotomy. To get to a fixed point one must cover the halfway mark, and then the halfway mark of what remains, etc.

Achilles. Essentially the same for a moving point.

Arrow. An object in flight occupies a space equal to itself but that which occupies a space equal to itself is not in motion.

Stade. Suppose there is a smallest instant of time. Then time must be further divisible!

Now, the idea is this: if there is a smallest instant of time and if the farthest that a block can move in that instant is the length of one block, then if we move the set B to the right that length in the smallest instant and the set C to the left in that instant, then the net shift of the sets B and C is two blocks. Thus there must be a smaller instant of time when the relative shift is just one block.

  • He was a proponent of the materialistic atomic doctrine.
  • He wrote books on numbers, geometry, tangencies, and irrationals. (His work in geometry was said to be significant.)
  • He discovered that the volumes of a cone and a pyramid are 1/3 the volumes of the respective cylinder and prism.

How to draw a trisectrix: Imagine a radial arm (like a minute hand of a clock) rotating at uniform speed about the origin from the vertical position to the horizontal position in some fixed period of time. (That is from 12 O'clock to 3 O'clock.) The tip of the arm makes a quarter circle as shown in red in the picture. Now imagine a horizontal (parallel to the x -axis) arm falling at uniform speed from the top of arm to the origin in exactly the same time. The trisectrix is the intersection of the two arms. The curve traced in black is the trisectrix. As you can see, the trisectrix is a dynamically generated curve. The Platonic School and those subsequent did not accept such curves as sufficiently ``pure" for the purposes of geometric constructions.

Hippocrates of Chios, though probably a Pythagorean computed the quadrature of certain lunes. (This is the first correct proof of the area of a curvilinear figure.) He also was able to duplicate the cube by finding two mean proportionals (Take a =1 and b =2 in a : x = x : y = y : b . Solution: , the cube root of 2.)

Pythagorean forerunners of the school, Theodorus of Cyrene and Archytas of Tarentum , through their teachings, produced a strong Pythagorean influence in the entire Platonic school.

  • Members of the school included Menaechmus and his brother Dinostratus and Theaetetus (c. 415-369 B.C.)
  • According to Proclus, Menaechmus was one of those who ``made the whole of geometry more perfect". We know little of the details. He was the teacher of Alexander the great, and when Alexander asked for a shortcut to geometry, he is said to have replied,

  • Eudoxus developed the theory of proportion, partly to account for and study the incommensurables (irrationals).
  • He produced many theorems in plane geometry and furthered the logical organization of proof.
  • He also introduced the notion of magnitude .
  • He gave the first rigorous proof on the quadrature of the circle. (Proposition. The areas of two circles are as the squares of their diameters. )

Aristotle set the philosophy of physics, mathematics, and reality on a foundations that would carry it to modern times.

He viewed the sciences as being of three types -- theoretical (math physics, logic and metaphysics), productive (the arts), and the practical (ethics, politics).

He contributed little to mathematics however,

Aristotle regards the notion of definition as a significant aspect of argument. He required that definitions reference to prior objects. The definition, 'A point is that which has no part' , would be unacceptable.

  • Axioms include the laws of logic, the law of contradiction, etc.
  • The postulates need not be self-evident, but their truth must be sustained by the results derived from them.

Aristotle explored the relation of the point to the line -- again the problem of the indecomposable and decomposable.

Aristotle makes the distinction between potential infinity and actual infinity . He states only the former actually exists, in all regards.

The Ancient Civilizations Historical Omnibus: Lost Civilizations, Greek Mythology, and Dictators from Ancient History

This book is a combined edition of three books: “Lost Civilizations: 10 Societies that Vanished Without a Trace” “Greek Gods and Goddesses Gone Wild: Bad Behavior and Divine Excess From Zeus&aposs Philandering to Dionysus&aposs Benders” and “History&aposs Worst Dictators: A Short Guide to the Most Brutal Rulers, From Emperor Nero to Ivan the Terribl THREE BOOKS IN ONE -- SAVE 40%!!

This book is a combined edition of three books: “Lost Civilizations: 10 Societies that Vanished Without a Trace” “Greek Gods and Goddesses Gone Wild: Bad Behavior and Divine Excess From Zeus's Philandering to Dionysus's Benders” and “History's Worst Dictators: A Short Guide to the Most Brutal Rulers, From Emperor Nero to Ivan the Terrible.”


From the #1 bestselling author of History's Greatest Generals comes an exciting new book on the greatest societies in history that vanished without a trace, and why their disappearance still haunts us today.

Whether it is Plato's lost city of Atlantis, a technological advanced utopia that sank into the ocean "in a single day and night of misfortune" the colony of Roanoke, whose early American settlers were swallowed up in the wild forest lands of the unexplored continent, or the Ancient American Explorers, who managed to arrive to the New World 2,000 years before Columbus, the disappearance of these societies is as cryptic as it is implausible.

This book will look at cultures of the 10 greatest lost civilizations in history. Some were millenia ahead their neighbors, such as the Indus Valley Civilization, which had better city planning in 3,000 B.C. than any European capital in the 18th century. Others left behind baffling mysteries, such as the Ancient Pueblo Peoples (formerly known as the Anasazi), whose cliff-dwelling houses were so inaccessible that every member of society would have to be an expert-level rock climber.

Whatever the nature of their disappearance, these lost civilizations offer many lessons for us today -- even the greatest of societies can disappear, and that includes us.


Why did the Greek gods and goddesses behave so badly? Because it is one thing for God to make man in his own image and quite another thing for man to return the favor.

Whether it is Zeus constantly philandering and turning his mistress into a cow in order to escape Hera's wrath or Artemis turning a Greek voyeur into a deer to be consumed by his own hunting dogs, petty feuding and revenge seemed to be the national pastime on Mount Olympus among the Greek gods and goddesses.

The actions of the ancient Greek gods and goddesses show that despite their intelligence, strength, and power over the affairs of life, they were all-too-human and subject to earthly temptation. They also demonstrate the dangers that come with having too much of a good thing.


This is the way English philosopher Thomas Hobbes described the living conditions into which humans inevitably fall without a strong, central authority. However, Hobbes would agree that living under a brutal dictator could lead to the same conditions. He would know -- he lived a century after the bloody reign of Henry VIII, 150 years after Spanish conquistadors witnessed Montezuma II offering up thousands of human sacrifices, and four centuries after Genghis Khan rode throughout Eurasia and left behind enough death and destruction to depopulate major parts of the globe.

This exciting new book from historian Michael Rank looks at the lives and times of the worst dictators in history. You will learn about their reigns and violent actions, such as.

- Emperor Nero's murder of family members, suspected arson of Rome, and widespread execution of religious minorities, which caused many early Christians to believe that he was the Antichrist

Downfall of Ancient Greece Caused by 300-Year Drought

A 300-year drought may have caused the demise of several Mediterranean cultures, including ancient Greece, new research suggests.

A sharp drop in rainfall may have led to the collapse of several eastern Mediterranean civilizations, including ancient Greece, around 3,200 years ago. The resulting famine and conflict may help explain why the entire Hittite culture, chariot-riding people who ruled most of the region of Anatolia, vanished from the planet, according to a study published in August in the journal PLOS ONE.

Lost golden period

Even during the heyday of Classical Greek civilization, there were hints of an earlier culture that was lost. Homer's "Iliad," written in the eighth century B.C. about a legendary war between Sparta and Troy, paints a picture of sophisticated Greek city-states, which archaeological evidence suggests once existed. [The 7 Most Mysterious Archaeological Discoveries]

"The classical Greek folks knew from the very beginning that they were coming out of a dark age," said Brandon Lee Drake, an archaeologist at the University of New Mexico, who was not involved in the study.

The ancient Hittite empire of Anatolia began a precipitous decline around 3,300 B.C. Around the same time, the Egyptian empire was invaded by marauding sea bandits, called the Sea People, and the ancient Mycenaean culture of Greece collapsed. Over the next 400 years, ancient cities were burned to the ground and were never rebuilt, Drake said.

But the cause of this Bronze Age collapse has been shrouded in mystery. Some archaeologists believed economic hardships caused the demise, while others proposed that massive tsunamis, earthquakes or a mega-drought was the cause.

Past studies looking for drought typically only found evidence showing it occurred for short periods of time, making it hard to make conclusions about the whole period, Drake said.


Toward that end, David Kaniewski, an archaeologist at the University of Paul Sabatier-Toulouse in France, and his colleagues collected ancient sediment cores from Larnaca Salt Lake, near Hala Sultan Tekke in Cyprus. The lake was once a harbor, but became landlocked thousands of years ago.

A decline in marine plankton and pollen from marine sea grass revealed that the lake was once a harbor that opened to the sea until around 1450 B.C., when the harbor transformed over 100 years into a landlocked lagoon. Pollen also revealed that by 1200 B.C., agriculture in the area dwindled and didn't rebound until about 850 B.C.

"This climate shift caused crop failures, dearth and famine, which precipitated or hastened socioeconomic crises and forced regional human migrations," the authors write in the paper.

The results bolster the notion that a massive drought caused the Bronze Age collapse, Drake said.

"It's getting hard to argue that there wasn't as significant change in climate at that time," Drake told LiveScience.

Famine may have caused the huge migration of people en masse — which may be the reason that the mysterious Sea People who invaded Egypt brought their families along, Drake said.

As ancient cultures battled for dwindling resources, they burned the great cities of the day to the ground. In the heart of these dark ages, the ancient Mycenaens lost their writing system, called Linear B, and correspondence between countries slowed to a trickle, Drake said.

Ironically, those who suffered through those dark times may not have realized the cause of their misery.

"It happened over 200 years. People may not have even recognized the climate was changing, because it was happening so slowly over their lifetime," Drake said.

Follow Tia Ghose on Twitter and Google+. Follow LiveScience @livescience, Facebook & Google+. Original article on LiveScience.

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There Were Pre-Adamic Lost Civilizations On Earth and the History Avoids Mentioning These

If we carefully read the Bible we find indications that before Adam’s civilization there was another civilization that God destroyed and then created Adam and Eve. Jeremiah’s book says that God “ravaged” the earth before he created Adam.

The Bible scholars believe that this passage in the Bible, and others, refers to the fact that God once destroyed the humans and animals he created before Adam.

I invite you to read the Old Testament carefully and you will find surprising things.

Emperor Roman Julian The Apostate, who lived between 331-363 AD, and Calvinist theologian Isaac of Peyrere, who lived between 1596 and 1676, said that in the distant past on Earth there was a civilization before Adam.

Historian Mayo says the beings that existed before Adam was a true race.

As is the case with the very old Earth’s history, there are many enigmas that we can not yet elucidate, but there are more and more clues that the history of human civilizations has interesting chapters and slowly, this pre-historic puzzle, will be completed.

Archaeologists have discovered in Colombia the skeleton of a 100 million-year-old man’s hand.

In Swaziland, they have discovered a gigantic humanoid footprint of 200 million years.

Where do dinosaurs are placed in this history?

All the clues lead us to the conclusion that Genesis was, in fact, a Re-Genesis. Is it possible that the dinosaurs lived before the Adamic civilization? Can the theologians finally find common ground with evolutionists?

Hidden history : lost civilizations, secret knowledge, and ancient mysteries


Watch the video: ΤΟ ΘΑΥΜΑ ΤΩΝ ΕΛΛΗΝΩΝ, ΕΛΛ. ΥΠΟΤΙΤΛΟΙ La légende des sciences (June 2022).


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