Pythagoras, Plato, Aristotle, Aristarchus, Eratosthenes and Ptolemy

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Pythagoras of Samos (approx. 570BC – 495 BC)

Pythagoras was a Greek philosopher who made a great many contributions to the history of mathematics, science, astronomy and music theory.  He is perhaps best known for his contribution to mathematics however  – the famed Pythagoras theorem. The Sumerians had known this theory to be true thousands of years earlier but it was Pythagoras who proved the idea correct. The theorem states that the square of the hypotenuse (the long side) of a right-angled triangle, is always the exact same as the sum of the squares of the other two sides.

This theory and trigonometry proved extremely useful in astronomy and science, when calculating distances between objects. Pythagoras was also the first person to suggest that the Earth is sphere shaped. This idea was proposed using constellation observations, by studying the earth’s circular shadow on the moon during a lunar eclipse and also his belief that every thing could be explained mathematically (he felt that the sphere was a perfect shape).  As well as this, he made the astronomic observation that the evening star and the morning star were in fact the very same object (Venus).

As well as founding the Brotherhood of Pythagoreans (who coined the term mathematics) it was Pythagoras who coined the term philosophy.
Others influenced by his thoughts and ideas included both Plato and Aristotle, but unfortunately none of his texts exist today.

Plato  (approx. 427 BC – 347 BC)

Plato, a Greek philosopher was once a student of  the famous philosopher Socrates. Philosophy is about reasoning, a fundamental study of knowledge and existence and of how everything fits together. Plato believed that the entire cosmos was precisely formed with geometric shapes and that they were the key to understanding the mysteries of the universe. Plato felt that complex orbit paths were actually just simple and circular paths, repeating inside of each other around the earth.

However, these observations couldn’t quite explain the complicated motion paths of the heavenly objects that each moved at different rates but he did use mathematics to try to explain movement. He  believed that we forget knowledge at birth but could begin to remember it in later life. “Although he believed the full truth would never be known”.  In the Timaeus, one of his dialogues, he states that the universe was created by a “divine craftsman” and believed that by learning about the movements of the stars and planets we can improve our soul – as it mirrors the world soul.

Plato also founded an Academy, where one of the students was the great Aristotle.

Aristotle  (384 BC – 322 BC)

Aristotle, a philosopher born in Macedonia, is sometimes known as the grandfather of science and having studied under Plato,  later opened his own school. Aristotle was a brilliant scholar in numerous fields but many of his astronomy theories were later proved wrong. He strongly believed in a geocentric universe which incorporated a series of spherical orbits. This meant that the Earth would be the centre of the universe and the planets and fixed stars revolved around it. He believed that although these objects were round, the earth was not and claimed that as the objects in the universe were circular, then all orbits must be circular also.

His ideas carried weight for many years but his astronomical theories were not based on scientific experimentation but more on a type of logical thinking, of what he believed to be common sense. Although eventually proved incorrect, he did inspire many other great thinkers and the questions he pondered, led others to also search for the truth. So respected and influential was Aristotle, that his incorrect views were supported for almost 2 thousand years and eagerly followed by the Catholic church before being proved wrong.

Aristarchus 310 BC –  230 BC

Aristarchus, a Greek astronomer and mathematician, is famously known as the first person to have proposed the new heliocentric idea of the solar system – that the earth rotated and revolved around a stationary sun. Like Galileo many years later however, his sun centred ideas were dismissed as most people found it easier to believe the views of Aristotle and Ptolemy. That it was the earth at the centre of the solar system.

His only work still in existence is “On the Dimensions and Distances of the Sun and Moon,” on his studies of the size of the sun and the moon and his attempts to calculate the distances between them. Although flawed, his estimations were geometrically correct as he attempted to estimate the size of the moon, using the ratio of it in comparison with the Earths shadow on the moon.

Many of his writings were later lost but do receive mention in the notes of later great thinkers including Archimedes. A book by Vitruvius, a Roman famous architect mentions that the commonly used sundial was invented by Aristarchus.

Eratosthenes (276 BC – 195 BC)

Eratosthenes, born in Cyrene (now Libya) was an important figure in the fields of astronomy, geography and mathematics. Known as the father of Geography, Eratosthenes was the first to accurately calculate the circumference of the earth. He observed that at approximately noon during the summer solstice in Syene, the sun would cast no shadow and the rays could reach straight down the bottom of a well (especially dug for this experiment). He also realized that at the very same time in Alexandria, a column or large object would be casting a shadow because the sun there was not directly overhead.

Therefore he concluded that, although the sun was far away, its rays were not parallel to earth.  He measured the angle of the shadow it cast to be approximately 1/50th of a 360-degree circle and estimated the distance between the cities to be 5000 stades (Greek measurement of scale). By doing so, he was able to conclude that the circumference of the earth must be fifty times by 5000 stades, which would total 250,000 stades –  approximately 25,000 miles! Although he was a little way off, his results are quite remarkable given his tools!

Eratosthenes also made many celestial data recordings and is said to have compiled a star catalogue of nearly 700 stars. He is also thought to have coined the term Geography and accurately sketched a large section of the river Nile.

Claudius Ptolemy (Approx. AD 90 – c. AD 168)

Ptolemy, a Roman citizen of Egypt who wrote in Greek, was one of the most influential of Greek astronomers and geographers of his era and in his lifetime did much to advance the sciences of both. Ptolemy was the author of several important scientific books. In his most famous work the Almagest, he proposed the theory that the Earth was stationary and lay the centre of the universe. In his Ptolemaic system, he refined the ideas of Aristotle and constructed a model that could also be used to calculate the appearances of lunar and solar eclipses. His ideas were a mixture of philosophy and of the outcome of his own experiments. Using advanced trigonometry in mathematics, he calculated the motion of the stars and planets, which he believed to move in perfect circular orbits.

Although his belief was incorrect, his calculations at the time also seemed to account for the occasional backwards (retrograde) movements of planet orbits and explained their variations in size and brightness.The Ptolemaic system view of the universe was an accepted theory for many centuries.

As well as this he also made many important contributions to the studies of geography,  astrology, music theory and optics. Using a system which introduced longitude and latitude, Ptolemy produced a map of the world as it was known then and later inspired generations of mapmakers.



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