Eratosthenes
Eratosthenes was born in Cyrene which is now in Libya in North Africa. His teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of Chios who had studied under Zeno, the founder of the Stoic school of philosophy. Eratosthenes also studied under the poet and scholar Callimachus who had also been born in Cyrene. Eratosthenes then spent some years studying in Athens.
The library at Alexandria was planned by Ptolemy I Soter and the project came to fruition under his son Ptolemy II Philadelphus. The library was based on copies of the works in the library of Aristotle. Ptolemy II Philadelphus appointed one of Eratosthenes' teachers Callimachus as the second librarian. When Ptolemy III Euergetes succeeded his father in 245 BC and he persuaded Eratosthenes to go to Alexandria as the tutor of his son Philopator. On the death of Callimachus in about 240 BC, Eratosthenes became the third librarian at Alexandria, in the library in a temple of the Muses called the Mouseion. The library is said to have contained hundreds of thousands of papyrus and vellum scrolls.
One of the important works of Eratosthenes was Platonicus which dealt with the mathematics which underlie Plato's philosophy. Theon of Smyrna tells us that Eratosthenes' work studied the basic definitions of geometry and arithmetic, as well as covering such topics as music.
Eratosthenes also worked on prime numbers. He is remembered for his prime number sieve, the 'Sieve of Eratosthenes' which, in modified form, is still an important tool in number theory research.
Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth. Details were given in his treatise On the measurement of the Earth which is now lost. However, some details of these calculations appear in works by other authors such as Cleomedes, Theon of Smyrna and Strabo. Eratosthenes compared the noon shadow at midsummer between Syene (now Aswan on the Nile in Egypt) and Alexandria. He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia.
Eratosthenes also measured the distance to the sun as 804,000,000 stadia and the distance to the Moon as 780,000 stadia. He computed these distances using data obtained during lunar eclipses. Ptolemy tells us that Eratosthenes measured the tilt of the Earth's axis with great accuracy obtaining the value of 11/83 of 180, namely 23° 51' 15".
Ptolemy of Alexandria, the Influential Astronomer Ptolemy of Alexandria was the most influential astronomer of the ancient world. The books and theories Ptolemy developed served as a major basis for future astronomers. It was during the Renaissance period that his work became thoroughly studied and revised. Ptolemy collected all ancient knowledge of astronomy and geography including it in his book Almagest around 140 A.D. It follows, he then wrote a four volume astrological study known as the Tretrabiblos.
After 3rd century BC, Eratosthenes calculation about Earth's circumference was used correctly in different locations such as Alexandria and syene (Aswan now) by simple geometry and the shadows cast. Eratosthenes's results undertaken in 1ST century by Posidonius, were corroborated in Alexandria and Rhodes by the comparison between remarks is excellent.
...to the Second Punic War with the defense of Syracuse. He even made amazing engineering tools and machines that benefitted the community, like the Archimedes screw, which helped irrigation among other things. The Archimedes’ principle, which is said to of helped King Hiero ll, showed the different densities between objects using the buoyancy of the water. The findings in mathematics from Archimedes like The Quadrature of the Parabola and the Measurement of a Circle have greatly benefitted mathematics and are still helping now. Archimedes wrote a lot of different works, including his most famous Archimedes Palimpsest, which contained many more important writing like On Floating Bodies. With his amazing inventions, intricate ideas on science, intelligent theorems and principles in mathematics, and his life in general, Archimedes has greatly affected society in many ways
Aristotle was born in 384 B.C., in Northern Greece. His father was a physician to the king of Macedonia, Amyntas II. Amyntas II was the grandfather of Alexander the Great. When Aristotle was still a boy, both of his parents died; so he was raised by a guardian named Proxenus. At the age of seventeen, he went to Athens to attend Plato's school, the Academy. Aristotle stayed at the Academy for twenty years as a student, a research assistant, a lecturer, and a research scientist. After Plato died, he moved and lived with Hermeias, a former pupil of Plato. During his three year stay, Aristotle married princess Pithias, Hermeias's daughter. The couple had two children: a son named Nicomachus and a daughter. In 342 B.C., Aristotle was invited to educate Alexander by Philip of Macedon. He taught Alexander until King Philip was assassinated, then Alexander became ruler. In 335 B.C., he left Macedonia and returned to Athens to found a school named Lyceum. Twelve years later, when Alexander died, the Athenians charged Aristotle with impiety because they resented his relationship with Alexander and other influential Macedonians. Aristotle said that he would not let the Athenians "sin twice against philosophy" (Soll, 663), so he fled to Chalcis. One year later he died at the age of sixty-two.
Within Ptolemy’s 13 part series, Mathematike, Syntaxis, and Mathematical Composition, he, “developed a theory of the universe which claims that the earth is stationary and all the planets and stars revolve around it,” (Document C). Ptolemy’s theory was accepted as the standard view of the universe, until Nicolaus Copernicus’ astronomical studies were published in 1543. Copernicus’ theory was the “simplest,” and “most accurate,” (Document C); it encompassed that the Sun is at rest near the center of the Universe, and that the Earth, spinning on its axis once daily, revolves annually around the Sun. The heliocentric, or Sun-centered, system is still used today, and without these discoveries we would not be as advanced as we are
Descartes was born in 1596 in Touraine, France. His education consisted of attendance to a Jesuit school of La Fleche. He studied a liberal arts program that emphasized philosophy, the humanities, science, and math. He then went on to the University of Poitiers where he graduated in 1616 with a law degree. Descartes also served as a volunteer in several different armies to broaden his horizons.
The great Greek thinker Aristotle was born in 384 B.C. in Stagirus, a city in ancient Macedonia in northern Greece. At the age of eighteen Aristotle went to Athens to begin his studies at Plato's Academy. He stayed and studied at the Academy for nineteen years and in that time became both a teacher and an independent researcher. After Plato's death in 347 B.C. Aristotle spent twelve years traveling and living in various places around the Aegean Sea. It was during this time that Aristotle was asked by Philip of Macedon to be a private tutor to his son, Alexander. Aristotle privately taught Alexander for three years before he returned to Athens after Philip gained control of the Greek capital. During this period back in Athens Aristotle founded his own school, the Lyceum, where he taught for twelve years. In 323 B.C. Alexander the Great died and the Macedonians lost control of Athens. Aristotle was forced to leave and he died one year later in Chalcis, north of Athens, at the age of 62.
Socrates was born in Athens, Greece in 469 B.C. where he lived all of his life. His father was a wealthy sculptor named Sophroniscus and friend to the family of Aristides, the founder of the Delian League from which the empire arose. His mother was said to be a “midwife” (which implies nothing about her place in society) named Phaenarete.
Aristarchus has only one existing book that is “On the Sizes and Distances of the Sun and Moon.” In it he calculated the diameter of the Sun, which is about seven times the diameter of the Earth, and estimating the Sun’s volume is about 300 times the volume of the Earth (the actual diameter of the Sun is about 300 times the diameter of the Earth.) In this book there is nothing indicating his heliocentric theory. Aristarchus’ book on the planetary system with the Sun in the center did not survive. He also added that the universe is many times larger than generally assumed by astronomers, and the fixed stars are at an enormous distance from the Sun and its planets. Aristarchus regarded the Sun as one of the fixed stars, the closest to the Earth.
Euclid and Archimedes are two of the most important scientists and mathematicians of all time. Their achievements and discoveries play a pivotal role in today’s mathematics and sciences. A lot of the very basic principles and core subjects of mathematics, physics, engineering, inventing, and astronomy came from the innovations, inventions, and discoveries that were made by both Euclid and Archimedes.
384 B.C.E., Aristotle was born in Stagira, Greece. At the age of fourteen, Aristotle went to Athens to study Philosophy with Plato. Although he studied with Plato, he did not always agree with some of his teachings. When Plato died, Aristotle left Athens and traveled to Macedonia. While in Macedonia, Aristotle tutored Alexander the Great. Later on in his life, Aristotle returned to Athens and created a school of him own, Lyceum. When Alexander the Great died in 323 B.C.E., Aristotle fled to Euboea to avoid charges and execution. He died shortly after in 322 B.C.E. (Aristotle Biography, 2015). Aristotle is seen as much more than just a great philosopher of his time. He practiced in ethics, biology, science, and much more (Chaffee, 2013, p. 250).
Plato is one of the most important people in the history of Philosophy. Throughout his life, he had made many contributions to the world of philosophy, but the most important contribution that he is most known for is his theory of the Ideas or Forms. Throughout his many works such as the Phaedo and Symposium, he presented his theory of Ideas by using both mythos and logos in his argument for support.
Obviously Euclid’s The Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Very little information is known about the author, beyond knowing the fact he lived in Alexandria around 300 BCE. Subjects of works includes geometry, proportion and number theory.