The Greeks... (part2)

Herophilus

Born: c. 335 BC

Birthplace: Chalcedon, Bithynia
Died: c. 280 BC
Location of death:unspecified

Cause of death: unspecified

Herophilus was an Alexandrian physician who was an early performer of public dissections on human cadavers; and often called the father of anatomy.

As a member of the well-known scholastic community in the newly founded city of Alexandria during the single, brief period in Greek medical history when the ban on human dissection was lifted. Herophilus studied the ventricles (cavities) of the brain, the organ he regarded as the centre of the nervous system; traced the sinuses of the dura mater (the tough membrane covering the brain) to their junction, known as the torcular Herophili; and classified the nerve trunks—distinguishing them from tendons and blood vessels—as motor or sensory.

In the field of medical treatment, Herophilus sensibly recommended good dietand exercise, but was also an enthusiastic advocate of bleeding and frequentdrug therapy.

Herophilus wrote at least nine works, including a commentary on Hippocrates, a book for midwives, and treatises on anatomy and the causes of sudden death, all lost in the destruction of the library of Alexandria around 272 AD.

Source/s: Encyclopedia Britannica

http://www.faqs.org/health/bios/67/Herophilus.html

ARISTARCHUS

Born: 310 B.C.

Died: about 230 B.C.

Aristarchus, or more correctly Aristarchos, was a Greek astronomer and mathematician, born in 310 BC on the island of Samos, in Greece. He presented the first known heliocentric model of the solar system, placing theSun, not the Earth, at the center of the known universe. He was influenced by the Pythagorean Philolaus of Croton, but, in contrast to Philolaus, he identified the "central fire" with the Sun, and put the other planets in their correct order of distance around the Sun. For some reason, however, Copernicus, who wrote 1700 years later and knew of Aristarchus' work, is the person most often credited with this heliocentric theory.

Aristarchus’ major extant work, On the Sizes and Distances of the Sun and Moon, consists mainly of meticulous geometric proofs of this and the other hypotheses which he proposes.  He describes a spherical Moon, illuminated by the Sun, and much closer to the Earth than the Sun is, a very accurate world-view for the third century B.C.  His results were only limited by the accuracy of the measurements of his day, which suffered from a lack of technology.

Source: http://en.wikipedia.org/wiki/Aristarchus_of_Samos 

 http://www.russellcottrell.com/greek/aristarchus.asp

ARCHIMEDES

Born: 278 B.C.

Died: 212 B.C.

Archimedes was a Greek mathematician, physicist, engineer, inventor, and astronomer. He was born in 278 BC in the port of Syracuse, Sicily (now Italy) in the colony of Magna Graecia. According to the Greek historian John Tzetzes, who was famous for his research on Byzantinne Greek era, Archimedes lived for 75 years. He died in 212 B.C. during the Second Punic war, when Syracuse was captured by the Roman forces after a two year siege.

Archimedes is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.

Here are some of the works of Archimedes:

On the Equilibrium of Planes (two volumes)

On the Measurement of a Circle

On Spirals

On the Sphere and the Cylinder (two volumes)

On Floating Bodies (two volumes)

Source: http://en.wikipedia.org/wiki/Archimedes

http://www.ancientgreece.com/s/People/Archimedes/

Eratosthenes of Cyrene

Born: 276 BC

Birthplace: Cyrene, North Africa (now Shahhat, Libya)

Died: 194 BC

Location of death: Alexandria, Egypt

Cause of death: suicide by voluntary starvation

Eratosthenes of Cyrene was a Greek scientific writer, astronomer, and poet, who made the first measurement of the size of Earth for which any details are known.

One of his major accomplishments in mathematics is his creation of a sieve that determines prime numbers up to any given limit. This sieve, which is called, the Sieve of Eratosthenes, is still important today in number research theory. Eratosthenes figured out that if you were to write down all the natural numbers from 2 to infinity and "sieve out" every second number after two (or multiples of two), then move to the next available number (3) and continue to "sieve out" every multiple of 3 and so on, one would end up with a list of prime numbers.

Eratosthenes is also known for his achievement in astronomy. He found the circumference of the Earth to be nearly 250,000 stadia (25,000 miles). To calculate the circumference of the Earth, Eratosthenes measured the angle of the shadow to the Earth.

As a historian, Eratosthenes decided to work on giving a systematic chronography of the known world by figuring out the dates of literary and political events from the siege of Troy up until his time. However, this was only a beginning. Others built on his foundation.

Sources: Encyclopædia Britannica

http://www.math.twsu.edu/history/men/eratosthenes.html

HIPPARCHUS

Born: 190 B.C.

Died: 120 B.C.

Hipparchus, or more correctly Hipparchos, was a Greek astrologer, astronomer, geographer, and mathematician of the Hellenistic period. He is considered the founder of trigonometry.

Hipparchus was born in Nicaea, which is now Iznik, Turkey, and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Chaldeans from Babylonia. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue. It would be three centuries before Claudius Ptolemaeus' synthesis of astronomy would supersede the work of Hipparchus; it is heavily dependent on it in many areas.

Source: http://en.wikipedia.org/wiki/Hipparchus

The Greeks... (part1)

THALES

Born: 620 B.C.
Birthplace: Miletus, Greek Ionia
Died: 546 B.C.
Location of death: unspecified
Cause of death: unspecified

Thales, an ancient Greek philosopher, was born in Miletus in Greek Ionia. Aristotle, the major source for Thales’s philosophy and science, identified Thales as the first person to investigate the basic principles, the question of the originating substances of matter and, therefore, as the founder of the school of natural philosophy.

Thales was interested in almost everything, investigating almost all areas of knowledge, philosophy, history, science, mathematics, engineering, geography, and politics. He proposed theories to explain many of the events of nature, the primary substance, the support of the earth, and the cause of change. He was much involved in the problems of astronomy and provided a number of explanations of cosmological events which traditionally involved supernatural entities. His questioning approach to the understanding of heavenly phenomena was the beginning of Greek astronomy. Thales’ hypotheses were new and bold, and in freeing phenomena from godly intervention, he paved the way towards scientific endeavor. He founded the Milesian school of natural philosophy, developed the scientific method, and initiated the first western enlightenment. A number of anecdotes is closely connected to Thales’ investigations of the cosmos. When considered in association with his hypotheses they take on added meaning and are most enlightening. Thales was highly esteemed in ancient times, and a letter cited by Diogenes Laertius, and purporting to be from Anaximenes to Pythagoras, advised that all our discourse should begin with a reference to Thales.

Source: http://www.iep.utm.edu/thales/

ANAXAGORAS

Born: Around 500 B.C.

Died: 428 B.C.

Anaxagoras was an important Presocratic natural philosopher and scientist who lived and taught in Athens for approximately thirty years. He was born in Ionia in the town of Clazamenae, a lively port on the coast of present-day Turkey, at the coast of Asia Minor around 500 BC.

Anaxagoras gained notoriety for his materialistic views, particularly his contention that the sun was a fiery rock. This led to charges of impiety, and he was sentenced to death by the Athenian court. He avoided this penalty by leaving Athens, and he spent his remaining years in exile.

While Anaxagoras proposed theories on a variety of subjects, he is most noted for two theories. First, he speculated that in the physical world everything contains a portion of everything else. His observation of how nutrition works in animals led him to conclude that in order for the food an animal eats to turn into bone, hair, flesh, and so forth, it must already contain all of those constituents within it. The second theory of significance is Anaxagoras’ postulation of Mind (Nous) as the initiating and governing principle of the cosmos.

Anaxagoras is said to have written only one book. As with all the Presocratics, Anaxagoras’ work survives only in fragments quoted by later philosophers and commentators. This work was a treatise on natural philosophy and, as it was indicated from Plato’s Apology, it was probably not a very long work, since it could be purchased for “a drachma, at most.” Although the book has not survived, it was available until at least the sixth-century CE.

Sources:http://en.wikipedia.org/wiki/Anaxagoras

http://www.iep.utm.edu/anaxagor/

 http://www.thebigview.com/greeks/anaxagoras.html

ZENO

Born: c. 495 BCE
Birthplace: Elea
Died: c. 430 BCE
Location of death: unknown
Cause of death: unknown

Zeno of Elea was a Greek philosopher and mathematician, whom Aristotle called the inventor of dialectic. Zeno is especially known for his paradoxes that contributed to the development of logical and mathematical rigor and that were insoluble until the development of precise concepts of continuity and infinity.

Zeno was famous for the paradoxes whereby, in order to recommend the Parmenidean doctrine of the existence of “the one” (i.e., indivisible reality), he sought to controvert the commonsense belief in the existence of “the many” (i.e., distinguishable qualities and things capable of motion). Zeno was the son of a certain Teleutagoras and the pupil and friend of Parmenides. In Plato’s Parmenides, Socrates, “then very young,” converses with Parmenides and Zeno, “a man of about forty”; but it may be doubted whether such a meeting was chronologically possible. Plato’s account of Zeno’s purpose (Parmenides), however, is presumably accurate. In reply to those who thought that Parmenides’ theory of the existence of “the one” involved inconsistencies, Zeno tried to show that the assumption of the existence of a plurality of things in time and space carried with it more serious inconsistencies. In early youth he collected his arguments in a book, which, according to Plato, was put into circulation without his knowledge.

Zeno made use of three premises: first, that any unit has magnitude; second, that it is infinitely divisible; and third, that it is indivisible. Yet he incorporated arguments for each: for the first premise, he argued that that which, added to or subtracted from something else, does not increase or decrease the second unit is nothing; for the second, that a unit, being one, is homogeneous and that therefore, if divisible, it cannot be divisible at one point rather than another; for the third, that a unit, if divisible, is divisible either into extended minima, which contradicts the second premise or, because of the first premise, into nothing. He had in his hands a very powerful complex argument in the form of a dilemma, one horn of which supposed indivisibility, the other infinite divisibility, both leading to a contradiction of the original hypothesis. His method had great influence and may be summarized as follows: he continued Parmenides’ abstract, analytic manner but started from his opponents’ theses and refuted them by reductio ad absurdum. It was probably the two latter characteristics which Aristotle had in mind when he called him the inventor of dialectic.

Some of the paradoxes of Zeno:

·         The Arguments Against Plurality

·         The Paradoxes of Motion

·         The Stadium, or The Dichotomy

·         The Achilles

·         The Arrow

·         The Moving Rows

·         The Millet Seed

·         A Paradox of Place

Sources: Encyclopedia Brittanica

http://plato.stanford.edu/entries/zeno-elea/

DEMOCRITUS

Born: 460 B.C.

Died: 357 B.C.

Democritus, known in antiquity as the ‘laughing philosopher’ because of his emphasis on the value of ‘cheerfulness, was born in the city of Abdera in Thrace, an Ionian colony of Teos, at about 460 BC ( although Thrasyllus placed his birth in 470 BC). He was an influential pre-Socratic philosopher and pupil of Leucippus, who formulated an atomic theory for the cosmos. After the death of his father Democritus traveled in search of wisdom, and devoted his inheritance to this purpose, amounting to one hundred talents. He is said to have visited Egypt, Ethiopia, Persia, and India. Whether, in the course of his travels, he visited Athens or studied under Anaxagoras is uncertain.

His exact contributions are difficult to disentangle from his mentor Leucippus, as they are often mentioned together in texts. Their speculation on atoms, taken from Leucippus, bears a passing and partial resemblance to the nineteenth-century understanding of atomic structure that has led some to regard Democritus as more of a scientist than other Greek philosophers; however their ideas rested on very different bases. Largely ignored in ancient Athens, Democritus was nevertheless well known to his fellow northern-born philosopher Aristotle. Plato is said to have disliked him so much that he wished all his books burned. Many consider Democritus to be the "father of modern science".

Here are the works of Democritus:

Ethics

·           Pythagoras

·           On the Disposition of the Wise Man

·           On the Things in Hades

Natural science

·           The Great World-ordering (may have been written by Leucippus)

·           Cosmography

·           On the Planets

Nature

·           Heavenly Causes

·           Atmospheric Causes

·           Terrestrial Causes 

Mathematics

·           On Different Angles or On contact of Circles and Spheres

·           On Geometry

·           Geometry

·           Description of Rays of Light

Literature

·           On the Rhythms and Harmony

·           On Poetry

·           On the Beauty of Verses

Sources: http://en.wikipedia.org/wiki/Democritus

http://plato.stanford.edu/entries/democritus/

http://www.iep.utm.edu/democrit/

Eudoxus of Cnidus

Born: c. 395–390 bc
Birthplace: Cnidus, Asia Minor (now in Turkey)
Died: c.342–337 bc
Location of death:  Cnidus
Cause of death:  unspecified

Eudoxus of Cnidus was Greek mathematician and astronomer who substantially advanced proportion theory, contributed to the identification of constellations and thus to the development of observational astronomy in the Greek world, and established the first sophisticated,geometrical model of celestial motion. He also wrote on geography and contributed to philosophical discussions in Plato’s Academy.

Eudoxus 's contributions to mathematics include:

• A theory of proportion; this allowed the study of irrationals (incommensurables)
• The concept of magnitude, as not a number but stood for such as line segments, angles, areas, etc, and which could vary continuously. Magnitudes were opposed to numbers, which could change discontinuously. This avoided giving numerical values to lengths, areas, etc. Consequently great advances in geometry were made
• The method of exhaustion
• Establishing rigorous methods for finding areas and volumes of curvilinear figures (e.g. cones and spheres)

Eudoxus described constellations schematically, the phases of fixed stars (the dates when they are visible), and the weather associated with different phases. Through a poem of Aratus (c. 315–245 bc) and the commentary on the poem by the astronomerHipparchus (c. 100 bc), these works had an enduring influence in antiquity. Eudoxus also discussed the sizes of the Sun, Moon, and Earth. He may have produced an eight-year cycle calendar (Oktaëteris).

Eudoxus also wrote an ethnographical work (“Circuit of the Earth”) of which fragments survive. It is plausible that Eudoxus also divided the spherical Earth into the familiar six sections (northern and southern tropical, temperate, and arctic zones) according to a division of the celestial sphere.

Sources: Encyclopedia brittanica

http://www.math.tamu.edu/~dallen/history/eudoxus/eudoxus.html

Heraclides Ponticus

Born: c. 387 BC

Birthplace: Heraclea, Pontus, Greece

Died: c. 312 BC

Location of death: Heraclea, Pontus, Greece 

Cause of death: unspecified

Heraclides Ponticus (387 - 312 BC), also known as Heraklides, was a Greek philosopher who lived and died at Heraclea, now  known as Eregli, Turkey. Heraclides' father was Euthyphron, a wealthy nobleman who sent him to study at the Academy in Athens under its founder Plato and under his successor Speusippus.

Heraclides, believed to be a rather vain and pompous man, was known to be a versatile and prolific writer on philosophy, mathematics, music, grammar, physics, history and rhetoric, notwithstanding doubts about attribution of many of the works.

He realized, through his observation, that Venus and Mercury orbit the Sun as satellites. This, as some writers had said,  has been an evidence that he originated the heliocentric theory prior to Aristarchus of Samos and Nicolaus Copernicus. This would mean that he anticipated the Tychonic system, an essentially geocentric model with heliocentric aspects. Also, the idea of a spinning Earth is said to be his.

Source: http://www.mlahanas.de/Greeks/Bios/HeraclidesPonticus.html


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