Hipparchus menelaus ptolemy and greek trigonometry essay

Rather than seeing water as a barrier Thales contemplated the Ionian yearly religious gathering for athletic ritual held on the promontory of Mycale and believed to be ordained by the ancestral kindred of Poseidon, the god of the sea. Ptolemy also wrote on trigonometry, optics, geography, map projections, and astrology; but is most famous for his astronomy, where he perfected the geocentric model of planetary motions.

He first described the dark band, named after him, between the brignt primary rainbow and the dim secondary rainbow. In mathematics, he popularized the use of the decimal system, developed spherical geometry, wrote on many other topics and was a pioneer of cryptography code-breaking.

His writings on conic sections have been studied until modern times; he developed methods for normals and curvature. Little else is known for certain about his life, but several very important mathematical achievements are credited to him. Archimedes and Newton might be the two best geometers ever, but although each produced ingenious geometric proofs, often they used non-rigorous calculus to discover results, and then devised rigorous geometric proofs for publication.

Some of his works were meant to be lecture notes: From a philosophic point of view, any grouping at all would have been just as effective.

Al-Kindi, called The Arab Philosopher, can not be considered among the greatest of mathematicians, but was one of the most influential general scientists between Aristotle and da Vinci.

Philosophical man is a "new cultural configuration" based in stepping back from "pregiven tradition" and taking up a rational "inquiry into what is true in itself;" that is, an ideal of truth. The idea did not originate with him, as the Greeks in general believed in the distinction between mind and matter, which was ultimately to lead to a distinction not only between body and soul but also between matter and energy.

Thales of Miletus

Philosophers were either Ionian or Italian. He was likely the most talented scientist of his time: Mythical thought does not differentiate between things and persons[ citation needed ] and furthermore it does not differentiate between nature and culture[ citation needed ].

His work with code-breakig also made him a pioneer in basic concepts of probability. Archytas of Tarentum ca BC Greek domain Archytas was an important statesman as well as philosopher. Archytas is sometimes called the "Father of Mathematical Mechanics.

Deferent and epicycle

Zhmud, who points out that the division of the day into twelve parts and by analogy the year was known to the Egyptians already in the second millennium, the gnomon was known to both Egyptians and Babylonians, and the idea of the "heavenly sphere" was not used outside of Greece at this time.

Other early cultures also developed some mathematics. Hipparchus was another ancient Greek who considered heliocentrism but, because he never guessed that orbits were ellipses rather than cascaded circles, was unable to come up with a heliocentric model that fit his data.

Other discoveries known only second-hand include the Archimedean semiregular solids reported by Pappus, and the Broken-Chord Theorem reported by Alberuni.

Ideas unique to that work are an anticipation of Riemann integration, calculating the volume of a cylindrical wedge previously first attributed to Kepler ; along with Oresme and Galileo he was among the few to comment on the "equinumerosity paradox" the fact that are as many perfect squares as integers.

He may have invented the They sought for the substance of phenomena and may have studied with each other. Thales the founder of this type of philosophy says that it is water. Others, especially Gherard of Cremona, had translated Islamic mathematics, e.

The emphasis was on pure, rather than practical, mathematics. For these theorems, Pappus is sometimes called the "Father of Projective Geometry.

The Sun-centered positions displayed a cyclical motion with respect to time but without retrograde loops in the case of the outer planets. Hence, Aristotle, immediately after he has called him the originator of philosophy brings forward the reasons which Thales was believed to have adduced in confirmation of that assertion; for that no written development of it, or indeed any book by Thales, was extant, is proved by the expressions which Aristotle uses when he brings forward the doctrines and proofs of the Milesian.

According to a historical Note, [35] when Thales visited Egypthe observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. He would have seen that minerals could be processed from water such as life-sustaining salt and gold taken from rivers.In the Hipparchian and Ptolemaic systems of astronomy, the epicycle (from Ancient Greek: ἐπίκυκλος, literally upon the circle, meaning circle moving on another circle) was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and mint-body.com particular it explained the apparent retrograde motion of the five planets known at.

Thales of Miletus (/ ˈ θ eɪ l iː z /; Greek: Θαλῆς (ὁ Μιλήσιος), Thalēs; c. – c. BC) was a pre-Socratic Greek philosopher, mathematician, and astronomer from Miletus in Asia Minor (present-day Milet in Turkey).He was one of the Seven Sages of mint-body.com, most notably Aristotle, regarded him as the first philosopher in the Greek tradition, and he is otherwise.

A Time-line for the History of Mathematics (Many of the early dates are approximates) This work is under constant revision, so come back later. Please report any errors to me at [email protected] The accomplishments of selected TOP SCIENTISTS summarizes the History of Science.

An amazing HISTOGRAM of their lifetimes reveals the cultural waves which nurtured or hindered progress. The Hundred Greatest Mathematicians of the Past.

This is the long page, with list and biographies. (Click here for just the List, with links to the mint-body.com Click here for a .

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Hipparchus menelaus ptolemy and greek trigonometry essay
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