Euclid

In the Middle Ages, writers sometimes referred to him as Euclid of Megara, confusing him with a Greek Socratic philosopher who lived approximately one century earlier.
. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: he was active at the great library in Alexandria and may have studied at Plato's Academe in Greece, but his exact lifespan and place of birth are unknown.
. Almost nothing is known about Euclid outside of what is presented in Elements and his few other surviving books. In accepting her 2003 Nobel Peace Prize, Shirin Ebadi said:. There are four works credibly attributed to Euclid which have been lost. Cyrus was still being cited in the twenty-first century.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions. Entitled The Garden of Cyrus, it may well be a Royalist criticism upon the autocratic rule of Cromwell. In addition to the Elements, four works of Euclid have survived to the present day. The English philosopher Sir Thomas Browne named his 1658 discourse after the benevolent ruler. The first correct axiomatic treatment of geometry by modern standards was provided by David Hilbert in 1899, in his Grundlagen der Geometrie. The Cyropaedia of Xenophon, based on the latter's knowledge of the great king's upbringing, was an influential political treatise in ancient times, and again during the Renaissance. While the Elements was used well into the 20th century as a geometry textbook and has been considered a fine example of the formally precise axiomatic method, Euclid's treatment does not hold up to modern standards of rigor; some logically necessary axioms are missing, and the definitions of primitive terms appeal to spatial intuition. His exploits, real and legendary, were used as moral instruction or a source of inspiration for political philosophies.

Most of these investigations involved attempts to prove the relatively complex and presumably non-intuitive fifth postulate using the other four (a feat which, if successful, would have shown the postulate to be in fact a theorem). His spectacular conquests triggered the age of empire building, as carried out by his successors as well as the Greeks and Romans in the following centuries. These new geometries grew out of more than two millennia of investigation into Euclid's fifth postulate, one of the most-studied axioms in all of mathematics. The Bible records a remnant of the Jewish population returning to the Promised Land from Babylon, following an edict from Cyrus. Today, however, it is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries which were discovered in the 19th century. A good example of this policy is found in his treatment of the Jews in Babylon. The geometrical system described in Elements was long known simply as "the" geometry. By pursuing a policy of generosity, instead of repression, and by favoring the local religion, he was able to make his new subjects his enthusiastic supporters.

In addition to providing some missing proofs, Euclid's text also includes sections on number theory and three-dimensional geometry. His statesmanship came out particularly in his treatments of newly conquered peoples. Although many of the results in Elements originated with earlier mathematicians, one of Euclid's major accomplishments was to present them in a single, logically coherent framework. Cyrus was distinguished no less as statesman than as a soldier. . The tomb northeast of Persepolis (پرسپولیس), which has been claimed as that of Cyrus, is evidently not his, as its location does not fit the reports. Neither the year nor place of his birth have been established, nor the circumstances of his death. Both Strabo and Arrian give descriptions of his tomb, based upon reports of men who saw it at the time of Alexander the Great's invasion.

Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces. He was buried in the town of Pasargadae. Within it, the properties of geometrical objects and integers are deduced from a small set of axioms, thereby anticipating (and partly inspiring) the axiomatic method of modern mathematics. Ctesias reports that Cyrus met his death in the year 529 BC, while warring against tribes northeast of the headwaters of the Tigris. Now known as "the father of geometry," his most famous work is Elements, widely considered to be history's most successful textbook. The Massagetae were similar to the Scythians in their dress and mode of living; they fought on horseback and on foot. 325 BC–265 BC) was a Greek mathematician who taught at Alexandria in Egypt almost certainly during the reign (323 BC–283 BC) of Ptolemy I. The queen of the Massagetae, Tomyris, prevailed after Cyrus previously defeated Tomyris's son Spargapises.

Euclid of Alexandria (Greek: Εὐκλείδης) (ca. According to Herodotus, Cyrus met his death in a battle with the Massagetae, a tribe from the southern deserts of Kharesm, Kizilhoum in the southernmost portion of the steppe region. ISBN 0-19-502754-X. Cyrus died in battle, but his empire was to reach its zenith long after his death. Mathematics: The Loss of Certainty. Oxford: Oxford University Press. Cyrus is the result of this union. Kline, Morris (1980). But they also consider him as being married to Princess Mandane of Media (ماد), a daughter of Astyages, King of the Medes and Princess Aryenis of Lydia.

ISBN 0-486-24073-8 / ISBN 0-486-24074-6. Cambyses is considered by Herodotus and Ctesias to be of humble origin. New York: Dover Publications. They were succeeded by their respective sons Cambyses I of Anshan and Arsames of Persia. A History of Greek Mathematics, 2 Vols. Inscriptions indicate that when the latter died, two of his sons shared the throne as Cyrus I of Anshan and Ariaramnes of Persia. (1981). 700 BC) who was succeeded by his son Teispes of Anshan.

Heath, Thomas L. The royal history given on the cylinder is as follows: The founder of the dynasty was King Achaemenes (ca. ISBN 0-486-60088-2. Many historians consider it to be the first declaration of human rights. New York: Dover Publications. It was discovered in 1879 in Babylon and today is kept in the British Museum. 1 (2nd ed.). Upon his taking of Babylon, Cyrus issued a declaration, inscribed on a clay barrel known as the Cyrus Cylinder, which contains an account of his victories and merciful acts as well as a documentation of his royal lineage.

The Thirteen Books of Euclid's Elements, Vol. The administrators of these provinces, called satraps, had considerable independence from the emperor, and from many parts of the realm Cyrus demanded no more than tribute and conscripts. (1956). Cyrus organized the empire into provincial administrations called satrapies. Heath, Thomas L. From the list of countries subject to Persian rule given on the first tablet of the great Behistun Inscription of Darius, written before any new conquests could have been made except that of Egypt, the dominion of Cyrus must have comprised the largest empire the world had yet seen, stretching from Asia Minor and Judah in the west to the Indus valley in the east. "Euclid." Dictionary of Scientific Biography.. Cyrus assumed the title of 'king of Babylon, king of Sumer and Akkad, king of the four sides of the world'.

Bulmer-Thomas, Ivor (1971). According to the Babylonian inscription this was in all probability a bloodless victory. Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces. In 538 BC, Cyrus defeated Nabonidus at Opis and occupied Babylon. Pseudaria, or Book of Fallacies, an elementary text about errors in reasoning. According to Herodotus, Cyrus spared the life of Croesus and kept him as an advisor throughout his life. Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial. But before the allies could unite, Cyrus had defeated Croesus at Pterium, occupied Sardis, overthrown the Lydian kingdom, and taken Croesus prisoner (546 BC).

Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. They reportedly intended to unite their armies against Cyrus and his Persians. Optics, the earliest surviving Greek treatise on perspective, contains propositions on the apparent sizes and shapes of objects viewed from different distances and angles. Astyages had been in alliance with his brother-in-law Croesus of Lydia, son of Alyattes, Nabonidus of Babylon, and Amasis II of Egypt. Phaenomena concerns the application of spherical geometry to problems of astronomy. Cyrus' wars had just begun. It is similar to a third century (AD) work by Heron of Alexandria, except Euclid's work characteristically lacks any numerical calculations. Thus the Persians gained dominion over the Iranian plateau.

On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. While he seems, at first, to have accepted the crown of Media, by 546 BC he had officially assumed the title of 'king of Persia'. Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements. With the help of Harpagus, Cyrus led the Persians and his armies to capture Ecbatana, and effectively conquered Media. 554 BC–553 BC and by 550 BC–549 BC. Harpagus, seeking vengeance, convinced Cyrus to rally the Persian people, then in a state of near-slavery to the Medes, to revolt ca.

Many years later, when Astyages discovered that his grandson was still alive, he ordered that the son of Harpagus be beheaded and served to his father on a dinner platter. Harpagus, morally unable to kill a newborn, switched the baby with a stillborn child and reported Cyrus dead. He then ordered his steward Harpagus to kill the infant Cyrus. After the birth of Cyrus, Astyages had a dream that his Magi interpreted as a sign of an eventual overthrow by his grandson.

According to Herodotus, Cyrus was said to be part-Persian (Parsua) and part Mede and his overlord was his own grandfather Astyages who had conquered all Assyrian kingdoms apart from Babylonia. In his Histories, Herodotus gives a detailed description of the rise to power of Cyrus according to the best sources available to him. Like his predecessors before him, Cyrus had to recognize Median overlordship. However, Cyrus was not yet an independent ruler.

Arsames was father of Hystaspes and would live to see his grandson become King Darius I of Persia. He apparently also soon managed to succeed Arsames to the throne of Persia though the latter was still living. In 559 BC, Cyrus succeeded his father Cambyses the Elder as King of Anshan. Cyrus had two sons: Cambyses and Smerdis, as well as several daughters, of whom Atossa is significant since she married Darius I of Persia and was mother of Xerxes I of Persia.(To see Cyrus's Portrait please visit: http://en.wikipedia.org/wiki/Image:Cyrus_portrait.jpg ).

Cyrus, the son of a Persian noble and a Median princess, was from the Achaemenid Dynasty, which ruled the kingdom of Anshan, in what is now southwestern Iran. In modern Persian, Cyrus is referred to as Kouroush Bozorg — his Persian name with the Persian-derived "Great"). The name "Cyrus" (a Latin transliteration of the Greek Κῦρος) is the Greek version of the Old Persian Koroush or Khorvash, [in Persian khour means "sun" and vash is a suffix meaning "like"]. .

He is perhaps best known for having declared the first ever charter of human rights (the Cyrus Cylinder) where he identifies himself as "King of Persia". 576 – July 529 BC) founded the Persian Empire under the Achaemenid Dynasty of Anshan by unifying two Iranian tribes: the Median and the Persian. Cyrus II of Persia, widely known as Cyrus the Great, (ca.