Renaissance
The Renaissance was a period in European history, from the 14th to the 17th century, regarded as the cultural bridge between the Middle Ages and modern history. It started as a movement in Italy in the Late Medieval period and spread to the rest of Europe. This new thinking became manifest in art, politics, Early examples were the development of perspective in oil painting and the recycled knowledge of how to make concrete. Although the invention of movable type sped the dissemination of ideas from the 15th century. In politics, the Renaissance contributed to the development of the customs and conventions of diplomacy, the Renaissance began in Florence, in the 14th century. Other major centres were northern Italian city-states such as Venice, Milan, the word Renaissance, literally meaning Rebirth in French, first appeared in English in the 1830s. The word occurs in Jules Michelets 1855 work, Histoire de France, the word Renaissance has been extended to other historical and cultural movements, such as the Carolingian Renaissance and the Renaissance of the 12th century.
The Renaissance was a movement that profoundly affected European intellectual life in the early modern period. Renaissance scholars employed the humanist method in study, and searched for realism, however, a subtle shift took place in the way that intellectuals approached religion that was reflected in many other areas of cultural life. In addition, many Greek Christian works, including the Greek New Testament, were back from Byzantium to Western Europe. Political philosophers, most famously Niccolò Machiavelli, sought to describe life as it really was. Others see more competition between artists and polymaths such as Brunelleschi, Ghiberti and Masaccio for artistic commissions as sparking the creativity of the Renaissance. Yet it remains much debated why the Renaissance began in Italy, several theories have been put forward to explain its origins. During the Renaissance and art went hand in hand, Artists depended entirely on patrons while the patrons needed money to foster artistic talent. Wealth was brought to Italy in the 14th, 15th, and 16th centuries by expanding trade into Asia, silver mining in Tyrol increased the flow of money.
Luxuries from the Eastern world, brought home during the Crusades, increased the prosperity of Genoa, unlike with Latin texts, which had been preserved and studied in Western Europe since late antiquity, the study of ancient Greek texts was very limited in medieval Western Europe. One of the greatest achievements of Renaissance scholars was to bring this entire class of Greek cultural works back into Western Europe for the first time since late antiquity, Arab logicians had inherited Greek ideas after they had invaded and conquered Egypt and the Levant. Their translations and commentaries on these ideas worked their way through the Arab West into Spain and Sicily and this work of translation from Islamic culture, though largely unplanned and disorganized, constituted one of the greatest transmissions of ideas in history
Ancient Greek astronomy
{{Refimprove|date=October 2011 Greek astronomy is written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Greco-Roman and it is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is known as Hellenistic astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum, the development of astronomy by the Greek and Hellenistic astronomers is considered by historians to be a major phase in the history of astronomy. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena, most of the constellations of the northern hemisphere derive from Greek astronomy, as are the names of many stars and planets. It was influenced by Egyptian and especially Babylonian astronomy, in turn, it influenced Indian, Arabic-Islamic, references to identifiable stars and constellations appear in the writings of Homer and Hesiod, the earliest surviving examples of Greek literature.
Though neither Homer nor Hesiod set out to write a scientific work, some stars rise and set, others are ever-visible. At certain times of the year, certain stars will rise or set at sunrise or sunset, speculation about the cosmos was common in Pre-Socratic philosophy in the 6th and 5th centuries BC. Anaximander described a cylindrical earth suspended in the center of the cosmos, philolaus the Pythagorean described a cosmos with the stars, Sun, Earth, and a counter-Earth —ten bodies in all—circling an unseen central fire. Such reports show that Greeks of the 6th and 5th centuries BC were aware of the planets and speculated about the structure of the cosmos. Also, a detailed description about the cosmos, Sun and the Earth can be found in the Orphism, which dates back to the end of the 5th century BC. The name planet comes from the Greek term πλανήτης, meaning wanderer, five planets can be seen with the naked eye, Venus, Mars and Saturn, the Greek names being Hermes, Ares and Cronus. Sometimes the luminaries, the Sun and Moon, are added to the list of naked eye planets to make a total of seven, since the planets disappear from time to time when they approach the Sun, careful attention is required to identify all five.
Observations of Venus are not straightforward and they eventually came to recognize that both objects were the same planet. Pythagoras is given credit for this realization, in classical Greece, astronomy was a branch of mathematics, astronomers sought to create geometrical models that could imitate the appearances of celestial motions. This tradition began with the Pythagoreans, who placed astronomy among the four mathematical arts, the study of number comprising the four arts was called the Quadrivium. Although he was not a mathematician, Plato included the quadrivium as the basis for philosophical education in the Republic. He encouraged a younger mathematician, Eudoxus of Cnidus, to develop a system of Greek astronomy, platos main books on cosmology are the Timaeus and the Republic
Deferent and epicycle
In the Hipparchian and Ptolemaic systems of astronomy, the epicycle was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon and planets. In particular it explained the apparent retrograde motion of the five planets known at the time, secondarily, it explained changes in the apparent distances of the planets from Earth. It was first proposed by Apollonius of Perga at the end of the 3rd century BC, in both Hipparchian and Ptolemaic systems, the planets are assumed to move in a small circle called an epicycle, which in turn moves along a larger circle called a deferent. Both circles rotate clockwise and are parallel to the plane of the Suns orbit. Despite the fact that the system is considered geocentric, each planets motion was not centered on the Earth, the orbits of planets in this system are similar to epitrochoids. In the Hipparchian system the epicycle rotated and revolved along the deferent with uniform motion, Ptolemy found that he could not reconcile that with the Babylonian observational data available to him, in particular, the shape and size of the apparent retrogrades differed.
The angular rate at which the epicycle traveled was not constant unless he measured it from another point which he called the equant and it was the use of equants to decouple uniform motion from the center of the circular deferents that distinguished the Ptolemaic system. Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest, all of his calculations were done with respect to a normalized deferent, considering a single case at a time. This is not to say that he believed the planets were all equidistant and he generally ordered the planets outward from the Earth based on their orbit periods. That means that all the bodies revolve in their epicycles in lock step with Ptolemys sun, Babylonian observations showed that for superior planets the planet would typically move through in the night sky slower than the stars. Each night the planet appeared to lag a little behind the stars, near opposition, the planet would appear to reverse and move through the night sky faster than the stars for a time in retrograde motion before reversing again and resuming prograde.
Epicyclic theory, in part, sought to explain this behavior, the inferior planets were always observed to be near the sun, appearing only shortly before sunrise or shortly after sunset. Their apparent retrograde motion occurs during the transition between evening star into morning star, as they pass between Earth and the sun, when ancient astronomers viewed the sky, they saw the Sun and stars moving overhead in a regular fashion. They saw the wanderers or planetai, the regularity in the motions of the wandering bodies suggested that their positions might be predictable. Furthermore, Aristotelian physics was not designed with these sorts of calculations in mind, the apparent motion of the heavenly bodies with respect to time is cyclical in nature. Apollonius of Perga realized that this variation could be represented visually by small circular orbits, or epicycles, revolving on larger circular orbits. Deferents and epicycles in the ancient models did not represent orbits in the modern sense, claudius Ptolemy refined the deferent/epicycle concept and introduced the equant as a mechanism for accounting for velocity variations in the motions of the planets.
The empirical methodology he developed proved to be accurate for its day and was still in use at the time of Copernicus
Equinox
An equinox is the moment in which the plane of Earths equator passes through the center of the Sun, which occurs twice each year, around 20 March and 23 September. On an equinox and night are of equal duration all over the planet. They are not exactly equal, due to the size of the sun. To avoid this ambiguity, the word equilux is sometimes used to mean a day in which the durations of light, see Length of equinoctial day and night for further discussion. The word is derived from the Latin aequinoctium and nox, the equinoxes are the only times when the solar terminator is perpendicular to the equator. As a result, the northern and southern hemispheres are equally illuminated, the word comes from Latin equi or equal and nox meaning night. In other words, the equinoxes are the times when the subsolar point is on the equator. The subsolar point crosses the equator moving northward at the March equinox, the equinoxes, along with solstices, are directly related to the seasons of the year. In the southern hemisphere, the equinox occurs in September.
When Julius Caesar established the Julian calendar in 45 BC, he set 25 March as the date of the spring equinox. Because the Julian year is longer than the tropical year. By 1500 AD, it had drifted backwards to 11 March and this drift induced Pope Gregory XIII to create a modern Gregorian calendar. However, the leap year intervals in his calendar were not smooth and this causes the equinox to oscillate by about 53 hours around its mean position. This in turn raised the possibility that it could fall on 22 March, the astronomers chose the appropriate number of days to omit so that the equinox would swing from 19 to 21 March but never fall on the 22nd. Vernal equinox and Autumnal equinox, these names are direct derivatives of Latin. The equivalent common language English terms spring equinox and autumn equinox are even more ambiguous, March equinox and September equinox, names referring to the months of the year they occur, with no ambiguity as to which hemisphere is the context. They are still not universal, however, as not all use a solar-based calendar where the equinoxes occur every year in the same month.
Northward equinox and southward equinox, names referring to the apparent direction of motion of the Sun
Constellation
A constellation is formally defined as a region of the celestial sphere, with boundaries laid down by the International Astronomical Union. The constellation areas mostly had their origins in Western-traditional patterns of stars from which the constellations take their names, in 1922, the International Astronomical Union officially recognized the 88 modern constellations, which cover the entire sky. They began as the 48 classical Greek constellations laid down by Ptolemy in the Almagest, Constellations in the far southern sky are late 16th- and mid 18th-century constructions. 12 of the 88 constellations compose the zodiac signs, though the positions of the constellations only loosely match the dates assigned to them in astrology. The term constellation can refer to the stars within the boundaries of that constellation. Notable groupings of stars that do not form a constellation are called asterisms, when astronomers say something is “in” a given constellation they mean it is within those official boundaries.
Any given point in a coordinate system can unambiguously be assigned to a single constellation. Many astronomical naming systems give the constellation in which an object is found along with a designation in order to convey a rough idea in which part of the sky it is located. For example, the Flamsteed designation for bright stars consists of a number, the word constellation seems to come from the Late Latin term cōnstellātiō, which can be translated as set of stars, and came into use in English during the 14th century. It denotes 88 named groups of stars in the shape of stellar-patterns, the Ancient Greek word for constellation was ἄστρον. Colloquial usage does not draw a distinction between constellation in the sense of an asterism and constellation in the sense of an area surrounding an asterism. The modern system of constellations used in astronomy employs the latter concept, the term circumpolar constellation is used for any constellation that, from a particular latitude on Earth, never sets below the horizon.
From the North Pole or South Pole, all constellations south or north of the equator are circumpolar constellations. In the equatorial or temperate latitudes, the term equatorial constellation has sometimes been used for constellations that lie to the opposite the circumpolar constellations. They generally include all constellations that intersect the celestial equator or part of the zodiac, usually the only thing the stars in a constellation have in common is that they appear near each other in the sky when viewed from the Earth. In galactic space, the stars of a constellation usually lie at a variety of distances, since stars travel on their own orbits through the Milky Way, the star patterns of the constellations change slowly over time. After tens to hundreds of thousands of years, their familiar outlines will become unrecognisable, the terms chosen for the constellation themselves, together with the appearance of a constellation, may reveal where and when its constellation makers lived.
The earliest direct evidence for the constellations comes from inscribed stones and it seems that the bulk of the Mesopotamian constellations were created within a relatively short interval from around 1300 to 1000 BC
Sun
The Sun is the star at the center of the Solar System. It is a perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99. 86% of the total mass of the Solar System. About three quarters of the Suns mass consists of hydrogen, the rest is mostly helium, with smaller quantities of heavier elements, including oxygen, neon. The Sun is a G-type main-sequence star based on its spectral class and it formed approximately 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into a disk that became the Solar System. The central mass became so hot and dense that it eventually initiated nuclear fusion in its core and it is thought that almost all stars form by this process.
The Sun is roughly middle-aged, it has not changed dramatically for more than four billion years and it is calculated that the Sun will become sufficiently large enough to engulf the current orbits of Mercury and probably Earth. The enormous effect of the Sun on Earth has been recognized since prehistoric times, the synodic rotation of Earth and its orbit around the Sun are the basis of the solar calendar, which is the predominant calendar in use today. The English proper name Sun developed from Old English sunne and may be related to south, all Germanic terms for the Sun stem from Proto-Germanic *sunnōn. The English weekday name Sunday stems from Old English and is ultimately a result of a Germanic interpretation of Latin dies solis, the Latin name for the Sun, Sol, is not common in general English language use, the adjectival form is the related word solar. The term sol is used by planetary astronomers to refer to the duration of a solar day on another planet. A mean Earth solar day is approximately 24 hours, whereas a mean Martian sol is 24 hours,39 minutes, and 35.244 seconds.
From at least the 4th Dynasty of Ancient Egypt, the Sun was worshipped as the god Ra, portrayed as a falcon-headed divinity surmounted by the solar disk, and surrounded by a serpent. In the New Empire period, the Sun became identified with the dung beetle, in the form of the Sun disc Aten, the Sun had a brief resurgence during the Amarna Period when it again became the preeminent, if not only, divinity for the Pharaoh Akhenaton. The Sun is viewed as a goddess in Germanic paganism, Sól/Sunna, in ancient Roman culture, Sunday was the day of the Sun god. It was adopted as the Sabbath day by Christians who did not have a Jewish background, the symbol of light was a pagan device adopted by Christians, and perhaps the most important one that did not come from Jewish traditions
Antoninus Pius
Antoninus Pius, known as Antoninus, was Roman Emperor from 138 to 161. He was one of the Five Good Emperors in the Nerva–Antonine dynasty and he died of illness in 161 and was succeeded by his adopted sons Marcus Aurelius and Lucius Verus as co-emperors. He was born as the child of Titus Aurelius Fulvus. The Aurelii Fulvii were therefore a new senatorial family from Gallia Narbonensis whose rise to prominence was supported by the Flavians. The link between Antoninus family and their home province explains the importance of the post of Proconsul of Gallia Narbonensis during the late Second Century. Antoninus was born near Lanuvium and his mother was Arria Fadilla, the Arrii Antoninii were an older senatorial family from Italy, very influential during Nervas reign. Arria Fadilla, Antoninus mother, married afterwards Publius Julius Lupus, a man of rank, suffect consul in 98. Some time between 110 and 115, Antoninus married Annia Galeria Faustina the Elder and they are believed to have enjoyed a happy marriage.
Faustina was the daughter of consul Marcus Annius Verus and Rupilia Faustina, Faustina was a beautiful woman, and despite rumours about her character, it is clear that Antoninus cared for her deeply. Faustina bore Antoninus four children, two sons and two daughters and they were, Marcus Aurelius Fulvus Antoninus, his sepulchral inscription has been found at the Mausoleum of Hadrian in Rome. Marcus Galerius Aurelius Antoninus, his sepulchral inscription has been found at the Mausoleum of Hadrian in Rome and his name appears on a Greek Imperial coin. Aurelia Fadilla, she married Lucius Lamia Silvanus, consul 145 and she appeared to have no children with her husband and her sepulchral inscription has been found in Italy. Annia Galeria Faustina Minor or Faustina the Younger, a future Roman Empress, married her maternal cousin, when Faustina died in 141, Antoninus was greatly distressed. In honour of her memory, he asked the Senate to deify her as a goddess and he had various coins with her portrait struck in her honor.
These coins were scripted ‘DIVA FAUSTINA’ and were elaborately decorated and he further created a charity which he founded and called it Puellae Faustinianae or Girls of Faustina, which assisted destitute girls of good family. Finally, Antoninus created a new alimenta, instead, he lived with Galena Lysistrata, one of Faustinas freed women. Concubinage was a form of female companionship sometimes chosen by powerful men in Ancient Rome, especially widowers like Vespasian and their union could not produce any legitimate offspring who could threaten any heirs, such as those of Antoninus. Also, as one could not have a wife and a concubine at the same time
Zodiac
The zodiac is an area of the sky centered upon the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets remain close to the ecliptic, within the belt of the zodiac, in western astrology and astronomy, the zodiac is divided into twelve signs, each sign occupying 30° of celestial longitude. Because the signs are regular, they do not correspond exactly to the boundaries of the twelve constellations after which they are named, the English word zodiac derives from zōdiacus, the Latinized form of the Ancient Greek zōidiakòs kýklos, meaning circle of little animals. Zōidion is the diminutive of zōion, the name reflects the prominence of animals among the twelve signs. The construction of the zodiac is described in Ptolemys vast 2nd century AD work, the term zodiac may refer to the region of the celestial sphere encompassing the paths of the planets corresponding to the band of about eight arc degrees above and below the ecliptic.
The zodiac of a planet is the band that contains the path of that particular body, e. g. the zodiac of the Moon is the band of five degrees above. By extension, the zodiac of the comets may refer to the band encompassing most short-period comets, the division of the ecliptic into the zodiacal signs originates in Babylonian astronomy during the first half of the 1st millennium BC. The zodiac draws on stars in earlier Babylonian star catalogues, such as the MUL. APIN catalogue, around the end of the 5th century BC, Babylonian astronomers divided the ecliptic into twelve equal signs, by analogy to twelve schematic months of thirty days each. Each sign contained thirty degrees of longitude, thus creating the first known celestial coordinate system. Because the division was made into equal arcs, 30° each, in Babylonian astronomical diaries, a planet position was generally given with respect to a zodiacal sign alone, less often in specific degrees within a sign. When the degrees of longitude were given, they were expressed with reference to the 30° of the zodiacal sign, in astronomical ephemerides, the positions of significant astronomical phenomena were computed in sexagesimal fractions of a degree.
For daily ephemerides, the positions of a planet were not as important as the astrologically significant dates when the planet crossed from one zodiacal sign to the next. The Babylonian star catalogs entered Greek astronomy in the 4th century BC, Babylonia or Chaldea in the Hellenistic world came to be so identified with astrology that Chaldean wisdom became among Greeks and Romans the synonym of divination through the planets and stars. Hellenistic astrology derived in part from Babylonian and Egyptian astrology, horoscopic astrology first appeared in Ptolemaic Egypt. The Dendera zodiac, a dating to ca.50 BC, is the first known depiction of the classical zodiac of twelve signs. The earliest extant Greek text using the Babylonian division of the zodiac into 12 signs of 30 equal degrees each is the Anaphoricus of Hypsicles of Alexandria. Particularly important in the development of Western horoscopic astrology was the astrologer and astronomer Ptolemy, whose work Tetrabiblos laid the basis of the Western astrological tradition.
Under the Greeks, and Ptolemy in particular, the planets, Ptolemy lived in the 2nd century AD, three centuries after the discovery of the precession of the equinoxes by Hipparchus around 130 BC
Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, after Mercury. Named after the Roman god of war, it is referred to as the Red Planet because the iron oxide prevalent on its surface gives it a reddish appearance. Mars is a planet with a thin atmosphere, having surface features reminiscent both of the impact craters of the Moon and the valleys and polar ice caps of Earth. The rotational period and seasonal cycles of Mars are likewise similar to those of Earth, Mars is the site of Olympus Mons, the largest volcano and second-highest known mountain in the Solar System, and of Valles Marineris, one of the largest canyons in the Solar System. The smooth Borealis basin in the northern hemisphere covers 40% of the planet, Mars has two moons and Deimos, which are small and irregularly shaped. These may be captured asteroids, similar to 5261 Eureka, a Mars trojan, there are ongoing investigations assessing the past habitability potential of Mars, as well as the possibility of extant life.
Future astrobiology missions are planned, including the Mars 2020 and ExoMars rovers, liquid water cannot exist on the surface of Mars due to low atmospheric pressure, which is about 6⁄1000 that of the Earths, except at the lowest elevations for short periods. The two polar ice caps appear to be largely of water. The volume of ice in the south polar ice cap, if melted. On November 22,2016, NASA reported finding a large amount of ice in the Utopia Planitia region of Mars. The volume of water detected has been estimated to be equivalent to the volume of water in Lake Superior, Mars can easily be seen from Earth with the naked eye, as can its reddish coloring. Its apparent magnitude reaches −2.91, which is surpassed only by Jupiter, the Moon, optical ground-based telescopes are typically limited to resolving features about 300 kilometers across when Earth and Mars are closest because of Earths atmosphere. Mars is approximately half the diameter of Earth with an area only slightly less than the total area of Earths dry land.
Mars is less dense than Earth, having about 15% of Earths volume and 11% of Earths mass, the red-orange appearance of the Martian surface is caused by iron oxide, or rust. It can look like butterscotch, other common colors include golden, tan. Like Earth, Mars has differentiated into a metallic core overlaid by less dense materials. Current models of its interior imply a core with a radius of about 1,794 ±65 kilometers, consisting primarily of iron and this iron sulfide core is thought to be twice as rich in lighter elements than Earths. The core is surrounded by a mantle that formed many of the tectonic and volcanic features on the planet
Ancient Greek
Ancient Greek includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD. It is often divided into the Archaic period, Classical period. It is antedated in the second millennium BC by Mycenaean Greek, the language of the Hellenistic phase is known as Koine. Koine is regarded as a historical stage of its own, although in its earliest form it closely resembled Attic Greek. Prior to the Koine period, Greek of the classic and earlier periods included several regional dialects, Ancient Greek was the language of Homer and of fifth-century Athenian historians and philosophers. It has contributed many words to English vocabulary and has been a subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical phases of the language, Ancient Greek was a pluricentric language, divided into many dialects. The main dialect groups are Attic and Ionic, Arcadocypriot, some dialects are found in standardized literary forms used in literature, while others are attested only in inscriptions.
There are several historical forms, homeric Greek is a literary form of Archaic Greek used in the epic poems, the Iliad and Odyssey, and in poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic, the origins, early form and development of the Hellenic language family are not well understood because of a lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between the divergence of early Greek-like speech from the common Proto-Indo-European language and the Classical period and they have the same general outline, but differ in some of the detail. The invasion would not be Dorian unless the invaders had some relationship to the historical Dorians. The invasion is known to have displaced population to the Attic-Ionic regions, the Greeks of this period believed there were three major divisions of all Greek people—Dorians and Ionians, each with their own defining and distinctive dialects.
Often non-west is called East Greek, Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian had come under a strong Northwest Greek influence, and can in some respects be considered a transitional dialect, thessalian likewise had come under Northwest Greek influence, though to a lesser degree. Most of the dialect sub-groups listed above had further subdivisions, generally equivalent to a city-state and its surrounding territory, Doric notably had several intermediate divisions as well, into Island Doric, Southern Peloponnesus Doric, and Northern Peloponnesus Doric. The Lesbian dialect was Aeolic Greek and this dialect slowly replaced most of the older dialects, although Doric dialect has survived in the Tsakonian language, which is spoken in the region of modern Sparta. Doric has passed down its aorist terminations into most verbs of Demotic Greek, by about the 6th century AD, the Koine had slowly metamorphosized into Medieval Greek
Gnomon
A gnomon is the part of a sundial that casts a shadow. The term has come to be used for a variety of purposes in mathematics, a painted stick from 2300 BCE found in China is the oldest known gnomon. Anaximander is credited with introducing this Babylonian instrument to the Greeks, oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another. Later, the term was used for an L-shaped instrument like a steel square used to right angles. This shape may explain its use to describe a shape formed by cutting a square from a larger one. Euclid extended the term to the figure formed by removing a similar parallelogram from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive figurate numbers, including square and triangular numbers, hero of Alexandria defined a gnomon as that which, when added to an entity, makes a new entity similar to the starting entity. In this sense Theon of Smyrna used it to describe a number added to a polygonal number produces the next one of the same type.
The most common use in this sense is an odd integer especially when seen as a number between square numbers. Perforated gnomons projecting an image of the sun were described in the Chinese Zhoubi Suanjing writings. The location of the circle can be measured to tell the time of day. In Arab and European cultures its invention was attributed to Egyptian astronomer. With markings on the floor it tells the time of each midday as well as the date of the summer solstice. Italian mathematician, engineer and geographer Leonardo Ximenes reconstructed the gnomon according to his new measurements in 1756, in the northern hemisphere, the shadow-casting edge of a sundial gnomon is normally oriented so that it points north and is parallel to the rotation axis of the Earth. That is, it is inclined to the horizontal at an angle equals the latitude of the sundials location. At present, such a gnomon should thus point almost precisely at Polaris, on some sundials, the gnomon is vertical. These were usually used in times for observing the altitude of the Sun.
The style is the part of the gnomon that casts the shadow and this can change as the sun moves
Nicolaus Copernicus
Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in law and was a mathematician, physician, classics scholar, governor, diplomat. In 1517 he derived a quantity theory of money – a key concept in economics –, Nicolaus Copernicus was born on 19 February 1473 in the city of Toruń, in the province of Royal Prussia, in the Crown of the Kingdom of Poland. His father was a merchant from Kraków and his mother was the daughter of a wealthy Toruń merchant, Nicolaus was the youngest of four children. His brother Andreas became an Augustinian canon at Frombork and his sister Barbara, named after her mother, became a Benedictine nun and, in her final years, prioress of a convent in Chełmno, she died after 1517. His sister Katharina married the businessman and Toruń city councilor Barthel Gertner and left five children, Copernicus fathers family can be traced to a village in Silesia near Nysa.
The villages name has been variously spelled Kopernik, Copernic, Coprirnik, in the 14th century, members of the family began moving to various other Silesian cities, to the Polish capital, Kraków, and to Toruń. The father, Mikołaj the Elder, likely the son of Jan, Nicolaus was named after his father, who appears in records for the first time as a well-to-do merchant who dealt in copper, selling it mostly in Danzig. He moved from Kraków to Toruń around 1458, Nicolaus father was actively engaged in the politics of the day and supported Poland and the cities against the Teutonic Order. In 1454 he mediated negotiations between Polands Cardinal Zbigniew Oleśnicki and the Prussian cities for repayment of war loans, Copernicuss father married Barbara Watzenrode, the astronomers mother, between 1461 and 1464. The Modlibógs were a prominent Polish family who had been known in Polands history since 1271. The Watzenrode family, like the Kopernik family, had come from Silesia from near Świdnica and they soon became one of the wealthiest and most influential patrician families.
Lucas Watzenrode the Elder, a merchant and in 1439–62 president of the judicial bench, was a decided opponent of the Teutonic Knights. In 1453 he was the delegate from Toruń at the Grudziądz conference that planned the uprising against them, Lucas Watzenrode the Younger, the astronomers maternal uncle and patron, was educated at the University of Kraków and at the universities of Cologne and Bologna. He was an opponent of the Teutonic Order, and its Grand Master once referred to him as the devil incarnate. In 1489 Watzenrode was elected Bishop of Warmia against the preference of King Casimir IV, as a result, Watzenrode quarreled with the king until Casimir IVs death three years later. Watzenrode was able to close relations with three successive Polish monarchs, John I Albert, Alexander Jagiellon, and Sigismund I the Old. He was a friend and key advisor to each ruler, Watzenrode came to be considered the most powerful man in Warmia, and his wealth and influence allowed him to secure Copernicus education and career as a canon at Frombork Cathedral
