SOLICITUD DE EMISIÓN DE COMPROBANTES FISCALES POR CONCEPTO DE COMPRA DE BASES DE LICITACIONES
NOTA INFORMATIVA PARA INCLUIR EN LAS BASES DE LICITACIÓN DEL GOBIERNO FEDERAL
Untiring efforts of many people have aroused the interest in and revival of the study of fixed stars. It is worth mentioning a few:
Thales of Miletus ('discovered' Ursa Minor)
There is considerable agreement that Thales was born in Miletus in Greek Ionia in the mid 620s BCE and died in about 546 BCE, but even those dates are indefinite. 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. Thales 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's hypotheses were new and bold, and in freeing phenomena from godly intervention, he paved the way towards scientific endeavour. 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's 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.
Callimachus reported that Thales 'discovered' Ursa Minor. This means only that he recognized the advantages of navigating by Ursa Minor, rather than by Ursa Major, as was the preferred method of the Greeks. Ursa Minor, a constellation of six stars, has a smaller orbit than does the Great Bear, which means that, as it circles the North Pole, Ursa Minor changes its position in the sky to a lesser degree than does the Great Bear. Thales offered this sage advice to the mariners of Miletus, to whom it should have been of special value because Miletus had developed a maritime trade of economic importance.
The next landmark in our study of Greek constellation lore is Eratosthenes (c.276–c.194 BC), to whom an essay called the Catasterisms is attributed. Eratosthenes was a Greek scientist and writer who worked in Alexandria at the mouth of the Nile. The Catasterisms gives the mythology of 42 separate constellations (the Pleiades cluster is treated individually), with a listing of the main stars in each figure. The version of the Catasterisms that survives is only a summary of the original, made at some unknown date, and it is not even certain that the original was written by the real Eratosthenes; hence the author of the Catasterisms is usually referred to as pseudo-Eratosthenes. The antiquity of his sources is certain, though, because he quotes in places from a long-lost work on astronomy by Hesiod (c.700 BC)
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Marcus Manilius, a Roman author of whom virtually nothing is known, wrote a book called Astronomica around the year AD 15, clearly influenced by the Phaenomena of Aratus. Manilius’s book deals mostly with astrology rather than astronomy, but it contains numerous insights into constellation lore.
Ptolemy (Claudius Ptolemaeus)
Mathematician, astronomer and geographer; worked c. 127 - 145 AD (Alexandria, Egypt)
Our knowledge about Ptolemy is based exclusively on his works; nothing is known about his life.
Ptolemy was an excellent geometrician, and his works on geometry are among his best. He was also a gifted mathematician, devising new geometrical theorems and proofs. Being primarily interested in astronomy, he studied the projection of points on the celestial sphere onto three perpendicular planes defined by the horizon, the meridian and the perpendicular, a system still used today.
By far the most important of his works is the Almagest. Its original title was The Mathematike Syntaxis ("The Mathematical Collection"). It was such an encyclopaedic summary of astronomical knowledge that it soon became known as Ho megas astonomos "The Great Astronomer"). Arab astronomers of the 9th century considered it Megiste ("Greatest"), added the Arabian definite article al and referred to it as al-Megiste ("The Greatest") or Almagest.
The Almagest describes in great detail the arrangement of the sun, the planets and all stars in a system where the Earth is at rest in the centre of the universe. It also contains a star catalogue of 1,022 stars, an effort not even surpassed by Kepler in the 15th century.
Ptolemy modified the mathematical model of deferents and epicycles (circles moving on circles) that existed at the time to describe the observed movement of the planets and improved its capability to predict their movement. His system, known as the Ptolemaic system, became the accepted view of the universe for 1,400 years. (During the 16th century the increased accuracy of star observations made it impossible to ignore the discrepancies between Ptolemy's system and actual star movement, and Galilei began to teach that the Earth revolves around the Sun.)
Other works of Ptolemy include several books on mathematics and geometry;
• five books on optics, where he discusses the theory of refraction and is the first known astronomer to discuss refraction of light from celestial bodies at different elevation from the horizon;
• eight books on geography, which tabulate places of the known world in latitude and longitude and give instructions how to construct maps; and
• thirteen books on astronomy, known since the 9th century as the Almagest.
Ptolemy's geographical works were of lesser quality. They contained many errors: The equator was too far north, the circumference of the Earth was 30% too small (other scientists had already established much more correct values), Asia reached much further east than in reality, and the Indian Ocean was bounded in the south by another continent. Scientifically the most important contribution was his application of mathematics to the mapping of positions on Earth according to latitude and longitude.
Ptolemy's reputation as an excellent geometer and astronomer made his geographical works more credible than they should have been, and their influence was far-reaching. Columbus used them in the 15th century as an argument that it would not be difficult to reach India going west. The belief in a great southern continent was not abandoned until 1775, when James Cook returned from his voyage to the Southern Hemisphere.
The Chinese
The Chinese have been observing the sky for several millennia, making them the oldest civilization with a continuous astronomical record. The Chinese required that their astronomers were correctly able to predict astronomical events, such as eclipses; otherwise, they were executed.
As far as cataloguing went, Shi Shen, Gan De, and Wu Xian (370-270 B.C.) in sum recorded 1464 stars in 284 constellations. This is 200 years before the first western catalogue (by Hipparchus). In A.D. 310, Astronomer Royal Qian Luozhi had a bronze celestial globe made with stars that were color-coded as to their source. From the Han Dynasty, there are carvings that show constellations and asterisms with stars linked to delineate the various groups. The sky was also divided into Nine Fields, which involved the circumpolar region and eight other divisions. The eight other divisions can be related to eight hexagrams which appear in the Yi Jing (The Book of Changes), which dates from the 2nd century B.C.
The Chinese constellations were in the form of Five Palaces; the number five possibly results from the five elements of earth, fire, water, metal, and wood.
• The Palace of Purple Tenuity was the circumpolar area.
• The Palace of the East was the Azure Dragon.
• The Palace of the South was the Vermillion Bird.
• The Palace of the West was the White Tiger.
• The Palace of the North was the Dark Warrior, represented by an intertwined turtle and snake.
Yet another type of sky division were the Lunar Mansions, which goes back to at least the 5th century B.C. It involves 28 divisions, based upon the lunar sidereal period being 27.32 days. This was of particular importance in astrology.
For charts, the earliest known dates to around A.D. 700. Though it has no grid lines, it contains over 1350 stars, and is a flat version of the Qian Luozhi globe. Nearly 400 years later, in A.D. 1094, the Song Dynasty created star charts. They show coordinates and were prepared for use with an "armillary sphere" - a sphere that consists of a number of rings arranged so as to model the circles of the celestial sphere. Until the Renaissance, these were the most accurate star charts available.
- 84 - The Polynesians
The Polynesian islanders were among the first people to navigate the oceans, and they used the stars to guide them. The sun marked their day, but very strict records of stars were kept in order to guide them during the night; this practice started before the dawn of the Christian era -- over 2000 years ago.
Often, the way they would keep track of stars was by creating mythologies around them, much as the Greeks did. For example, the Pleiades (an open cluster), Jupiter, and Aldebaran (a bright red star), are central to the founding story of the polynesian culture
The Religion of the Parsian
Mir Du'l-feqar Ardestani (ca. 1671-70) in 'School of religious doctrines' speaks of the speaks of the Religion of the Parsian. He states that “The first creation of his existence -- bestowing bounty was the precious jewel of the intellectual principle, called Yazad Vohuman; the solar ray which constitutes the excellence of His august existence is from the essence of the light of lights. From the effulgence of Vohuman, or the "First Intelligence," proceeded another, along with the spirit and body of the Pure Ether or Crystalline Sphere. In like manner, from the second Srosh or "angel" there emanated three similar rays; so that every star in the universe, whether in motion or at rest, that is, every planet and fixed star, and also every one of the heavens, has its peculiar intellect and spirit.”
The contribution of the Arabs to the study of the fixed stars Prof. Paul Kunitzsch in “Arabs and the Stars” states:
“The important role played by the Arabs in transmission and development of the sciences is well known.”
The inhabitants of the Arabian Peninusla, mostly Bedouins, possessed a good knowledge of the sky. A large number of fixed stars and asterisms were known and used for orientation in the desert, and for calendrical purposes such as determnining seasons, agricultural activities and social or religious events.
After the spread of Islam, the Arabs became acquainted with the scientific heritage of Greece, India and Persia and by about eighth century A.D. onwards, the Islamic world took part in the transmission and development of sciences.
The most influential source for scientific knowledge of the fixed stars now became the star catalogue in Ptolemy’s Almagest, comprising l025 stars arranged in the 48 classical constellations.
Another important aspect of historical importance is the transmission of Arabic-Islamic science to medieval Europe, through translations into Latin, in twelfth century Spain. Thus their knowledge exerted a fundamental influence on the West.
Technical terms in astronomy such as Zenith, Nadir, and more than 200 star names, appearing at various stages of the scientific development of the West, are enough testimonies to the Arabic influence of that time and they remain alive into our own days.
Abd Al-Rahman Al Sufi (December 7, 903 - May 25, 986) was a Muslim astronomer also known as 'Abd ar-Rahman as-Sufi, or 'Abd al-Rahman Abu al-Husain, and known in the west as Azophi.
He lived in the court of Emire Adud ad-Daula in Isfahan, Persia, and worked on translating and expanding Greek astronomical works, especially the Almagest of Ptolemy. He contributed several corrections to Ptolemy's star list and did his own brightness and magnitude estimates which frequently deviated from those in Ptolemy's work. He was the first to attempt to relate the Greek with the traditional Arabic star names and constellations, which were completely unrelated and overlapped in complicated ways.
He observed that the ecliptic plane is inclined with respect to the celestial equator and more accurately calculated the length of the solar year. He observed and described the stars, their positions, their magnitudes (brightness) and their colour, setting out his results constellation by constellation. For each constellation, he provided two drawings, one from the outside of a celestial globe, and the other from the inside (as seen from the sky). Al Sufi also wrote on the astrolabe, finding numerous additional uses for it.
Al Sufi published his famous "Book of Fixed Stars" in 964, describing much of his work, both in textual descriptions and pictures. Al Sufi was honoured by the Astronomical community when a Moon Crater was named after him. It is Moon Crater Azophi and is at lunar co-ordinates 22.1S, 12.7E and 47 km in diameter
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Arabic Constellation Name
Constellation Arabic Name Arabic Name Arabic Meaning N/S Andromeda Al-Mara'ah Al-Musalsalah The Shackled Woman N
Antlia Mefraghat Al-Hawa' The Air Pump S
Apus Tta'er Al-Ferdaws Bird of Paradise S
Aquarius Ad-Dalw The Well-bucket S
Aquila Al-'Okab The Eagle N-S
Ara Al-Mijmarah The Censer S
Aries Al-Hamal The Ram N
Auriga Momsek Al-A'aennah The Reins-holder N
Bootes Al-'Awwa' The Howler N
Caelum Aalat An-
Naqqash
The Sculptor's
Tool S
Camelopardalis Az-Zarafah The Giraffe N
Cancer As-Sarattan The Crab N
Canes Venatici As-Sloqeyyan The Two Hunting Dogs N Canis Major Al-Kalb Al-A'kbar The Greater Dog S Canis Minor Al-Kalb Al-A'sghar The Lesser Dog N
Capricornus Al-Jadi The Young Goat S
Cassiopeia That Al-Korsi Who (Lady) Has Chair N
Centaurus Qanttorus Centaur S
Cepheus Al-Multaheb Inflammatus N
Cetus Qayttas Cetus N-S
Chamaeleon Al-Hirba' The Chameleon S
Circinus Al-Bikar The Compasses S
Columba Al-Hamamah The Dove S
Coma Berenices Al-Hulbah Bristle N
Corona Australis Al-I'klil Al- Janobi The Southern Crown S
Corona Borealis Al-I'klil Ash- Shamali
The Northern
Crown N
Corvus Al-Ghurab The Raven S
Crater Al-Battiyah The Great Cup S
Crux As-Ssaleeb Al-
Janobi
The Southern
Cross S
Cygnus Ad-Dajajah The Hen N
Delphinus Ad-Dulfin The Dolphin N
Dorado Abu-Saif The Swordfish S
Draco At-Tinneen The Dragon N
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Eridanus An-Nahr The River N-S
Fornax Al-Koor The Furnace S
Gemini At-Tawa'man The Twins N
Grus Al-Kurki The Crane (bird) S
Hercules Al-Jathi The Kneeling (Man) N
Horologium As-Sa'ah The Clock S
Hydra Ash-Shuja'a The Brave N-S
Hydrus Hayyat Al-Ma' The Water Snake S
Indus Al-Hindi The Indian S
Lacerta Al-'Adha'ah The Lizard N
Leo Al-A'sad The Lion N
Leo Minor Al-A'sad Al-A'sghar The Lesser Lion N
Lepus Al-A'rnab The Hare S
Libra Al-Mizan The Balance S
Lupus As-Sab'a The Beast of Prey S
Lynx Al-Washaq The Lynx N
Lyra Al-Qitharah The Lyre N
Microscopium Al-Mijhar The Microscope S
Monoceros Waheed Al-Qarn The Unicorn N-S
Musca Ath-Thubabah The Fly S
Norma Morabba'a An-Najjar The Carpenter's Square S
Octans Ath-Thomon The Octant S
Ophiuchus Al-Hawwa' The Snake Charmer N-S
Orion Al-Jabbar The Giant N-S
Pavo Att-Ttawoos The Peacock S
Pegasus Al-Faras Al-A'adham The Great Horse N
Perseus Hamil Ra's Al-Ghul Bearer of the Demon's Head N
Phoenix Al-'Anqa' The Phoenix S
Pictor Aalat Ar-Rassam The Painter's Tool S
Pisces Al-Hut The Whale N
Piscis Austrinus Al-Hut Al-Janubi The Southern
Whale S
Puppis Al-Kawthal The Stern S
Pyxis Bayt Al-Ebrah The Compass S
Reticulum Ash-Shabakah The Reticle S
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Sagittarius Ar-Rami The Archer S
Scorpius Al-'Aqrab The Scorpion S
Sculptor M'amal An-Nahhat The Sculptor's Mill S
Scutum At-Tirs The Shield S
Serpens Al-Hayyah The Snake N-S
Sextans As-Sodos The Sextant N-S
Taurus Ath-Thawr The Bull N
Telescopium Al-Merqab The Telescope S
Triangulum Al-Muthallath The Triangle N
Triangulum
Australe Al-Muthallath Al-Janobi The Southern Triangle S
Tucana Att-Ttuqan The Toucan S
Ursa Major Ad-Dubb Al-
A'kbar The Greater Bear N
Ursa Minor Ad-Dubb Al-A'sghar The Lesser Bear N
Virgo Al-'Athra' The Maiden N-S
Volans As-Samakah Att-Tta'erah The Flying Fish S
Vulpecula Ath-Th'alab The Fox N
N/S: Indicates whether the constellation is a Northern or Southern one. Arabic References:-
1. "Suwarul-Kawakib", by As-Sufi, (Uranometry, by Azophi).
2. "Encyclopedia of Arab Star Names in Ancient and Modern Astronomy", by Dr. Abdul-Rahim Bader.
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The Arabic Mansions of the Moon, and one version of their alignment with the Zodiac. The fixed stars outside the circles are the traditional marker stars associated with each Mansion, and they often share a name, although the star names have been altered through European adoption (two Mansions do not contain any prominent stars). Because of the linkage with the fixed stars, which change their positions with respect to the Sun’s equinoxes because of precession there has been a greater tendency to treat the Mansions as sidereal than tropical, or to shift the Mansion which is regarded as the first one in accordance with the shift of the Vernal Equinox.
Traditionally in both the Indian and Arabic systems the first Mansion was Al Thurayya (the ‘Many Little Ones’; Indian, Krittika, the ‘General of the Celestial Armies’; Greek, the Pleiades). With the systematisation of Greek astronomy and the fixing of Aries as the first sign of the Zodiac, Sheratan, the horns of Aries, became the first Mansion; it is listed as such by Al Biruni (973-1048 CE) and its equivalent Alnath was treated as the first Mansion by, for instance, Chaucer (1340-1400) and Aggrippa (1486-1535) — Botein seems to have missed out. If the marker stars are used, precessional slippage means that the star Scheat (Beta Pegasi) is currently closest to 0° Aries, and will reach the exact longitude of the Spring Equinox in 2045. The alignment given here is based on a list made by George Yeats, but using the Arabic names from Vivian Robson, TheFixed Stars and Constellations in Astrology(YL1772).
The Mansions of the Moon according to H.C, Agrilla’s Occult Philosopy. 1883
Name (Name –
Latin)
From Significance Talisman
For
With Image Of
1 Alnath horns of
Aries
0° Aries journeys and discord the
destruction of someone
A black man in a garment made of hair, and girdled round, casting a small lance with his right hand 2 Albothaim Albocham belly of Aries 12°51'22" Aries
finding treasure and retaining captives reconciliati on with a prince A king crowned 3 Achaomazo ne Athoraye rainy ones or Pleiades 25°42'51" Aries profits sailors, huntsmen, alchemists happy fortune and every good thing A woman well clothed, sitting in a chair, her right hand being lifted up on her head 4 Aldebram Aldelamen eye or head of Taurus