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Topic: Hipparchus

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Hipparchos

Kidinnu

History of astronomy

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140 BC

Equinox

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250 BCE

432 BC

153 BC

Logarithmic tangent

151 BC

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2nd century BC

Tropical year

	Hipparchus
		Hipparchus had been stimulated in 134 BC by observing a "new star." Concluding that such a phenomenon indicated a lack of permanency in the number of "fixed" stars, he determined to catalog them, and no criticism was able to deflect him from his original purpose.
		Hipparchus satisfactorily accounted for that inequality of the Moon's motion that is now known to be due to the elliptical form of its orbit; he utilized the system of circular epicycles and deferent but proposed that the deferent was inclined at an angle of 5 to the ecliptic.
		Hipparchus followed the method used by Aristarchus, a procedure that depends upon measuring the breadth of the Earth's shadow at the distance of the Moon (the measurement being made by timing the transit of the shadow across the Moon's disk during a lunar eclipse).
	abyss.uoregon.edu /~js/glossary/hipparchus.html (1752 words)

	Hipparchus the Astronomer
		Hipparchus discovered the precession of the equinoxes and was influential in the development of trigonometry, redefined and formalized the projection as a method for solving complex astronomical problems without spherical trigonometry and probably proved its main characteristics.
		Hipparchus determined the distance from the Earth to the Moon from observations of a solar eclipse in Syene and in Alexandria.
		Hipparchus, according to Ptolemy, considered that the Earth is not the center of the circular orbit of the Sun.
	www.mlahanas.de /Greeks/Hipparchus.htm (963 words)

	Encyclopedia: Hipparchus (Site not responding. Last check: 2007-10-22)
		Hipparchus (Greek Ἳππαρχος) (circa 190 BC –; circa 120 BC) was a Greek astronomer, geographer, and mathematician.
		Hipparchus is considered the greatest astronomical observer, and by some the greatest astronomer of antiquity.
		Hipparchus is believed to have died on the island of Rhodes, where he spent most of his later life — Ptolemy attributes observations to him from Rhodes in the period from 141 BC to 127 BC.
	www.nationmaster.com /encyclopedia/Hipparchus (6580 words)

	Hipparchus Biography
		That Hipparchus continued to be held in high regard is demonstrated by the various depictions of him on frontispieces of astronomical works published long after his death.
		But Hipparchus did compile the planetary observations to which he had access into a more useful arrangement, and demonstrated that the phenomena were 'not in agreement with the hyotheses of the astronomers of that time'.
		Hipparchus' discussion of the motion of the points of solstice and equinox slowly from east to west against the background of the fixed stars is perhaps his most famous achievement; he has been therefore credited with the discovery of the precession of the equinoxes.
	www.hps.cam.ac.uk /starry/hipparchus.html (773 words)

	Hipparchus (Site not responding. Last check: 2007-10-22)
		Since when Ptolemy refers to results of Hipparchus he does so often in an obscure way, at least he seems to assume that the reader will have access to the original writings by Hipparchus, and it is certainly surprising that neither Theon or Pappus fills in the details.
		Hipparchus appears to know that 67 earth radii for the distance of the moon comes from this upper limit of solar parallax, while the lower value of 59 earth radii corresponds to the sun being at infinity.
		Hipparchus was also able to give an epicycle model for the motion of the sun (which is easier), but he did not attempt to give an epicycle model for the motion of the planets.
	www-gap.dcs.st-and.ac.uk /~history/Mathematicians/Hipparchus.html (2396 words)

	Hipparchus.htm
		Hipparchus also believed that the world was round, and, when attempting to understand the sphere better, he realized that the best way was with a grid of lines dividing it up into 360 degrees.
		Hipparchus not only gave observational data for the moon which enabled him to compute accurately the various periods, but he developed a theoretical model of the motion of the moon based on its circular motion, also known as epicycles.
		Hipparchus was also able to give an epicycle model for the motion of the sun, but he did not attempt to give an epicycle model for the motion of the planets.
	www.astro.utoronto.ca /~bclarke/AST199M/Hipparchus.htm (1784 words)

	Hipparchus on Encyclopedia.com (Site not responding. Last check: 2007-10-22)
		Ptolemy's geocentric theory of the universe was based largely on the conclusions of Hipparchus, a record of whose researches is preserved in the Almagest of Ptolemy.
		In it Hipparchus is credited with the discovery of the precession of the equinoxes, the eccentricity of the sun's apparent orbit, and certain inequalities of the motions of the moon.
		Hipparchus suggested a method of determining longitude by observing the parallax of the moon in eclipse.
	www.encyclopedia.com /html/H/Hipparch2.asp (462 words)

	Hipparchus: Works (Site not responding. Last check: 2007-10-22)
		The term is still in current use, although the phenomenon is more usually referred to merely as "precession." This notable discovery was the result of painstaking observations worked upon by an acute mind.
		Hipparchus observed the positions of the stars and then compared his results with those of Timocharis of Alexandria about 150 years earlier and with even earlier observations made in Babylonia.
		Hipparchus satisfactorily accounted for that inequality of the Moon's motion that is now known to be due to the elliptical form of its orbit; he utilized the system of circular epicycles and deferent but proposed that the deferent was inclined at an angle of 5
	www.space.com /reference/brit/hipparchus/works.html (1196 words)

	[No title]
		Hipparchus is believed to be the first person to determine exactly the times of the rising and setting of the zodiacal signs.
		Hipparchus is credited as generalizing Hypsicles' idea of dividing the ecliptic into 360 degrees, an idea borrowed from the Babylonian astronomers, by dividing every circle into 360 degrees (Sarton 287).
		Hipparchus, in the middle of the first century BC, was the first person known to have treated trigonometry as an applied science, and the first person to compile a table of chords.
	www.math.rutgers.edu /~cherlin/History/Papers2000/hunt.html (1833 words)

	Hipparchus (c. 190-120 BC) (Site not responding. Last check: 2007-10-22)
		Hipparchus or Hipparchos of Nicaea did his observations from Rhodes between 146 and 127 BC.
		He was the first astronomer who compiled a catalog of 850 stars; this work was perhaps triggered by the observation of a "New Star" (Nova) in the constellation Scorpius in 134 BC (according to Roman historian Pliny).
		To remarkable acuracy, he obtained measurements of the value of precession, the length of the year, and (from eclipse observations) the distance of the Moon.
	www.seds.org /messier/xtra/Bios/hipparchus.html (126 words)

	Hipparchus's Understanding of the Precession
		His essential argument is that Hipparchus suggested several possible explanations of precession, and that the one which is the basis of the argument in my book-- i.e., that the precession was a continuous movement of the entire cosmic structure-- was merely one among many suggestions, all of them of more or less equal importance.
		Hipparchus may also have proposed that the sphere of the fixed stars might oscillate back and forth over a short arc of eight degrees, a theory doubtless related to the Babylonian location of the equinoxes at the eighth degree of Aries and Libra.
		Hipparchus may or may not have had definitive proof for his understanding of the nature of the precession of the equinoxes.
	www.well.com /user/davidu/appendix4.html (2285 words)

	Hipparchus on Compound Statements
		(Hipparchus, to be sure, refuted this by showing that on the affirmative side there are 103,049 compound statements, and on the negative side 310,952.)" The exactly meaning of these numbers has been something of a mystery for Greek scholars.
		For example, Heath's "History of Greek Mathematics" says "In pure mathematics [Hipparchus] is said to have considered a problem in permutations and combinations, the problem of finding the number of different possible combinations of 10 axioms or assumptions, which he made to be 103,049 (v.l.
		This does not seem like enough information to pinpoint exactly what Hipparchus had in mind." It might be worth noting that the number 103,049 appears, slightly disguised, in another sequence in Sloane's Encyclopedia, namely M1659, which are identified as the number of "Royal paths in a lattice".
	www.mathpages.com /home/kmath397.htm (781 words)

	How distant is the Moon?
		Hipparchus, who used an eclipse of the Moon to deduce the precession of the equinoxes (here), used a total eclipse of the Sun--probably in 129 BC--to estimate how far the Moon was.
		Hipparchus knew that when the Sun was eclipsed, it and the Moon occupied the same spot on the sphere of the heavens.
		In the time of Hipparchus the pole of the heavens wasn't near Polaris (because of the precession of the equinoxes), but Hipparchus, who had mapped the positions of about 850 stars, must have known its position quite well.
	www-istp.gsfc.nasa.gov /stargaze/Shipparc.htm (1775 words)

	sofTouch APpLications - HIPPARCHUS 5.2.1a
		HIPPARCHUS is not just another generic "desk top planetarium" program, but a fully integrated software package for positional astronomy.
		The instantaneous positions, or orbital tracks, of any of the planets, Sun, Moon (drawn to scale, or designated by their symbols), minor planets, comets and artificial Earth-orbiting satellites may also be indicated on any star chart or horizon view when they fall within the selected area boundary for a specified date or range of dates.
		The precision of the HIPPARCHUS solar system ephemerides is more than sufficient to examine the topocentrically viewed appearance of phenomena such as solar eclipses, planetary transits, and lunar occultations of stars.
	balder.prohosting.com /stouch/HIPPARCHUS.html (694 words)

	TMTh:: HIPPARCHUS OF RHODES
		Hipparchus invented an improved type of astrolabe, which he used to determine with accuracy the co-ordinates of the stars.
		He improved the dioptra, an instrument used to estimate the apparent diameter, distance and size of the sun and the moon, and used and improved various older instruments, including the plumb, the gnomon, the polos, the sundial, the clepsydra, the fixed sphere, the water clock and the rings.
		Hipparchus was the first to divide the circle into 360?.
	www.tmth.edu.gr /en/aet/3/58.html (549 words)

	What Is Visual Magnitude? (Site not responding. Last check: 2007-10-22)
		The term "visual" means the brightness is being measured in the visible part of the spectrum, the part you can see with your eye (usually around 5500 angstroms).
		Hipparchus listed the stars that could be seen in each constellation, described their positions, and rated their brightness on a scale of 1 to 6, the brightest being 1.
		Of course, Hipparchus had no telescope, and so could only see stars as dim as 6th magnitude, but today we can see stars with ground-based telescopes down to about 22nd magnitude.
	liftoff.msfc.nasa.gov /academy/universe/MAG.HTML (385 words)

	Hipparchus
		Hipparchus was a Greek astronomer who lived between 190-120 B.C. He created the first accurate star map and kept a catalogue of over 850 stars with their relative brightnesses.
		He also developed the system of epicycles (where everything in space moved in perfect circles) for the planets that both agreed with observation, and preserved the Earth-centered universe of Aristotle.
		Hipparchus compiled a table of chord lengths, similar to modern trigonometry tables, and is considered the founder of trigonometry, a branch of mathematics which studies the angles of sides of triangles.
	www.windows.ucar.edu /tour/link=/people/ancient_epoch/hipparchus.html (134 words)

	Combinatorics and Hipparchus
		"In pure mathematics [Hipparchus] is said to have considered a problem in permutations and combinations, the problem of finding the number of different possible combinations of 10 axioms or assumptions, which he made to be 103049 (v.l.
		This certainly suggests that Hipparchus was calculating something that was somehow related to the number of bracketing of n letters, although as Stanley says:
		Hipparchus could consider the combinatorics of certain compound statements in Boolean logic involving n ordered elements with the connectives 'and', 'or', and parentheses.
	www.mlahanas.de /Greeks/Combinatorics.htm (642 words)

	Long-lost star catalog discovered on Roman statue
		Hipparchus was one of the greatest astronomers of antiquity and his star catalog was the first in the world, as well as the most influential.
		Precession, as discovered by Hipparchus, is a process whereby the stars and constellation figures slowly move with respect to the celestial equator, tropics and lines of constant right ascension.
		However, it is Hipparchus who is known to have a star catalog created around the correct time, 129 B.C., whereas the next catalog, created by Ptolemy, came much too late, in A.D. In addition, Schaefer said it is known that Hipparchus constructed many sky globes based on his star catalog.
	www.physorg.com /news2711.html (1250 words)

	Hipparchus (disambiguation) - Wikipedia, the free encyclopedia
		A lunar crater named in his honour; see Hipparchus (lunar crater);
		A dialogue ascribed to Plato; see Hipparchus (dialogue).
		This is a disambiguation page, a list of pages that otherwise might share the same title.
	en.wikipedia.org /wiki/Hipparchus (112 words)

	Astro-Fact (Site not responding. Last check: 2007-10-22)
		Hipparchus of Rhodes was a Greek astronomer and geographer, born in 170 BC.
		Inspired by the observation of a new star in 134 BC, Hipparchus constructed a catalogue of about 850 stars and was the first to assign a scale of magnitude to indicate their apparent brightness.
		His scale, numbered from 1 to 6,from brightest to faintest, is still used today although it has since been refined.
	ottawa.rasc.ca /astronomy/astro_facts/hipparcus.html (145 words)

	Hipparchus -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-22)
		The eccenter and epicyclic models sufficed to describe the motion of a body that has a single periodic variation in apparent speed, which so far as Hipparchus knew was the case with the Sun and Moon.
		According to Ptolemy, Hipparchus was aware that the movements of the planets were too complex to be accounted for by the same simple models, but he did not attempt to devise...
		It was included by Hipparchus in the earliest known star catalog, c.
	www.britannica.com /eb/article-9040534 (744 words)

	Ptolemy
		Although noting the discrepancies, Hipparchus seems not to have worked out a better model, but Ptolemy does this in Book 5 where the model he gives improves markedly on the one proposed by Hipparchus.
		In these two book Ptolemy also discusses precession, the discovery of which he attributes to Hipparchus, but his figure is somewhat in error mainly because of the error in the length of the tropical year which he used.
		He suggested that perhaps the errors came from Hipparchus and that Ptolemy might have done nothing more serious than to have failed to correct Hipparchus's data for the time between the equinoxes and solstices.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Ptolemy.html (3086 words)

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