Hipparchus of Rhodes:
Hipparchus, (b. Nicaea, Bithynia--d. after 127 BC, Rhodes?), Greekastronomer and mathematician who discovered the precession of theequinoxes, calculated the length of the year to within 6 1/2 minutes,compiled the first known star catalog, and made an early formulationof trigonometry.
Hipparchus carried out his observations in Bithynia, at Rhodes, wherehe spent much time, and also, it seems, at Alexandria. The year 127BC is usually cited as the last date known for his actual work, and aFrench astronomer, Jean-Baptiste-Joseph Delambre (1749-1822), clearlydemonstrated that some observations of Hipparchus on the star EtaCanis Majoris could well have been carried out in that year.
Most of contemporary knowledge of Hipparchus is contained in thewritings of Strabo of Amaseia (flourished c. AD 21) and in the greatastronomical compendium Almagest by Ptolemy (flourished AD 127-151).Ptolemy often quotes Hipparchus, and it is obvious that he thoughthighly of him; indeed, as a result of the slow progress of earlyscience, he speaks of him with the respect due a distinguishedcontemporary, although almost three centuries separated the work ofthe two men. It is difficult always to determine to which of themcredit is due.
It is certain, however, that in all his work Hipparchus showed aclear mind and a dislike for unnecessarily complex hypotheses. Herejected not only all astrological teaching but also the heliocentricviews of the universe that seem to have been proposed, according toArchimedes (c. 287-212 BC), by Aristarchus of Samos (flourished c.270 BC) and that were resuscitated by Seleucus the Babylonian, acontemporary of Hipparchus. In this connection, it is necessary torecall that strong arguments had been advanced against the idea ofthe motion of the Earth, and the general climate of opinion had neverbeen favourable to following up the lead given by Aristarchus.Moreover, the system of movable eccentrics, and that of epicycles anddeferents, accounted well for most of the irregularities observed inthe motions of the Sun, the Moon, and the planets. These two systemswere based on the erroneous belief that all celestial movement isregular and circular, or at least that it is best described in termsof a system of regular motion in circles. In the system of movableeccentrics, the centres of the supposed orbits of bodies around theEarth were themselves revolving around the Earth. In the other,epicycles were small circles theoretically imposed on the greatcircular orbital paths, which were called deferents. Theepicycle-deferent mechanism was found with that of the movableeccentric in Ptolemy's late form of the geocentric system ofcosmology. It was, of course, this Ptolemaic geocentric system thatwas handed down to western European science, but it must beremembered that the views of Hipparchus had a profound influence onPtolemy, as he himself acknowledged. It was not until the 15thcentury that regular observations over very long periods showed thegeocentric hypothesis to be too complex to be acceptable andCopernicus proposed that the Sun is the centre of the universe.
Few details are known of the instruments that Hipparchus used. Itseems likely that he observed with the usual devices current in hisday, although Ptolemy credits him with the invention of an improvedtype of theodolite with which to measure angles.
Hipparchus is best known for his discovery of the precessionalmovement of the equinoxes; i.e., the alterations of the measuredpositions of the stars resulting from the movement of the points ofintersection of the ecliptic (the plane of the Earth's orbit) and ofthe celestial equator (the great circle formed in the sky by theprojection outward of the Earth's equator). It appears that he wrotea work bearing "precession of the equinoxes" in the title. The termis still in current use, although the phenomenon is more usuallyreferred to merely as "precession." This notable discovery was theresult of painstaking observations worked upon by an acute mind.Hipparchus observed the positions of the stars and then compared hisresults with those of Timocharis of Alexandria about 150 yearsearlier and with even earlier observations made in Babylonia.
He discovered that the celestial longitudes were different and thatthis difference was of a magnitude exceeding that attributable toerrors of observation. He therefore proposed precession to accountfor the size of the difference and he gave a value of 45" or 46"(seconds of arc) for the annual changes. This is very close to thefigure of 50.26" accepted today and is a value much superior to the36" that Ptolemy obtained.
The discovery of precession enabled Hipparchus to obtain more nearlycorrect values for the tropical year (the period of the Sun'sapparent revolution from an equinox to the same equinox again), andalso for the sidereal year (the period of the Sun's apparentrevolution from a fixed star to the same fixed star). Again he wasextremely accurate, so that his value for the tropical year was toogreat by only 6 1/2 minutes.
Observations of star positions measured in terms of celestiallatitude and longitude, as was customary in antiquity, were carriedout by Hipparchus and entered in a catalog--the first star catalogever to be completed. Hipparchus measured the stellar positions withgreater accuracy than any observer before him, and his observationswere of use to Ptolemy and even later to Edmond Halley. To catalogthe stars was thought by some of Hipparchus' contemporaries to be animpiety, but he persevered. Hipparchus had been stimulated in 134 BCby observing a "new star." Concluding that such a phenomenonindicated a lack of permanency in the number of "fixed" stars, hedetermined to catalog them, and no criticism was able to deflect himfrom his original purpose.
Hipparchus' catalog, completed in 129 BC, listed about 850 stars (not1,080 as is often stated), the apparent brightnesses of which werespecified by a system of six magnitudes similar to that used today.For its time, the catalog was a monumental achievement.
In his work on the Sun and Moon Hipparchus used the observations ofothers as well as his own. He showed that the system based on movableeccentrics and that based on epicycles and deferents were equivalentin the motions they gave for the Sun and Moon and, indeed, for theplanets. Both methods gave the position of the Sun correct to within1', and Hipparchus rejected the peculiar notion, prevalent in hisday, that the Sun moved in an orbit inclined to the ecliptic.Hipparchus also redetermined the inclination of the ecliptic andobtained a value correct to within 5' of the modern figure.
The motion of the Moon is more complex than that of the Sun, owing tothe perturbations that the Moon suffers from both Earth and Sun; inconsequence, there are more irregularities to be taken intoconsideration. Hipparchus satisfactorily accounted for thatinequality of the Moon's motion that is now known to be due to theelliptical form of its orbit; he utilized the system of circularepicycles and deferent but proposed that the deferent was inclined atan angle of 5 to the ecliptic. His theory gave reasonablysatisfactory results for the motion at Full and New Moon. Hipparchuswas dissatisfied however, for, as he appreciated, the errors atquadrature (when the Moon stands at first and last quarters) were toogreat. He concluded that there was some further inequality in theMoon's motion, but he was unable to discover any means of solvingthis problem, and he said candidly that he was leaving the solutionof this question to those who were to follow him.
Hipparchus also attacked the problem of the relative size of the Sunand Moon and their distance from the Earth. It had long beenappreciated, of course, that the apparent diameter of each was thesame, and various astronomers had attempted to measure the ratio ofsize and distance of the two bodies. Eudoxus obtained a value of 9:1,Phidias (father of Archimedes) 12:1, Archimedes himself 30:1; whileAristarchus believed 20:1 to be correct. The present-day value is,approximately, 393:1. Hipparchus followed the method used byAristarchus, a procedure that depends upon measuring the breadth ofthe Earth's shadow at the distance of the Moon (the measurement beingmade by timing the transit of the shadow across the Moon's diskduring a lunar eclipse). This method really gives the parallax (theapparent change in the position of a celestial body when observedfrom two different directions), and thus the distance, of the Moon,the parallax for the Sun being too small to give a significantresult; moreover the accuracy obtainable for the distance even of theMoon is poor. Dissatisfied with his results, Hipparchus attempted tofind the limits within which the solar parallax must lie forobservations and calculations of a solar eclipse to agree; he hopedthat differences between solar and lunar parallax might thus also berevealed. He obtained no satisfactory result from his efforts,however, and concluded that the solar parallax was probablynegligible. At least he appreciated that the distance of the Sun wasvery great indeed.
Hipparchus was unsuccessful in forming a satisfactory planetarytheory and was scientist enough to avoid building hypotheses oninsufficient evidence. In his work Hipparchus adopted the generallyaccepted order for the Sun, Moon, and planets. With the Earth as thecentre, they were, in order from the Earth, the Moon, Mercury, Venus,the Sun, Mars, Jupiter, and Saturn.
It is to be expected that the astronomical work of Hipparchus shouldhave led him to develop certain departments of mathematics. He madean early formulation of trigonometry and tabulated a table ofchords--i.e., the length of the line joining two points on a unitcircle corresponding to the given angle at the centre; e.g., chordof = 2 sin (/2): he is known to have had a method of solvingspherical triangles. It is also generally agreed that the theorem inplane geometry known as "Ptolemy's theorem" was originally due toHipparchus and was later copied by Ptolemy. During the 18th centurythe French statesman and mathematician Lazare Carnot showed that thewhole of plane trigonometry can be deduced from these formulas.
Hipparchus criticized severely the geographical work of Eratosthenes(c. 276-c. 194 BC) and himself did some work in this field. His maincontribution was to apply rigorous mathematical principles to thedetermination of places on the Earth's surface, and he was the firstto do so by specifying their longitude and latitude--the method usedtoday. Hipparchus was, no doubt, led to this method by his work onthe trigonometry of the sphere. He tried to measure latitude byutilizing the ratio of the longest to the shortest day at aparticular place instead of following the customary method of theBabylonians of measuring the difference in length of day as onetravels northward. Hipparchus also divided the then known inhabitedworld into climatic zones, and suggested that the longitude of placescould be determined by observing, from these places, the moments whena solar eclipse began and ended; but this bold scheme, whiletheoretically satisfactory for a small area of the Earth's surface,was not a practical proposition in his day.
Excerpt from the Encyclopedia Britannica without permission.
