__Hipparchus of Rhodes__:

Hipparchus, (b. Nicaea, Bithynia--d. after 127 BC, Rhodes?), Greek astronomer and mathematician who discovered the precession of the equinoxes, calculated the length of the year to within 6 1/2 minutes, compiled the first known star catalog, and made an early formulation of trigonometry.

Hipparchus carried out his observations in Bithynia, at Rhodes, where he spent much time, and also, it seems, at Alexandria. The year 127 BC is usually cited as the last date known for his actual work, and a French astronomer, Jean-Baptiste-Joseph Delambre (1749-1822), clearly demonstrated that some observations of Hipparchus on the star Eta Canis Majoris could well have been carried out in that year.

Most of contemporary knowledge of Hipparchus is contained in the writings of Strabo of Amaseia (flourished c. AD 21) and in the great astronomical compendium Almagest by Ptolemy (flourished AD 127-151). Ptolemy often quotes Hipparchus, and it is obvious that he thought highly of him; indeed, as a result of the slow progress of early science, he speaks of him with the respect due a distinguished contemporary, although almost three centuries separated the work of the two men. It is difficult always to determine to which of them credit is due.

It is certain, however, that in all his work Hipparchus showed a clear mind and a dislike for unnecessarily complex hypotheses. He rejected not only all astrological teaching but also the heliocentric views of the universe that seem to have been proposed, according to Archimedes (c. 287-212 BC), by Aristarchus of Samos (flourished c. 270 BC) and that were resuscitated by Seleucus the Babylonian, a contemporary of Hipparchus. In this connection, it is necessary to recall that strong arguments had been advanced against the idea of the motion of the Earth, and the general climate of opinion had never been favourable to following up the lead given by Aristarchus. Moreover, the system of movable eccentrics, and that of epicycles and deferents, accounted well for most of the irregularities observed in the motions of the Sun, the Moon, and the planets. These two systems were based on the erroneous belief that all celestial movement is regular and circular, or at least that it is best described in terms of a system of regular motion in circles. In the system of movable eccentrics, the centres of the supposed orbits of bodies around the Earth were themselves revolving around the Earth. In the other, epicycles were small circles theoretically imposed on the great circular orbital paths, which were called deferents. The epicycle-deferent mechanism was found with that of the movable eccentric in Ptolemy's late form of the geocentric system of cosmology. It was, of course, this Ptolemaic geocentric system that was handed down to western European science, but it must be remembered that the views of Hipparchus had a profound influence on Ptolemy, as he himself acknowledged. It was not until the 15th century that regular observations over very long periods showed the geocentric hypothesis to be too complex to be acceptable and Copernicus proposed that the Sun is the centre of the universe.

Few details are known of the instruments that Hipparchus used. It seems likely that he observed with the usual devices current in his day, although Ptolemy credits him with the invention of an improved type of theodolite with which to measure angles.

Hipparchus is best known for his discovery of the precessional movement of the equinoxes; i.e., the alterations of the measured positions of the stars resulting from the movement of the points of intersection of the ecliptic (the plane of the Earth's orbit) and of the celestial equator (the great circle formed in the sky by the projection outward of the Earth's equator). It appears that he wrote a work bearing "precession of the equinoxes" in the title. 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.

He discovered that the celestial longitudes were different and that this difference was of a magnitude exceeding that attributable to errors of observation. He therefore proposed precession to account for 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 the figure of 50.26" accepted today and is a value much superior to the 36" that Ptolemy obtained.

The discovery of precession enabled Hipparchus to obtain more nearly correct values for the tropical year (the period of the Sun's apparent revolution from an equinox to the same equinox again), and also for the sidereal year (the period of the Sun's apparent revolution from a fixed star to the same fixed star). Again he was extremely accurate, so that his value for the tropical year was too great by only 6 1/2 minutes.

Observations of star positions measured in terms of celestial latitude and longitude, as was customary in antiquity, were carried out by Hipparchus and entered in a catalog--the first star catalog ever to be completed. Hipparchus measured the stellar positions with greater accuracy than any observer before him, and his observations were of use to Ptolemy and even later to Edmond Halley. To catalog the stars was thought by some of Hipparchus' contemporaries to be an impiety, but he persevered. 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' catalog, completed in 129 BC, listed about 850 stars (not 1,080 as is often stated), the apparent brightnesses of which were specified 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 of others as well as his own. He showed that the system based on movable eccentrics and that based on epicycles and deferents were equivalent in the motions they gave for the Sun and Moon and, indeed, for the planets. Both methods gave the position of the Sun correct to within 1', and Hipparchus rejected the peculiar notion, prevalent in his day, that the Sun moved in an orbit inclined to the ecliptic. Hipparchus also redetermined the inclination of the ecliptic and obtained a value correct to within 5' of the modern figure.

The motion of the Moon is more complex than that of the Sun, owing to the perturbations that the Moon suffers from both Earth and Sun; in consequence, there are more irregularities to be taken into consideration. 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. His theory gave reasonably satisfactory results for the motion at Full and New Moon. Hipparchus was dissatisfied however, for, as he appreciated, the errors at quadrature (when the Moon stands at first and last quarters) were too great. He concluded that there was some further inequality in the Moon's motion, but he was unable to discover any means of solving this problem, and he said candidly that he was leaving the solution of this question to those who were to follow him.

Hipparchus also attacked the problem of the relative size of the Sun and Moon and their distance from the Earth. It had long been appreciated, of course, that the apparent diameter of each was the same, and various astronomers had attempted to measure the ratio of size and distance of the two bodies. Eudoxus obtained a value of 9:1, Phidias (father of Archimedes) 12:1, Archimedes himself 30:1; while Aristarchus believed 20:1 to be correct. The present-day value is, approximately, 393:1. 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). This method really gives the parallax (the apparent change in the position of a celestial body when observed from two different directions), and thus the distance, of the Moon, the parallax for the Sun being too small to give a significant result; moreover the accuracy obtainable for the distance even of the Moon is poor. Dissatisfied with his results, Hipparchus attempted to find the limits within which the solar parallax must lie for observations and calculations of a solar eclipse to agree; he hoped that differences between solar and lunar parallax might thus also be revealed. He obtained no satisfactory result from his efforts, however, and concluded that the solar parallax was probably negligible. At least he appreciated that the distance of the Sun was very great indeed.

Hipparchus was unsuccessful in forming a satisfactory planetary theory and was scientist enough to avoid building hypotheses on insufficient evidence. In his work Hipparchus adopted the generally accepted order for the Sun, Moon, and planets. With the Earth as the centre, 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 should have led him to develop certain departments of mathematics. He made an early formulation of trigonometry and tabulated a table of chords--i.e., the length of the line joining two points on a unit circle corresponding to the given angle at the centre; e.g., chord of = 2 sin (/2): he is known to have had a method of solving spherical triangles. It is also generally agreed that the theorem in plane geometry known as "Ptolemy's theorem" was originally due to Hipparchus and was later copied by Ptolemy. During the 18th century the French statesman and mathematician Lazare Carnot showed that the whole 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 main contribution was to apply rigorous mathematical principles to the determination of places on the Earth's surface, and he was the first to do so by specifying their longitude and latitude--the method used today. Hipparchus was, no doubt, led to this method by his work on the trigonometry of the sphere. He tried to measure latitude by utilizing the ratio of the longest to the shortest day at a particular place instead of following the customary method of the Babylonians of measuring the difference in length of day as one travels northward. Hipparchus also divided the then known inhabited world into climatic zones, and suggested that the longitude of places could be determined by observing, from these places, the moments when a solar eclipse began and ended; but this bold scheme, while theoretically 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.*