In 134 B. C. a new star blazed out in the constellation Scorpio, and this set Hipparchus at work on a catalogue of the brighter stars of the firmament, a monumental work of true scientific conception, because it would enable the astronomers of future generations to ascertain what changes, if any, were taking place in the stellar universe. There were 1,080 stars in his catalogue, and he referred their positions to the ecliptic and the equinoxes. Also he originated the present system of stellar magnitudes or orders of brightness, and his catalogue was in use as a standard for many centuries.
Hipparchus was a great mathematician as well, and he devoted himself to the improvement of the method of applying numerical calculations to geometrical figures: trigonometry, both plane and spherical, that is; and by some authorities he is regarded as the inventor of original methods in trigonometry. The system of spheres of Eudoxus did not satisfy him, so he devised a method of representing the paths of the heavenly bodies by perfectly uniform motion in circles. There is slight evidence that Apollonius of Perga may have been the originator of the system, but it was reserved for Hipparchus to work it out in final form. This enabled him to ascertain the varying length of the seasons, and he fixed the true length of the year as 365¼ days. He had almost equal success in dealing with the irregularities of the moon's motion, although the problem is much more complicated. The distance and size of the moon, by the method of Aristarchus, were improved by him, and he worked out, for the distance of the sun, 1,200 radii of the earth—a classic for many centuries.
Hipparchus devoted much attention to eclipses of both sun and moon, and we owe to him the first elucidation of the subject of parallax, or the effect of difference of position of an observer on the earth's surface as affecting the apparent projection of the moon against the sun when a solar eclipse takes place; whereas an eclipse of the moon is unaffected by parallax and can be seen at the same time by observers everywhere, no matter what their location on the earth. Indeed, with all that Hipparchus achieved, we need not be surprised that astronomy was regarded as a finished science, and made practically no progress whatever for centuries after his time.
Then came Claudius Ptolemæus, generally known as Ptolemy, the last great name in Greek astronomy. He lived in Alexandria about the middle of the second century A. D. and wrote many minor astronomical and astrological treatises, also works on geography and optics, in the last of which the atmospheric refraction of rays of light from the heavenly bodies, apparently elevating them toward the zenith, is first dealt with in true form.
CHAPTER VI
PTOLEMY AND HIS GREAT BOOK
Ptolemy was an observer of the heavens, though not of the highest order; but he had all the work of his predecessors, best of all Hipparchus, to build upon. Ptolemy's greatest work was the "Megale Syntaxis," generally known as the Almagest. It forms a nearly complete compendium of the ancient astronomy, and although it embodies much error, because built on a wrong theory, the Almagest nevertheless is competent to follow the motions of all the bodies in the sky with a close approach to accuracy, even at the present day. This marvelous work written at this critical epoch became as authoritative as the philosophy of Aristotle, and for many centuries it was the last word in the science. The old astrology held full sway, and the Ptolemaic theory of the universe supplied everything necessary: further progress, indeed, was deemed impossible.
The Almagest comprises in all thirteen books, the first two of which deal with the simpler observations of the celestial sphere, its own motion and the apparent motions of sun, moon, and planets upon it. He discusses, too, the postulates of his system and exhibits great skill as an original geometer and mathematician. In the third book he takes up the length of the year, and in the fourth book similarly the moon and the length of the month. Here his mathematical powers are at their best, and he made a discovery of an inequality in the moon's motion known as the evection. Book five describes the construction and use of the astrolabe, a combination of graduated circles with which Ptolemy made most of his observations. In the sixth book he follows mainly Hipparchus in dealing with eclipses of sun and moon. In the seventh and eighth books he discusses the motion of the equinox, and embodies a catalogue of 1,028 stars, substantially as in Hipparchus. The five remaining books of the Almagest deal with the planetary motions, and are the most important of all of Ptolemy's original contributions to astronomy. Ptolemy's fundamental doctrines were that the heavens are spherical in form, all the heavenly motions being in circles. In his view, the earth too is spherical, and it is located at the center of the universe, being only a point, as it were, in comparison. All was founded on mere appearance combined with the philosophical notion that the circle being the only perfect curve, all motions of heavenly bodies must take place in earth-centered circles. For fourteen or fifteen centuries this false theory persisted, on the authority of Ptolemy and the Almagest, rendering progress toward the development of the true theory impossible.
Ptolemy correctly argued that the earth itself is a sphere that is curved from east to west, and from north to south as well, clinching his argument, as we do to-day, by the visibility of objects at sea, the lower portions of which are at first concealed from our view by the curved surface of the water which intervenes. To Ptolemy also the earth is at the center of the celestial sphere, and it has no motion of translation from that point; but his argument fails to prove this. Truth and error, indeed, are so deftly intermingled that one is led to wonder why the keen intelligence of this great philosopher permitted him to reject the simple doctrine of the earth's rotation on its axis. But if we reflect that there was then no science of natural philosophy or physics proper, and that the age was wholly undeveloped along the lines of practical mechanics, we shall see why the astronomers of Ptolemy's time and subsequent centuries were content to accept the doctrines of the heavens as formulated by him.