574 PTOLEMAEUS. Delarabre remarks of Alhazen that he is "plus riche, plus savant, et plus geometre que PtoMmee." Taking all this with confidence, for Delambre, though severe, was an excellent judge of relative merit, we think the reader of the Almagest will pause before he believes that the man who had tvritten this last work (which supposition is abso- lutely necessary) became a poor geometer, on the authority of one manuscript headed with his name. The subject wants further investigation from such sources as still exist : it is not unlikely that the Arabic original may be found. Were we speaking for Ptolemy, we should urge that a little diminu- tion of his fame as a mathematician would be well compensated by so splendid an addition to his ex- perimental character as the credit of a true theory of refraction. But the question is, how stands the fact ? and for our own parts, we cannot but suspend our opinion. We now come to speak of Ptolemy as an astro- nomer, and of the contents of the Almagest. And with his name we must couple that of his great pre- decessor, Hipparchus. The latter was alive at b. c. 150, and the former at a. d. 150, which is of easy remembrance. From the latter labours of Hip- parchus to the earlier ones of Ptolemy, it is from 250 to 260 years. Between the two there is nothing to fill the gap : we cannot construct an in- termediate school out of the names of Geminus, Poseidonius, Theodosius, Sosigenes, Hyginus, Ma- nilius, Seneca, Menelaus. Cleomedes, &c.: and we have no others. We must, therefore, regard Pto- lemy as the first who appreciated Hipparchus, and followed in his steps. This is no small merit in itself. What Hipparchus did is to be collected mostly from the writings of Ptolemy himself, who has evidently intended that his predecessor should lose no fame in his hands. The historian who has taken most pains to discriminate, and to separate what is due to Hipparchus, is Delambre. If he should be held rather too partial to the predecessor of Ptolemy, those who think so will be obliged to admit that he gives his verdict upon the evidence, and not upon any prepossession gained before trial. He is too much given, it may be, to try an old as- tronomer by what he has done for as, but this does not often disturb his estimate of the relative merit of the ancients. And it is no small testimony that an historian so deeply versed in modern practice, so conversant with ancient writings, so niggard of his praise, and so apt to deny it altogether to any thing which has since been surpassed, cannot get through his task without making it evident that Hipparchus has become a chief favourite. The summing up on the merits of the trtie father of as- tronomy^ as the historian calls him, is the best enumeration of his services which we can make, and will save the citation of authorities. The fol- lowing is translated from the preliminary discourse (which, it is important to remember, means the last part written) of the Histoire de VAstronomie Ancienne. " Let no one be astonished at the errors of half a degree with which we charge Hipparchus, perhaps with an air of reproach. We must bear in mind that his astrolabe was only an armillary sphere ; that its diameter was but moderate, the subdivisions of a degree hardly sensible ; and that he had neither telescope, vernier, nor micrometer. What could we do even now, if we were deprived of PTOLEMAEUS. these helps, if we were ignorant of refraction and of the true altitude of the pole, as to which, even at Alexandria, and in spite of armillary circles of every kind, an error of a quarter of a degree was committed. In our day we dispute about the frac- tion of a second ; in that of Hipparchus they could not answer for the fraction of a degree ; they might mistake* by as much as the diameter of the sun or moon. Let us rather turn our attention to the essential services rendered by Hipparchus to astro- nomy, of which he is the real founder. He is the first who gave and demonstrated the means of solv- ing all triangles, rectilinear and spherical, both. He constructed a table of chords, of which he made the same sort of use as we make of our sines. He made more observations than his predecessors, and understood them better. He established the theory of the sun in such a manner that Ptolemy, 263 years afterwards, found nothing to change for the better. It is true that he was mistaken in the amount of the sun's inequality ; but I have shown that this arose from a mistake of half a day in the time of the solstice. He himself admits that his result may be wrong by a quarter of a day ; and we may always, without scruple, double the error supposed by any author, without doubting his good faith, but only attributing self-delusion. He deter- mined the first inequality of the moon, and Ptolemy changed nothing in it ; he gave the motion of the moon, of her apogee and of her nodes, and Pto- lemy's corrections are but slight and of more than doubtful goodness. He had a glimpse {il a entrevu) of the second inequality ; he made all the observa- tions necessary for a discovery the honour of which was reserved for Ptolemy ; a discovery which per- haps he had not time to finish, but for which he had prepared every thing. He showed that all the hypotheses of his predecessors were insufficient to explain the double inequality of the planets ; he predicted that nothing would do except the combi- nation of the two hypotheses of the excentric and epicycle. Observations were wanting to him, be- cause these demand intervals of time exceeding the duration of the longest life : he prepared them for his successors. We owe to his catalogue the im- portant knowledge of the retrograde motion of the equinoctial points. We could, it is true, obtain this knowledge from much better observations, made during the last hundred years : but such ob- servations would not give proof that the motion is sensibly uniform for a long succession of centuries ; and the observations of Hipparchus, by their num- ber and their antiquity, in spite of the errors which we cannot help finding in them, give us this important confirmation of one of the fundamental points of Astronomy. He was here the first dis- coverer. He invented the planisphere, or the mode of representing the starry heavens upon a plane, and of producing the solutions of problems of spherical astronomy, in a manner often as exact as, and more commodious than, the use of the globe itselt He is also the father of true geography, by his happy idea of marking the position of spots on
- The reader must not think that Delambre says
the diameter of the sun is a degree, or near it. By not answering for the fraction of a degree, he means that they could be sure of no more than the nearest degree, which leaves them open to any error under half a degree, which is about the diameter of the sun or moon.
