A Dictionary of Greek and Roman biography and mythology. By various writers. Ed. by William Smith. Illustrated by numerous engravings on wood.

574 PTOLEMAEUS. PTOLEMAEUS.
Delambre remarks of Alhazen that he is "plus these helps, if we were ignorant of refraction and
riche, plus savant, et plus gdomdtre que Ptoldmde." of the true altitude of the pole, as to which, even
Taking all this witil confidence, for Delambre, at Alexandria, and in spite of armillary circles of
though severe, was an excellent judge of relative every kind, an error of a quarter of a degree was
merit, we think the reader of the Almagest will committed. In our day we dispute about the fiacpause before he believes that the man who had tion of a second; in that of Hipparchus they could
written this last work (which supposition is abso- not answer for the fraction of a degree; they might
lutely necessary) became a poor geometer, on the mistake* by as much as the diameter of the sun or
authority of one manuscript headed with his name. moon. Let us rather turn our attention to the
The subject wants further investigation from such essential services rendered by Hipparchus to astrosources as still exist: it is not unlikely that the nomy, of which he is the real founder. He is the
Arabic original may be found. Were we speaking first who gave and demonstrated the means of solvfor Ptolemy, we should urge that a little diminu- ing all triangles, rectilinear and spherical, both.
tion of his fame as a mathematician would be well He constructed a table of chords, of which he made
compensated by so splendid an addition to his ex- the same sort of use as we make of our sines. lHe
perimental character as the credit of a true theory made more observations than his predecessors, and
of refraction. But the question is, how stands the understood them better. He established the theory
fact? and for our own parts, we cannot but suspend of the sun in such a manner that Ptolemy, 2!'3
our opinion. years afterwards, found nothing to change for the
We now come to speak of Ptolemy as an astro- better. It is true that he was mistaken in the
nomer, and of the contents of the Almagest. And amount of the sun's inequality; but I have shown
with his name we must couple that of his great pre- that this arose from a mistake of half a day in the
decessor, Hipparchus. The latter was alive at B. c. time of the solstice. He himself admits that his
150, and the former at A. D. 150, which is of easy result may be wrong by a quarter of a day; and
remembrance. From the latter labours of Hip- we may always, without scruple, double the error
parchus to the earlier ones of Ptolemy, it is from supposed by any author, without doubting his good
250 to 260 years. Between the two there is faith, but only attributing self-delusion. He deternothing to fill the gap: we cannot construct an in- mined the first inequality of the moon, and Ptolemy
termediate school out of the names of Geminns, changed nothing in it; he gave the motion of the
Poseidonius, Theodosius, Sosigenes, Hyginus, Ma- moon, of her apogee and of her nodes, and Ptonilius, Seneca, Menelaus, Cleomedes, &c.: and we lemy's corrections are but slight and of mere than
have no others. VVe must, therefore, regard Pto- doubtful goodness. He had a glimpse (il a entrevsn)
lemy as the first who appreciated Hipparchus, and of the second inequality; he made all the observafollowed in his steps. This is no small merit in tions necessary for a discovery the honour of which
itself, was reserved for Ptolemy; a discovery which perWhat Hipparchus did is to be collected mostly haps he had not time to finish, but for which he
from the writings of Ptolemy himself, who has had prepared every thing. He showed that all the
evidently intended that his predecessor should lose hypotheses of his predecessors were insufficient to
no fame in his hands. The historian who has taken explain the double inequality of the planets; he
most pains to discriminate, and to separate what predicted that nothing would do except the combiis due to Hipparchus, is Delambre. If he should nation of the two hypotheses of the excentric and
be held rather too partial to the predecessor of epicycle. Observations were wanting to him, bePtolemy, those who think so will be obliged to cause these demand intervals of time exceeding the
admit that he gives his verdict upon the evidence, duration of the longest life: he prepared them for
and not upon anly prepossession gained before trial. his successors. We owe to his catalogue the imI-e is too much given, it may be, to try an old as- portant knowledge of the retrograde motion of the
tronomer by what he has done for us, but this does equinoctial points. We could, it is true, obtain
not often disturb his estimate of the relative merit this knowledge from much better observations,
of the ancients. And it is no small testimony that made during the last hundred years: but such oban historian so deeply versed in modern practice, servations would not give proof that the motion is
so conversant with ancient writings, so niggard of sensibly uniform for a long succession of centuries;
his praise, and so apt to deny it altogether to any and the observations of Hipparchus, by their numthing which has since been surpassed, cannot get ber and their antiquity, in spite of the errors
through his task without making it evident that which we cannot help finding in them, give us this
Ilipparchus has become a chief favourite. The important confirmation of one of the fundamental
summing up on the merits of the true fhtlher of as- points of Astronomy. He was here the first distrononmy, as the historian calls him, is the best coverer. He invented the planisphere, or the mode
enumeration of his services which we can make, of representing the starry heavens upon a plane,
and will save the citation of authorities. The fol- and of producing the solutions of problems of
lowing is translated from the preliminary discourse spherical astronomy, in a manner often as exact as,
(which, it is important to remember, means the and more commodious than, the use of the globe
last part written) of the flisto2re de l'Astronomnie itself. He is also the father of true geography, by
Ancienne. his happy idea of marking the position of spots on
" Let no one be astonished at the errors of half
a degree with which we charge Hipparchus, perhaps * The reader must not think that Delambre says
with an air of reproach. We must bear in mind the diameter of the sun is a degree, or near it. By
that his astrolabe was only an armillary sphere; not answering for the fraction of a degree, he means
that its diameter was but moderate, the subdivisions that they could be sure of no more than the near(est
of a degree hardly sensible; and that he had degree, which leaves them open to any error under
neither telescope, vernier, nor micrometer. What half a degree, which is about the diameter of the
could we do even now, if we were deprived of sun or moon.