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

PTOLEMAEUS. PTOLEMAEUS. 575.the earth, as was done with the stars, by circles as in many other instances, he shows no attempt to
drawn from the pole perpendicularly to the equator, judge a mathematical argument by any thing except
that is, by latitudes and longitudes. His method its result: had it been otherwise, the unity and
of eclipses was long the only one by which difference power of this chapter would have established a
of neridians could be determined; and it is by the strong presumption in favour of its originality.
projection of his invention that to this day we con- Though Hipparchus constructed chords, it is to be
struct our maps of the world and our best geogra- remembered we know nothing of his manner as a
phical charts." mathematician; nothing, indeed, except some reWe shall now proceed to give a short synopsis suits. The next chapter is on the obliquity of
of the subjects treated in the Almagest: the reader the ecliptic as determined by observation. It is
will find a longer and better one in the second vo- followed by spherical geometry and trigonometry
lame of the work of Delambre just cited. enough for the determination of the connection
The first book opens with some remarks on between the sun's right ascension, declination, and
theory and practice, on the division of the sciences, longitude, and for the formation of a table of deand the certainty of mathematical knowledge: clinations to each degree of longitude. Delambre
this preamble concludes with an announcement of says he found both this and the table of chords
the author's intention to avail himself of his pre- very exact.
decessors, to run over all that has been sufficiently The second book is one of deduction from the
explained, and to dwell upon what has not been general doctrine of the sphere, on the effect of podone completely and well. It then describes as sition on the earth, the longest days, the determithe intention of the work to treat in order: -the nation of latitude, the points at which the sun is
relations of the earth and heaven; the effect of vertical, the equinoctial and solsticial shadows of
position upon the earth; the theory of the sun and the gnomon, and other things which change with
moon, without which that of the stars cannot be the spectator's position. Also on the arcs of the
undertaken; the sphere of the fixed stars, and ecliptic and equator which pass the horizon simulthose of the five stars called placknets. Arguments taneously, with tables for different climates, or
are then produced for the spherical form and motion parallels of latitude having longest days of given
of the heavens, for the sensibly spherical form of durations. This is followed by the consideration
the earth, for the earth being in the centre of the of oblique spherical problems, for the purpose of
heavens, for its being but a point in comparison calculating angles made by the ecliptic with the
with the distances of the stars, and its having no vertical, of which he gives tables.
motion of translation. Some, it is said, admitting The third book is on the length of the year, and
these reasons, nevertheless think that the earth may on the theory of the solar motion. Ptolemy inhave a motion of rotation, which causes the (then) forms us of the manner in which Hipparchus made
only apparent motion of the heavens. Admiring the discovery of the precession of the equinoxes,
the simplicity of this solution, Ptolemy then gives by observation of the revolution from one equinox
his reasons why it cannot be. With these, as well to the same again being somewhat shorter than
as his preceding arguments, our readers are familiar. the actual revolutiofi in the heavens. He discusses
Two circular celestial motions are then admitted: the reasons which induced his predecessor to think
one which all the stars have in common, another there was a small inequality in the length of the
which several of them have of their own. From year, decides that he was wrong, and produces the
several expressions here used, various writers have comparison of his own observations with those of
imagined that Ptolemy held the opinion maintained Hipparchus, to show that the latter had the true
by many of his followers, namely, that the celestial and constant value (one three-hundredth of a day
spheres are solid. Delambre inclines to the con- less than 3654 days). As this is more than six
trary, and we follow him. It seems to us that, minutes too great, and as the error, in the whole
though, as was natural, Ptolemy was led into the interval between the two, amounted to more than
phraseology of the solid-orb system, it is only in a day and a quarter, Delambre is surprised, and
the convenient mode which is common enough in with reason, that Ptolemy should not have detected
all systems. When a modern astronomer speaks it. He hints that Ptolemy's observations may
of the variation of the eccentricity of the moon's have been calculated from their required result; on
orbit as producing a certain effect upon, say her which we shall presently speak. It must be relongitude, any one might suppose that this orbit membered that Delambre watches every process of
was a solid transparent tube, within which the Ptolemy with the eye of a lynx, to claim it for
moon is materially restrained to move. Had it not Hipparchus, if he can; and when it is certain that
been for the notion of his successors, no one would the latter did not attain it, then he might have
have attributed the same to Ptolemy: and if the attained it, or would if he had lived, or at the least
literal meaning of phrases have weight, Copernicus it is to be matter of astonishment that he did not.
is at least as much open to a like conclusion as Ptolemy then begins to explain his mode of apPtolemy. plying the celebrated theory of excentrics, or revoThen follows the geometrical exposition of the lutions in a circle which' has the spectator out of its
mode of obtaining a table of chords, and the table centre; of epicycles, or circles, the centres of which
itself to half degrees for the whole of the semi- revolve on other circles, &c. As we cannot here
circle, with differences for minutes, after the man- give mathematical explanations, we shall refer the
ner of recent modern tables. This morsel of reader to the general notion which he probably has
geometry is one of the most beautiful in the Greek on this subject, to Narrien's History of Astronomy,
writers: some propositions from it are added to or to Delambre himself. As to the solar theory, it
many editions of Euclid. Delambre, who thinks may be sufficient to say that Ptolemy explains the
as meanly as he can of Ptolemy on all occasions, one ineqmality then known, as Hipparchus did
mentions it with a doubt as to whether it is his before him, by the supposition that the circle of
own, or collected from his predecessors. In this, the sun is an excentric; and that he does not