A history of Greek mathematics - Wilbourhall.org

238 SOME HANDBOOKS
larger than the earth ;
and the remaining chapters deal with
the size of the moon and the stars (chap. 3), the illumination
of the moon by the sun (chap. 4), the phases of the moon and
its conjunctions with the sun (chap. 5), the eclipses of the
moon (chap. 6), the maximum deviation in latitude of the five
planets (given as 5° for Venus, 4° for Mercury, 2|° for Mars
and Jupiter, 1° for Saturn), the maximum elongations of
Mercury and Venus from the sun (20° and 50° respectively),
and the synodic periods of the planets (Mercury 116 days,
Venus 584 days, Mars 780 days, Jupiter 398 days, Saturn
378 days) (chap. 7).
There is only one other item of sufficient interest to be
mentioned here. In Book II, chap. 6, Cleomedes mentions
that there were stories of extraordinary eclipses which ' the
more ancient of the mathematicians had vainly tried to explain
'-£ the supposed 'paradoxical' case was that in which,
while the sun seems to be still above the horizon, the eclipsed
moon rises in the east. The passage has been cited above
(vol. i, pp. 6-7), where I have also shown that Cleomedes himself
gives the true explanation of the phenomenon, namely
that it is due to atmospheric refraction.
The first and second centuries of the Christian era saw
a continuation of the work of writing manuals or introductions
to the different mathematical subjects. About A. D. 100
came Nicomachus, who wrote an Introductio n to Arithmetic
and an Introduction to Harmony ;
if we may judge by a
remark of his own, 1 he would appear to have written an introduction
to geometry also. The Arithmetical Introduction has
been sufficiently described above (vol. i, pp. 97-112).
There is yet another handbook which needs to be mentioned
separately, although we have had occasion to quote from it
several times already. This is the book by Theon OF Smyrna
which goes by the title Expositio rerum mathematicarum ad
legendum Platonem utilium. There are two main divisions
of this work, contained in two Venice manuscripts respectively.
The first was edited by Bullialdus (Paris, 1644), the
second by T. H. Martin (Paris, 1849); the whole has been
1
Nicom. Arith. ii. 6. 1.