A history of Greek mathematics - Wilbourhall.org

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256 TRIGONOMETRY
Improved Instruments.
7. He made great improvements in the instruments used for
observations. Among those which he used were an improved
dioptra, a ' meridian-instrument ' designed for observations in
the meridian only, and a universal instrument {acrTpoXdPov
opyavov) for more general use. He also made a globe on
which he showed the positions of the fixed stars as determined
by him ; it appears that he showed a larger number of stars
on his globe than in his catalogue.
Geography.
In geography Hipparchus wrote a criticism of Eratosthenes,
in great part unfair. He checked Eratosthenes's data by
means of a sort of triangulation ; he insisted on the necessity
of applying astronomy to geography, of fixing the position of
places by latitude and longitude, and of determining longitudes
by observations of lunar eclipses.
Outside the domain of astronomy and geography, Hipparchus
wrote a book On things borne doivn by their weight from
which Simplicius (on Aristotle's De caelo, p. 264 sq.) quotes
two propositions. It is possible, however, that even in this
work Hipparchus may have applied his doctrine to the case of
the heavenly bodies.
In pure mathematics he is said to have considered a problem
in permutations and combinations, the problem of finding the
number of different possible combinations of 10 axioms or
assumptions, which he made to be 103,049 (v. I. 101,049)
or 310,952 according as the axioms were affirmed or denied 1 :
When
it seems impossible to make anything of these figures.
'
the Fihrist attributes to him works On the art of algebra,
known by the title of the Rules ' and On the division of num-
'
bers we have no confirmation ', : Suter
suspects some confusion,
in view of the fact that the article immediately following in
the Fihrist is on Diophantus, who also ' wrote on the art of
algebra
1
Plutarch, Quaest. Conviv, viii. 9. 3, 732 f, De Stoicorum repugn. 29.
1047 d.