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 (da-rpoXa/Sor 
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 horne down 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.l. 101,049) 
or 310,952 according as the axioms were affirmed or denied 1 : 
it seems impossible to make anything of these figures. When 
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. 8, 732 f, De Stoicorum repugn. 29. 
1047 d.