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by Geeky Nigeria

GROWTH OF MATHEMATICAL SCIENCE 17 

Thales presented his geometrical teaching. We infer, how- 
ever, from Proclus that it consisted of a number of isolated 
propositions which were not arranged in a logical sequence, but 
that the proofs were deductive, so that the theorems were not 
a mere statement of an induction from a large number of special 
instances, as probably was the case with the Egyptian geo- 
metricians. The deductive character which he thus gave to 
the science is his chief claim to distinction. Pythagoras (born 
about 580 B.C.) changed geometry into the form of an abstract 
science, regarding its principles in a purely abstract manner, 
and investigated its theorems from the immaterial and intel- 
lectual point of view. Among the successors of these men, the 
best known are Archytas of Tarentum (428-347 B.C.), Plato 
(429-348 B.C.), Hippocrates of Chios (born about 470 B.C.), 
Meuaechmus (about 375-325 B.C.), Euclid (about 330-275 B.C.), 
Archimedes (287-212 B.C.), and Apollonius (260-200 B.C.). 

The only geometry known to the Egyptian priests was that 
of surfaces, together with a sketch of that of solids, a geometry 
consisting of the knowledge of the areas contained by some 
simple plane and solid figures, which they had obtained by 
actual trial. Thales introduced the ideal of establishing by 
exact reasoning the relations between the different parts of a 
figure, so that some of them could be found by means of others 
in a manner strictly rigorous. This was a phenomenon quite 
new in the world, and due, in fact, to the abstract spirit of 
the Greeks. In connection with the new impulse given to 
geometry, there arose with Thales, moreover, scientific astro- 
nomy, also an abstract science, and undoubtedly a Greek 
creation. The astronomy of the Greeks differs from that of 
the Orientals in this respect : the astronomy of the latter, 
which is altogether concrete and empirical, consisted merely in 
determining the duration of some periods or in indicating, by 
means of a mechanical process, the motions of the sun and 
planets, whilst the astronomy of the Greeks aimed at the 
discovery of the geometrical laws of the motions of the heavenly 
bodies. 

Let us consider a simple case. The area of a right-angled 
field of length 80 yards and breadth 50 yards is 4000 square 
yards. Other fields which are not rectangular can be approxi- 
mately measured by mentally dissecting them a process which 

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