MEASUREMENT OF PYRAMIDS 
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with a capital at Teos, that being the most central place in 
Ionia. And when Croesus sent envoys to Miletus to propose 
an alliance, Thales dissuaded his fellow-citizens from accepting 
the proposal, with the result that, when Cyrus conquered, the 
city was saved.) * 
(a) Measurement of height of 'pyramid. 
The accounts of Thales’s method of measuring the heights 
of pyramids vary. The earliest and simplest version is that 
of Hieronymus, a pupil of Aristotle, quoted by Diogenes 
Laertius: 
‘ Hieronymus says that he even succeeded in measuring the 
pyramids by observation of the length of their shadow at 
the moment when our shadows are equal to our own height.’ 1 
Pliny says that 
‘ Thales discovered how to obtain the height of pyramids 
and all other similar objects, namely, by measuring the 
shadow of the object at the time when a body and its shadow 
are equal in length.’ 2 
Plutarch embellishes the story by making Niloxenus say 
to Thales: 
‘ Among other feats of yours, he (Amasis) was particularly 
pleased with your measurement of the pyramid, when, without 
trouble or the assistance of any instrument, you-merely set 
up a stick at the extremity of the shadow cast by the 
pyramid and, having thus made two triangles by the impact 
of the sun’s rays, you showed that the pyramid has to the 
stick the same ratio which the shadow has to the shadow.’ 3 
The first of these versions is evidently the original one and, 
as the procedure assumed in it is more elementary than the 
more general method indicated by Plutarch, the first version 
seems to be the more probable. Thales could not have failed 
to observe that, at the time when the shadow of a particular 
object is equal to its height, the same relation holds for all 
other objects casting a shadow; this he would probably 
infer by induction, after making actual measurements in a 
1 Diog. L. i. 27. 2 N. H. xxxvi. 12 (17). 
3 Plat. Conv. sept. sap. 2, p. 147 a. 
1523 K