132 THE EARLIEST GREEK GEOMETRY. THALES 
The most usual supposition is that Thales, observing the ship 
from the top of a tower on the sea-shore, used the practical 
equivalent of the proportionality of the sides of two similar 
right-angled triangles, one small and one large. Suppose B 
to be the base of the tower, C the ship. It was only necessary 
for a man standing at the top of the 
tower to have an instrument with 
two legs forming a right angle, to 
place it with one leg BA vertical and 
in a straight line with B, and the 
other leg BE in the direction of the 
ship, to take any point A on BA, 
and then to mark on BE the point E 
where the line of sight from A to G cuts the leg BE. Then 
AD {— l, say) and BE { = m, say) can be actually measured, 
as also the height BB (= h, say) from B to the foot of the 
tower, and, by similar/triangles, 
m 
J 
BG — {h + l). 
The objection to this solution is that it does not depend 
directly on End. I. 26, as Eudemus implies. Tannery 1 there 
fore favours the hypothesis of a solution on the lines followed 
by the ’Roman agrimensor Marcus Junius Nipsus in his 
fiuminis varatio.—To find the distance from 
A to an inaccessible point B. Measure from A, 
along a straight line at right angles to AB, 
a distance AC, and bisect it at B. From G, on 
the side of AG remote from B, draw GE at 
right angles to AC, and let E be the point on 
it which is in a straight line with В and B. 
Then clearly, by Eucl. I. 26, CE is equal to 
AB] and GE can be measured, so that AB 
is known. 
This hypothesis is open to a different objec 
tion, namely that, as a rule, it would be 
difficult, in the supposed case, to get a sufficient amount of 
free and level space for the construction and measurements. 
I have elsewhere 2 suggested a still simpler method free 
1 Tannery, La géométrie grecque, pp. 90-1. 
2 The Thirteen Books of Euclid's Elements, vol. i, p. 805.