370 
EUCLID 
a text-book which it maintained; till recently. I cannot help 
thinking that it was Barrow’s influence which contributed 
most powerfully to this. We are told that Newton, when 
he first bought a Euclid in 1662 or 1663, thought it ‘ a trifling 
book’, as the propositions seemed to him obvious; after 
wards, however, on Barrow’s advice, he studied the Elements 
carefully and derived, as he himself stated, much benefit 
therefrom. 
Technical terms connected with the classical form 
of a proposition. 
As the classical form of a proposition in geometry is that 
which we find in Euclid, though it did not originate with 
him, it is desirable, before we proceed to an analysis of the 
Elements, to give some account of the technical terms used by 
the Greeks in connexion with such propositions and their 
proofs. We will take first the terms employed to describe the 
formal divisions of a proposition. 
(a) Terms for the formal divisions of a proposition. 
In its completest form a proposition contained six parts, 
(1) the npoTaa-Ls, or enunciation in general terms, (2) the 
e/cdea-Ls, or setting-out, which states the particular data, e. g. 
a given straight line AB, two given triangles ABC, DEF, and 
the like, generally shown in a figure and constituting that 
upon which the proposition is to operate, (3) the Siopurpos, 
definition or specification, which means the restatement of 
what it is required to do or to prove in terms of the particular 
data, the object being to fix our ideas, (4) the KaracrKevij, the 
construction or machinery used, which includes any additions 
to the original figure by way of construction that are necessary 
to enable the proof to proceed, (5) the diroSet^Ls, or the proof 
itself, and (6) the crvyiripaapa, or conclusion, which reverts to 
the enunciation, and states what has been proved or done ; 
the conclusion can, of course, be stated in as general terms 
as the enunciation, since it does not depend on the particular 
figure drawn ; that figure is only an illustration, a type of the 
class of figure, and it is legitimate therefore, in stating 
the conclusion, to pass from the particular to the general.