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.
