e of Alexander after his death in 323 B.C. The name includes
Antigonus and his son Demetrius Poliorcetes, Antipater and his son
Cassander, Seleucus, Ptolemy, Eumenes and Lysimachus. The kingdoms into
which the Macedonian empire was divided under these rulers are known as
Hellenistic. The chief were Asia Minor and Syria under the SELEUCID
DYNASTY (q.v.), Egypt under the PTOLEMIES (q.v.), Macedonia under the
successors of Antigonus Gonatas, PERGAMUM (q.v.) under the Attalid
dynasty. Gradually these kingdoms were merged in the Roman empire. (See
MACEDONIAN EMPIRE.)

DIAGONAL (Gr. [Greek: dia], through, [Greek: gonia], a corner), in
geometry, a line joining the intersections of two pairs of sides of a
rectilinear figure.

DIAGORAS, of Melos, surnamed the Atheist, poet and sophist, flourished
in the second half of the 5th century B.C. Religious in his youth and a
writer of hymns and dithyrambs, he became an atheist because a great
wrong done to him was left unpunished by the gods. In consequence of his
blasphemous speeches, and especially his criticism of the Mysteries, he
was condemned to death at Athens, and a price set upon his head
(Aristoph. _Clouds_, 830; _Birds_, 1073 and Schol.). He fled to Corinth,
where he is said to have died. His work on the Mysteries was called
[Greek Phrygioi logoi] or [Greek: Apopyrgizontes], in which he probably
attacked the Phrygian divinities.

DIAGRAM (Gr. [Greek: diagramma], from [Greek: diagraphein], to mark out
by lines), a figure drawn in such a manner that the geometrical relations
between the parts of the figure illustrate relations between other
objects. They may be classed according to the manner in which they are
intended to be used, and also according to the kind of analogy which we
recognize between the diagram and the thing represented. The diagrams in
mathematical treatises are intended to help the reader to follow the
mathematical reasoning. The construction of the figure is defined in
words so that even if no figure were drawn the reader could draw one for
himself. The diagram is a good one if those features which form the
subject of the proposition are clearly represented.

Diagrams are also employed in an entirely different way--namely, for
purposes of measurement. The plans and designs drawn by architects and
engineers are used to determine the value of certain real magnitudes by
measuring certain distances on the diagram. For such purposes it is
essential that