THE DEFINITIONS 
315 
‘ concave ’ and ‘ convex lune, garland (these last two are 
composite of homogeneous parts) and axe (neXeicvs), bounded by- 
four circular arcs, two concave and two convex, Defs. 27-38. 
Rectilineal figures follow, the various kinds of triangles and 
of quadrilaterals, the gnomon in a parallelogram, and the 
gnomon in the more general sense of the figure which added 
to a given figure makes the whole into a similar figure, 
polygons, the parts of figures (side, diagonal, height of a 
triangle), perpendicular, parallels, the three figures which will 
fill up the space round a point, Defs. 39-73. Solid figures are 
next classified according to the surfaces bounding them, and 
lines on surfaces are divided into (1) simple and circular, 
(2) mixed, like the conic and spiric curves, Defs. 74, 75. The 
sphere is then defined, with its parts, and stated to be 
the figure which, of all figures having the same surface, is the 
greatest in content, Defs. 76-82. Next the cone, its different 
species and its parts are taken up, with the distinction 
between the three conics, the section of the acute-angled cone 
(‘ by some also called ellipse ’) and the sections of the right- 
angled and obtuse-angled cones (also called parabola and 
hyperbola), Defs. 83-94; the cylinder, a section in general, 
the spire or tore in its three varieties, open, continuous (or 
just closed) and ‘ crossing-itself ’, which respectively have 
sections possessing special properties, ‘ square rings 5 which 
are cut out of cylinders (i. e. presumably rings the cross-section 
of which through the centre is two squares), and various other 
figures cut out of spheres or mixed surfaces, Defs. 95-7 ; 
rectilineal solid figures, pyramids, the five regular solids, the 
semi-regular solids of Archimedes two of which (each with 
fourteen faces) were known to Plato, Defs. 98-104; prisms 
of different kinds, parallelepipeds, with the special varieties, 
the cube, the beam, Sokos (length longer than breadth and 
depth, which may be equal), the brick, ttXlvOls (length less 
than breadth and depth), the a-cpyria-Kos or (3copia-Kos with 
length, breadth and depth unequal, Defs. 105-14. 
Lastly come definitions of relations, equality of lines, sur 
faces, and solids respectively, similarity of figures, ‘reciprocal 
figures’, Defs. 115-18; indefinite increase in magnitude, 
parts (which must be homogeneous with the wholes, so that 
e. g. the horn-like angle is not a part or submultiple of a right