from the vertex of the segment to a point on the circle which is the base of the segment; (3) that, if we have a cylinder circumscribed to a sphere and with height equal to the diameter, then (a) the volume of the cylinder is 1½ times that of the sphere and (b) the surface of the cylinder, including its bases, is 1½ times the surface of the sphere.
Next come a few definitions, followed by certain Assumptions, two of which are well known, namely:—
- Of all lines which have the same extremities the straight line is the least (this has been made the basis of an alternative definition of a straight line).
- Of unequal lines, unequal surfaces and unequal solids the greater exceeds the less by such a magnitude as, when (continually) added to itself, can be made to exceed any assigned magnitude among those which are comparable [with it and] with one another (i.e. are of the same kind). This is the Postulate of Archimedes.