MENSURATION
319
Heiberg puts side by side with corresponding sections of the
Geometrica in parallel columns ; others he inserts in suitable
places ; sections 78, 79 contain two important problems in
indeterminate analysis (= Geom. 24, 1-2, Heib.). Heiberg
adds, from the Constantinople manuscript containing the
Metrica, eleven more sections (chap. 24, 3-13) containing
indeterminate problems, and other sections (chap. 24,14-30 and
37-51) giving the mensuration, mainly, of figures inscribed in or
circumscribed to others, e. g. squares or circles in triangles,
circles in squares, circles about triangles, and lastly of circles
and segments of circles.
The Stereometrica I has at the beginning the title Eùra-
ycùyaì tcùv (TT€peofxeTpovfj.ivcou ''Hpcovos but, like the Geometrica,
seems to have been edited by Patricius. Chaps. 1-40 give the
mensuration of the geometrical solid figures, the sphere, the
cone, the frustum of a cone, the obelisk with circular base,
the cylinder, the ‘pillar’, the cube, the cr^rjviaKos (also called
ovv£), the peiovpov Trpoecn«xpL(f)tvp.évov, pyramids, and frusta.
Some portions of this section of the book go back to Heron ;
thus in the measurement of the sphere chap. 1 = Metrica
II. 11, and both here and elsewhere the ordinary form of
fractions appears. Chaps. 41-54 measure the contents of cer
tain buildings or other constructions, e. g. a theatre, an amphi
theatre, a swimming-bath, a well, a ship, a wine-butt, and
the like.
The second collection, Stereometrica II, appears to be of
Byzantine origin and contains similar matter to Stereometrica I,
parts of which are here repeated. Chap. 31 (27, Heib.) gives
the problem of Thales, to find the height of a pillar or a tree
by the measurement of shadows ; the last sections measure
various pyramids, a prism, a (Scopia-Kos (little altar).
The Geodaesia is not an independent work, but only con
tains extracts from the Geometry, thus chaps. 1—16 = Geom.
5-31, Hultsch ( = 5, 2-12, 32, Heib.); chaps. 17-19 give the
methods of finding, in any scalene triangle the sides of which
are given, the segments of the base made by the perpendicular
from the vertex, and of finding the area direct by the well-
known ‘ formula of Heron ’ ; i.e. we have here the equivalent of
Metrica I. 5-8.
Lastly, the perpijaeis, or Mensurae, was attributed to Heron
