318 
HERON OF ALEXANDRIA 
formed by the intersection of two cylinders with axes at right 
angles inscribed in a cube, also measured in the Method (15), 
the five regular solids (16-19). Book III deals with the divi 
sion of figures into parts having given ratios to one another, 
first plane figures (1-19), then solids, a pyramid, a cone and a 
frustum, a sphere (20-3). 
The Geometria or Geometrumena is a collection based upon 
Heron, but not his work in its present form. The addition of 
a theorem due to Patricius 1 and a reference to him. in the 
Stereometrica (I. 22) suggest that Patricius edited both works, 
but the date of Patricius is uncertain. Tannery identifies 
him with a mathematical professor of the tenth century, 
Nicephorus Patricius; if this is correct, he would be contem 
porary with the Byzantine writer (erroneously called Heron) 
who is known to have edited genuine works of Heron, and 
indeed Patricius and the anonymous Byzantine might be one 
and the same person. The mensuration in the Geometry has 
reference almost entirely to the same figures as those 
measured in Book I of the Metrica, the difference being that 
in the Geometry (1) the rules are not explained but merely 
applied to examples, (2) a large number of numerical illustra 
tions are given for each figure, (3) the Egyptian way of 
writing fractions as the sum of submultiples is followed, 
(4) lengths and areas are given in terms of particular 
measures, and the calculations are lengthened by a consider 
able amount of conversion from one measure into another. 
The first chapters (1-4) are of the nature of a general intro 
duction, including certain definitions and ending with a table 
of measures. Chaps. 5-99, Hultsch ( = 5-20,14, Heib.), though 
for the most part corresponding in content to Metrica I, 
seem to have been based on a different collection, because 
chaps. 100-3 and 105 (= 21, 1-25, 22, 3-24, Heib.) are clearly 
modelled on the Metrica, and 101 is headed ‘A definition 
(really ‘ measurement ’) of a circle in another book of Heron ’. 
Heiberg transfers to the Geometrica a considerable amount of 
the content of the so-called Liber Geeponicus, a badly ordered 
collection consisting to a large extent of extracts from the 
other works. Thus it begins with 41 definitions identical 
with the same number of the Definitiones. Some sections 
1 Geometrica, 21 26 (vol. iv, p. 886. 23).