A history of Greek mathematics - Wilbourhall.org

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 division
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 Geometrla 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 contemporary
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 illustrations
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 considerable
amount of conversion from one measure into another.
The first chapters (1-4) are of the nature of a general introduction,
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 U 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. 386. 23).