PREFACE
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vii
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Ulrico Hoepli, Milano). Professor Loria arranges his material
in five Books, (1) on pre-Euclidean geometry, (2) on the
Golden Age of Greek geometry (Euclid to Apollonius), (3) on
applied mathematics, including astronomy, sphaeric, optics,
&c., (4) on the Silver Age of Greek geometry, (5) on the
arithmetic of the Greeks. Within the separate Books the
arrangement is chronological, under the names of persons or
schools. I mention these details because they raise the
question whether, in a history of this kind, it is best to follow
chronological order or to arrange the material according to
subjects,and, if the latter,in what sense of the word ‘subject’
and within what limits. As Professor Loria says, his arrange
ment is ‘a compromise between arrangement according to
subjects and a strict adherence to chronological order, each of
which plans has advantages and disadvantages of its own’.
In this book I have adopted a new arrangement, mainly
according to subjects, the nature of which and the reasons for
which will be made clear by an illustration. Take the case of
a famous problem which plays a great part in the history of
Greek geometry, the doubling of the cube, or its equivalent,
the finding of two mean proportionals in continued proportion
between two given straight lines. Under a chronological
arrangement this problem comes up afresh on the occasion of
each new solution. Now it is obvious that, if all the recorded
solutions are collected together, it is much easier to see the
relations, amounting in some cases to substantial identity,
between them, and to get a comprehensive view of the history
of the problem. I have therefore dealt with this problem in
a separate section of the chapter devoted to ‘ Special Problems’,
and I have followed the same course with the other famous
problems of squaring the circle and trisecting any angle.
Similar considerations arise with regard to certain well-
defined subjects such as conic sections. It would be incon
venient to interrupt the account of Menaechmus’s solution
of the problem of the two mean proportionals in order to
