PREFACE 
* 
vii 
« 
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