132 
APOLLONIUS OF PERGA 
Preface to Book YI. 
Apollonius to Attains, greeting. 
I send you the sixth book'of the conics, which embraces 
propositions about conic sections and segments of conics equal 
and unequal, similar and dissimilar, besides some other matters 
left out by those who have preceded me. In particular, you 
will find in this book how, in a given right cone, a section can 
be cut which is equal to a given section, and how a right cone 
can be described similar to a given cone but such as to contain 
a given conic section. And these matters in truth I have 
treated somewhat more fully and clearly than those who wrote 
before my time on these subjects. Farewell. 
Preface to Book VII. 
Apollonius to Attalus, greeting. 
I send to you with this letter the seventh book on conic 
sections. In it are contained a large number of new proposi 
tions concerning diameters of sections and the figures described 
upon them; and all these propositions have their uses in many 
kinds of problems, especially in the determination of the 
limits of their possibility. Several examples of these occur 
in the determinate conic problems solved and demonstrated 
by me in the eighth book, which is by way of an appendix, 
and which I will make a point of sending to you as soon 
as possible. Farewell. 
Extent of claim to originality. 
We gather from these prefaces a very good idea of the 
plan followed by Apollonius in the arrangement of the sub- 1 
ject and of the extent to which he. claims originality. The 
first four Books form, as he says, an elementary introduction, 
by which he means an exposition of the elements of conics, 
that is, the definitions and the fundamental propositions 
which are of the most general use and application; the term 
‘ elements ’ is in fact used with reference to conics in exactly 
the same sense as Euclid uses it to describe his great work. 
The remaining Books beginning with Book Y are devoted to 
more specialized investigation of particular parts of the sub 
ject. It is only for a very small portion of the content of the 
treatise that Apollonius claims originality; in the first three 
Books the claim is confined to certain propositions bearing on 
the ‘ locus with respect to three or four lines ’; and in the 
fourth Book (on the number of points at which two conics