A history of Greek mathematics - Wilbourhall.org

132 APOLLONIUS OF PERGA
Preface to Book VI.
Apollonius to Attalus, greeting.
I send you the sixth book of the conies, which embraces
propositions about conic sections and segments of conies 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 propositions
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 subject
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 conies,
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 conies in exactly
the same sense as Euclid uses it to describe his great work.
The remaining Books beginning with Book V are devoted to
more specialized investigation of particular parts of the subject.
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 conies