THE CONICS, BOOK VII 
175 
Pappus, vii, pp. 640-8, 660-72. 
As we have said, Book VIII is lost. The nature of its 
contents can only be conjectured from Apollonius’s own 
remark that it contained determinate conic problems for 
which Book VII was useful, particularly in determining 
limits of possibility. Unfortunately, the lemmas of Pappus 
do not enable us to form any clearer idea. But it is probable 
enough that the Book contained a number of problems having 
for tjieir object the finding of conjugate diameters in a given 
conic such that certain functions of their lengths have given 
values. It was on this assumption that Halley attempted 
a restoration of the Book. 
If it be thought that the above account of the Conics is 
disproportionately long for a work of this kind, it must be 
remembered that the treatise is a great classic which deserves 
to be more known than it is. What militates against its 
being read in its original form is the great extent of the 
exposition (it contains 387 separate propositions), duo partly 
to the Greek habit of proving particular cases of a general 
proposition separately from the proposition itself, but more to 
the cumbrousness of the enunciations of complicated proposi 
tions in general terms (without the help of letters to denote 
particular points) and to the elaborateness of the Euclidean 
form, to which Apollonius adheres throughout. 
Other works by Apollonius. 
Pappus mentions and gives a short indication of the con 
tents of six other works of Apollonius which formed part of the 
Treasury of Analysis} Three of these should be mentioned 
in close connexion with the Conics. 
(a) On the Cutting-off of a Ratio (A6yov d-rroToyr/), 
two Books, 
This work alone of the six mentioned has survived, and 
that only in the Arabic; it was published in a Latin trans 
lation by Edmund Halley in 1706. It deals with the general 
problem, ‘ Given two straight lines, parallel to one another or 
intersecting, and a fixed point on each line, to draw through