THE COLLECTION. BOOKS I, II, III 
361 
plete Greek text, with apparatus, Latin translation, com 
mentary, appendices and indices, by Friedrich Hultsch ; this 
great edition is one of the first monuments of the revived 
study of the history of Greek mathematics in the last half 
of the nineteenth century, and has properly formed the model 
for other definitive editions of the Greek text of the other 
classical Greek mathematicians, e.g. the editions of Euclid, 
Archimedes, Apollonius, &c., by Heiberg and others. The 
Greek index in this edition of Pappus deserves special mention 
because it largely serves as a dictionary of mathematical 
terms used not only in Pappus but by the Greek mathe 
maticians generally. 
(S) Summary of contents. 
At the beginning of the work, Book I and the first 13 pro 
positions (out of 26) of Book II are missing. The first 13 
propositions of Book II evidently, like the rest of the Book, 
dealt with Apollonius’s method of working with very large 
numbers expressed in successive powers of the myriad, 10000. 
This system has already been described (vol. i, pp. 40, 54-7). 
The work of Apollonius seems to have contained 26 proposi 
tions (25 leading up to, and the 26th containing, the final 
continued multiplication). 
Book III consists of four sections. Section (1) is a sort of 
history of the problem of finding two mean proport ionals, in 
continued proportion, between two given straight lines. 
It begins with some general remarks about the distinction 
between theorems and problems. Pappus observes that, 
whereas the ancients called them all alike by one name, some 
regarding them all as problems and others as theorems, a clear 
distinction was drawn by those who favoured more exact 
terminology. According to the latter a problem is that in 
which it is proposed to do or construct something, a theorem 
that in which, given certain hypotheses, we investigate that 
which follows from and is necessarily implied by them. 
Therefore he who propounds a theorem, no matter how he has 
become aware of the fact which is a necessary consequence of 
the premisses, must state, as the object of inquiry, the right 
result and no other. On the other hand, he who propounds