494 
Notices of Books. [July* 
Since the Association Syllabus admits ot angles equal to or 
greater than two right angles, this is open to the objection that 
it does not debar the case in which one line stands on the end of 
the other, making the adjacent angles equal to one another, and 
to two right angles as right angles are generally considered. 
That is certainly a grave obje<5tion, but the same applies equally 
to Euclid’s definition, or else a proof must be supplied, which is 
not that in the case mentioned the two lines are in one and the 
same straight line ; and so this interpretation is debarred by 
Euclid’s limiting clause. 
In fadt, though Mr. Dodgson’s book is interesting and often 
witty, he fails to prove his point, because he takes a one-sided 
view of the question, and merely exhibits the blunders of Euclid’s 
Rivals without balancing them against Euclid’s own. Besides 
which — though perhaps it is more readable than an essay — a 
dialogue does not seem to be the clearest form for setting forth 
arguments and facfts. It is certainly an advantage that the more 
solid part of a treatise of this sort should be enlivened here and 
there by lighter matter, more especially as it is so managed as 
not to break the thread of the argument. 
The Tables of Problems — though there is a somewhat com- 
plex system of notation to be mastered before they become 
intelligible — are extremely interesting ; more especially Table II., 
which is described as “ consisting of theorems admitted to be 
real and valid, but not deducible from undisputed axioms.” 
