Reviews and Notices of Books. 123 
too, relative to the phenomena of nature, it matters little what were 
the theories of Plato and Aristotle; but in a question of abstract 
truth,—their opinions are valuable in proportion to the massiveness 
of their intellects, and the attention they bestowed on the subject. 
Hamilton, in his remarkable review of Dr Whewell’s “ Thoughts 
on the Study of Mathematics as a part of a Liberal Education,” 
exemplifies the use of such opinions; and the value which he him- 
self attached to them may be inferred from the labour and re- 
search which he bestowed in their collection. Take one example, 
‘in the original essay (Edinburgh Review, January 1836) he had 
quoted from the Life of Descartes the opinion of that philosopher, 
extracted from his Fourth Rule for the direction of the mind on 
the subject of the utility of the mathematical sciences. In subse- 
quently turning up Descartes’ own words, Hamilton perceived 
that they contained an allusion to the well-known statement that 
Plato had inscribed on the vestibule of his study the injunction, 
“Tet no one unacquainted with geometry enter.” And it must 
have struck hin that the word attributed to Plato, dyeamérgyros, 
was far more definite in its meaning than the word mathesis which 
Descartes had employed, and was not to be so easily explained 
away as applying to something very different from the ordinary 
geometry of Euclid. This consideration, if admitted to take 
effect, would suffice to destroy the arguinent. Accordingly, 
Hamilton boldly questions the genuineness of the tradition, and 
sets to work to trace it to its rightful authority. For some years 
he followed the opinion of Fuelleborn, that the inscription had no 
higher authority than that of Bessarion in the seventeenth century, 
It was however pointed out to him in the jingling rhymes of 
Tzetzes, a Greek writer of the twelith century; and when in 1852 
he published his collected ‘ Discussions on Philosophy,” &c., he 
referred to it as a “fable, the oldest recorder of which flourished 
some sixteen centuries subsequent to Plato” (p 271). Another 
year revealed to him the fact that it was some centuries older 
stil. Accordingly, in the second edition of the ‘ Discussions,” 
published in 1853, he remarks in a note (p. 278) “ Fuelleborn, 
I may observe, questioned the antiquity of this story. ; 
The oldest testimonies which I have noticed are Ammonius 
Wermie (or Philoponus) and David the Armenian, Ammonius 
and David flourished towards the conclusion of the fifth century ; 
they were both scholars of Proclus, Are there any earlier autho- 
rities?” Now we would ask the mathematician who takes up these 
lectures of Barrow’s, whether he considers this question put by 
Sir William Hamilton to be worth answering or no. On his 
reply will depend, we think, the pleasure he will derive from a 
perusal of these lectures. Those who hold that the opinions of 
antiquity are worthless on mathematical questions, will require 
some training before they can reach a position from which Bar- 
