384 Notices respecting New Books. 
and to 'the same perfection, that we know that the co-efficients 
of any idea of relation must be some two things, between which 
the mind perceives this relation. —_— I must refer to the small 
tract ] published some time ago upon * necessary connection ;’ in 
which my object is to show that we absolutely know the co-effi- 
ciency of all our ideas of relation; and in which I suppose the 
thing is rigidly proved. New sensations of cclours are ideas; 
and I repeat it here, that we have the same degree of cognisance 
of their relations (one to another) that we have of the relations 
ef equal, double, or half, between any two mathematica] quan- 
tities; that is, we perceive the necesstty of the relation so long as 
the two subjeots exist, and we intuitively perceive that the rela- 
tion cannot ‘exist unless its two subjects exist. 
€ What a change in the assumptions of mathematics, to find, 
that its conclusions are not limited to hypothetical or conditional 
truth, but embrace also facts,—conerete facts! What an enlarge- 
ment of the field of demonstrable subjects! 
*¢ VISIBLE LINES ARE VOID OF BREAD?H. 
¢ Phis general fact (it is always to be remembered) is wholly 
snbordinate'to the laws of vision, being included in those laws 
but not necessary to their truth. At the same time, however, it 
is a fact rigidly demonstrable. ' 
“¢ A mathematical line (of the schools) is demonstrated to be 
void of breadth, in consequence of its being defined to be “ the 
common boundary of two contiguous surfaces.’ ‘Now, if one of 
the two surfaces be supposed blue, and the other one yellow, it 
is plain the mathematical line of contiguity, and the line of con- 
trast of the two colours, is one same line; and since it has no 
breadth as the common boundary between the two surfaces, it 
can‘have no breadth as the common boundary between the two 
sensations of colours. 
© To.attempt to invalidate this upon the ground of the imper- 
fection of sense, would only prove that the person who under- 
takes it does not apprehend ald the terms of the subject. The 
subject is a line that we see: and (without any appeal “to the 
suffrage of 'Proclus) we may safely maintain that we don’t see 
what we don’t see. The imperfection of sense only makes us 20#- 
see breadth, in some instances where breadth really is before us, 
and where a magnifying power makes it evident: but the im- 
perfection of sense cannot make us see breadth when it makes us 
not see it. Inrigid'truth, therefore, the imperfection of the or- 
ganic process of sense causes the perfection of the mathematical 
Tine we see; ; for the organ will not convey a report of breadth to 
the sentient, in some cases wherein the external object that we 
look at-really has some minute breadth. 
<¢ A visible 
