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4 
the le Diy 2 Magnitude., 331 
evi Biation of ideas in the human mind is, at the same time, the 
process of all existence,” in a word, in which “the dialectic pro- 
cess is the Method, the dialectic process the Deity, the dialectic 
process everything ;? a system no less remarkable - for the un- 
soundness of its premises, than for the logical rigor and scientific Fi. 
beauty with which it marches forward to its fatal results. * 
With the preceding distinction in view, the way is opened Nira 
a decision of the much vexed question respecting the divisibi 
of magnitude. In every age, from that of the earliest Guontie “Be ain 
the present moment, the contradictions on this subject, which the 
reasoning of geometry seems fairly to involve, have furnished 
weapons by which the certainty of human knowledge has been 
assailed ; leaving room for a doubt, which the defenders of truth 
have appeared more willing to avoid than directly to meet; very 
many of them seeming to think, that the solution of the problem i in- 
cluded something beyond the limits of the human understanding. 
- The difficulty referred to isthis. It is well known to the | 
i sen that according to the principles of mathemati 
, every li i itude is divisible 
nde oe 
the given aetrode For, let any. magnitude whatever, be 
“posed, and, for the sake of argument, let it be considered as 
least conceivable. This magnitude is some assignable ‘distance 
It can therefore become the radius of acircle. But® “if a poin 
the straight lines which can be drawn from it to the circumfe 
) ence, ‘the greatest is that in which the centre is, and the other 
Beg of the diameter is the least.” 
‘That is, a point being taken in the radius which is neither at 
“the centre nor at the circumference of the circle, a magnitude can 
gen and the ceéntre,) less than radius. But, by supp ta 
“dius was the least conceivable magnitude, a magnitude t 
has heen found dess than the least conceivable. Now he 
cess can be repeated as oftén as a new radius is taken, § 
on the principles of geometry, magnitude is divisible bg 
assignable ‘limit, in other words, magnitude is inde 
it is commonly called, infinitely divisible. 
| nthe other hand, itis urged by the natural 
| well as by common sense, Mee here i is a world 1 
| dependent of our gonce prone. governed 
> * Ettelid, bib: iii, Prop. 1 Vil. 
ie. a 
