1 Prohl. xvi. 6. 914 a 25. 2 Phys. v. B. 227 all; vii. 1. 231 a 24. 
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FROM PLATO TO EUCLID 
a certain class of investigation. If a book in the form of a 
cylindrical roll is cut by a plane and then unrolled, why is it 
that the cut edge appears as a straight line if the section 
is parallel to the base (i. e. is a right section), but as a crooked 
line if the section is obliquely inclined (to the axis). 1 The 
Problems are not by Aristotle; but, whether this one goes 
back to Aristotle or not, it is unlikely that he would think of 
investigating the form of the curve mathematically. 
(e) The continuous and the infinite. 
Much light was thrown by Aristotle on certain general 
conceptions entering into mathematics such as the c continuous ’ 
and the ‘ infinite The continuous, he held, could not be 
made up of indivisible parts; the continuous is that in which 
the boundary or limit between two consecutive parts, where 
they touch, is one and the same, and which, as the name 
itself implies, is kept together, which is not possible if the 
extremities are two and not one. 2 The ‘ infinite ’ or ‘ un 
limited ’ only exists potentially, not in actuality. The infinite 
is so in virtue of its endlessly changing into something else, 
like day or the Olympic games, and is manifested in different 
forms, e.g. in time, in Man, and in the division of magnitudes. 
For, in general, the infinite consists in something new being 
continually taken, that something being itself always finite 
but always different. There is this distinction between the 
forms above mentioned that, whereas in the case of magnitudes 
what is once taken remains, in the case of time and Man it 
passes or is destroyed, but the succession is unbroken. The 
case of addition is in a sense the same as that of division; 
in the finite magnitude the former takes place in the converse 
way to the latter; for, as we see the finite magnitude divided 
ad infinitum, so we shall find that addition gives a’ sum 
tending to a definite limit. Thus, in the case of a finite 
magnitude, you may take a definite fraction of it and add to 
it continually in the same ratio; if now the successive added 
terms do not include one and the same magnitude, whatever 
it is [i. e. if the successive terms diminish in geometrical 
progression], you will not come to the end of the finite 
magnitude, but, if the ratio is increased so that each term