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Democritus’s Cone

by Sarah Adams

A paradox, one less well-known,
Asks us to contemplate a cone:
A figure with smooth sloping sides
Which horizontally divides
Into two halves, so that have we
Two surfaces: one a, one b.
The bottom of the top we’ll say
Is denoted by the letter a,
And b denotes the upper side
Of the half which did reside
Directly underneath the top
Antecedent to the chop.

So let us turn now and reflect
Upon the cone we did bisect.
Something will be shown amiss
When we now consider this:
Is the area of b the same
As that of a (the surface plane
at the bottom of the top, we said),
Or is unequal b instead?
Either answer can’t be true,
The reasons I will talk you through:
If a unequal is to b
Then after all cannot have we
A cone with edges smoothly sloping
(This is surely thought-provoking)
But a pyramid: something stepped.
This you will have to accept,
For surfaces different in size
Lead us to the cone’s demise.
And yet if b to a is equal
To the cone this too proves lethal,
For once we’ve chosen to profess
That indeed we do possess
Surfaces stacked up high,
The same in size (not just nearby)
Then somewhat paradoxically,
The cone is not a cone, you see,
But a cylinder.

© Sarah Adams 2014

Sarah Adams is a PhD student at the University of Leeds who works on Metaphysics, Philosophy of Religion, and, in her non-existent spare time, the lesser-known field of Philosophical Poetry.

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