An instance will do more than a volume of generalities to make
my meaning clear.
Suppose I see two individuals approaching whose rank I wish to ascertain.
They are, we will suppose, a Merchant and a Physician, or in other words,
an Equilateral Triangle and a Pentagon; how am I to distinguish them?
It will be obvious, to every child in Spaceland who has touched
the threshold of Geometrical Studies, that, if I can bring my eye
so that its glance may bisect an angle (A) of the approaching stranger,
my view will lie as it were evenly between the two sides that are next
to me (viz. CA and AB), so that I shall contemplate the two impartially,
and both will appear of the same size.
Now in the case of (1) the Merchant, what shall I see? I shall see
a straight line DAE, in which the middle point (A) will be very bright
because it is nearest to me; but on either side the line will shade
away RAPIDLY TO DIMNESS, because the sides AC and AB RECEDE RAPIDLY
INTO THE FOG and what appear to me as the Merchant's extremities,
viz. D and E, will be VERY DIM INDEED.
On the other hand in the case of (2) the Physician, though I shall
here also see a line (D'A'E') with a bright centre (A'), yet it will
shade away LESS RAPIDLY to dimness, because the sides (A'C', A'B')
RECEDE LESS RAPIDLY INTO THE FOG: and what appear to me the Physician's
extremities, viz.
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