Women are Straight Lines.

Our Soldiers and Lowest Classes of Workmen are Triangles with two equal
sides, each about eleven inches long, and a base or third side so short
(often not exceeding half an inch) that they form at their vertices a
very sharp and formidable angle. Indeed when their bases are of the
most degraded type (not more than the eighth part of an inch in size),
they can hardly be distinguished from Straight Lines or Women; so
extremely pointed are their vertices. With us, as with you, these
Triangles are distinguished from others by being called Isosceles; and
by this name I shall refer to them in the following pages.

Our Middle Class consists of Equilateral or Equal-Sided Triangles.

Our Professional Men and Gentlemen are Squares (to which class I myself
belong) and Five-Sided Figures or Pentagons.

Next above these come the Nobility, of whom there are several degrees,
beginning at Six-Sided Figures, or Hexagons, and from thence rising in
the number of their sides till they receive the honourable title of
Polygonal, or many-sided. Finally when the number of the sides becomes
so numerous, and the sides themselves so small, that the figure cannot
be distinguished from a circle, he is included in the Circular or
Priestly order; and this is the highest class of all.

It is a Law of Nature with us that a male child shall have one more
side than his father, so that each generation shall rise (as a rule)
one step in the scale of development and nobility. Thus the son of a
Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on.

But this rule applies not always to the Tradesmen, and still less often
to the Soldiers, and to the Workmen; who indeed can hardly be said to
deserve the name of human Figures, since they have not all their sides
equal. With them therefore the Law of Nature does not hold; and the
son of an Isosceles (i.e. a Triangle with two sides equal) remains
Isosceles still. Nevertheless, all hope is not shut out, even from the
Isosceles, that his posterity may ultimately rise above his degraded
condition. For, after a long series of military successes, or diligent
and skilful labours, it is generally found that the more intelligent
among the Artisan and Soldier classes manifest a slight increase of
their third side or base, and a shrinkage of the two other sides.
Intermarriages (arranged by the Priests) between the sons and daughters
of these more intellectual members of the