Measures of 3 and 1 balanced by a measure of 2,
the point of balance dividing the space in good proportion.]

The balance of three or more masses within a rectangle involves the
consideration of two at a time, balancing the pair or pairs with the
remaining mass or masses.

In Fig. 15, masses 1, 2 and 3 are to be balanced within the rectangle.
Balancing 3 with 1 gives the balancing point P. Taking 3 plus 1 from the
point P, we locate the mass 2 to balance them across the line AB which
divides the rectangle in good proportion. The point _p_ then becomes the
balancing point for the entire group. Mathematically, 3 plus 1 equal 4;
4 is twice 2; therefore the mass 2 must be twice as far from the point
_p_ as the balanced masses 3 plus 1.

Two other combinations might have been worked out with the masses in
Fig. 15: 3 plus 2, balanced by 1, the mass 1 being placed five times as
far from the point _p_ as would the point P. Or 2 plus 1 might have been
balanced by 3, in which case the distances would have been equal.

The application of these principles of balance to the problems of
typography is largely a matter of influence. The typographer should be
guided by them but he need not make mathematical calculations if his
eyes be trained to judge relative attraction values so that he can
arrange his various masses to secure balance.

_Symmetry_

When two parts of a design are equal in every respect so that if the
design were folded over one-half would superimpose in every detail with
the other half, then a state of _symmetry_ exists and the design is said
to be _symmetrical_. The line upon which such a design would be folded,
or, in other words, the line which bisects a symmetrical design, is
called its _axis_.

The printed page is often symmetrical with respect to its vertical axis
(Fig. 16).

In Fig. 16 the line AB is the vertical axis of the page.

[Illustration: Fig. 16. Type page, symmetrical with respect to its
vertical axis.]

[Illustration: Fig. 17. Page arranged for variety. Not symmetrical on
either axis. This arrangement is frequently used in advertising display,
but is rare in book work.]

It is rarely possible that the printed page can be symmetrical with
respect to its horizontal axis. Such a state would involve a division
of the page below its optical center and would also have an
uninteresting division of its spaces, with equal masses above and below.
It should be noted that symmetry on the ver