The Theory and Practice of Perspective | Page 6

One of
the most beautiful examples of the application of this knowledge to
architecture is the Campanile of the Cathedral, at Florence, built by
Giotto and Taddeo Gaddi, who were painters as well as architects. Here
it will be seen that the height of the windows is increased as they are
placed higher up in the building, and the top windows or openings into
the belfry are about six times the size of those in the lower story.

WHAT IS PERSPECTIVE?
[Illustration: Fig. 1.]
Perspective is a subtle form of geometry; it represents figures and
objects not as they are but as we see them in space, whereas geometry

represents figures not as we see them but as they are. When we have a
front view of a figure such as a square, its perspective and geometrical
appearance is the same, and we see it as it really is, that is, with all its
sides equal and all its angles right angles, the perspective only varying
in size according to the distance we are from it; but if we place that
square flat on the table and look at it sideways or at an angle, then we
become conscious of certain changes in its form--the side farthest from
us appears shorter than that near to us, and all the angles are different.
Thus A (Fig. 2) is a geometrical square and B is the same square seen
in perspective.
[Illustration: Fig. 2.]
[Illustration: Fig. 3.]
The science of perspective gives the dimensions of objects seen in
space as they appear to the eye of the spectator, just as a perfect tracing
of those objects on a sheet of glass placed vertically between him and
them would do; indeed its very name is derived from perspicere, to see
through. But as no tracing done by hand could possibly be
mathematically correct, the mathematician teaches us how by certain
points and measurements we may yet give a perfect image of them.
These images are called projections, but the artist calls them pictures.
In this sketch K is the vertical transparent plane or picture, O is a cube
placed on one side of it. The young student is the spectator on the other
side of it, the dotted lines drawn from the corners of the cube to the eye
of the spectator are the visual rays, and the points on the transparent
picture plane where these visual rays pass through it indicate the
perspective position of those points on the picture. To find these points
is the main object or duty of linear perspective.
Perspective up to a certain point is a pure science, not depending upon
the accidents of vision, but upon the exact laws of reasoning. Nor is it
to be considered as only pertaining to the craft of the painter and
draughtsman. It has an intimate connexion with our mental perceptions
and with the ideas that are impressed upon the brain by the appearance
of all that surrounds us. If we saw everything as depicted by plane
geometry, that is, as a map, we should have no difference of view, no

variety of ideas, and we should live in a world of unbearable monotony;
but as we see everything in perspective, which is infinite in its variety
of aspect, our minds are subjected to countless phases of thought,
making the world around us constantly interesting, so it is devised that
we shall see the infinite wherever we turn, and marvel at it, and delight
in it, although perhaps in many cases unconsciously.
[Illustration: Fig. 4.]
[Illustration: Fig. 5.]
In perspective, as in geometry, we deal with parallels, squares, triangles,
cubes, circles, &c.; but in perspective the same figure takes an endless
variety of forms, whereas in geometry it has but one. Here are three
equal geometrical squares: they are all alike. Here are three equal
perspective squares, but all varied in form; and the same figure changes
in aspect as often as we view it from a different position. A walk round
the dining-room table will exemplify this.
It is in proving that, notwithstanding this difference of appearance, the
figures do represent the same form, that much of our work consists; and
for those who care to exercise their reasoning powers it becomes not
only a sure means of knowledge, but a study of the greatest interest.
Perspective is said to have been formed into a science about the
fifteenth century. Among the names mentioned by the unknown but
pleasant author of The Practice of Perspective, written by a Jesuit of
Paris in the eighteenth century, we find Albert Dürer, who has left us
some rules and principles in the fourth book of his Geometry; Jean
Cousin, who has an express treatise on the art wherein are many
valuable things; also