AMERICAN PREFACE. 
xli 
of objects for manufacture and in decorative art, as well as by 
draugktsmen and architects, wko use them for purposes of con- 
struction. Nature, too, emploj'S them: tkus her use of the vari 
able spiral is charmingly illustrated by the longitudinal section of 
a nautilus shell. Indeed, her whole fabric rests upon geometry, 
from whose rigid outlines she departs only in matters of detail. 
The artist should, therefore, be perfectly familiär with geometric 
forms and mathematical lines, making this knowledge aid him, as 
it can most effectually, in the production of new forms for indus 
trial purposes, and in the rendering of natural forms for purely 
artistic purposes. Now, these things can be taught with mathe 
matical precision ; a “ feeling for form ” is not at all essential. 
SK KING WITH THE UNDERSTANDING. 
All art involves the seeing of objects just as they are pre- 
sented to the eye by their outlines, and by the modifications of light 
and shade. If the forms are imaginary, they must be represented 
as they would appear if they existed and were seen under the 
given conditions. Mere possession of the faculty of sight is no 
guaranty of that true vision which is required by art. If one 
would see truly, he must see with the understanding. To this end 
the essential thing is a knowledge of the laws of vision, of fore- 
shortening, of perspective effects, of the projection of shadows; 
and all'this knowledge rests upon a rigid mathematical basis, and 
so can be imparted with mathematical precision. Mere “ feeling 
for light and shade,” or for any thing eise, has nothing to do with 
the matter. Of course there is much about chiaroscuro that can- 
not be taught with such positive assurance. 
COLOR. 
Both decorative and pictorial art have much to do with color. 
Now, in the study of color there are three definite things to be 
regarded : facts, scientific laws, historic usage. Different colors 
can be learned as facts ; and, in learning them, one has the fixed 
solar spectrum for his guidance. Thus the eye can learn readily 
to distinguish thousands of colors. There is also a knowledge of 
dyes, of pigments, of approaching and retreating colors, and of