140 } THE FINE ARTS. 
greatest divergence of the curve from the chord, the proportion of the dis- 
tance of this point to the length of the chord, and the precise direction of 
the latter. Or if we employ tangents we measure the various distances on 
both sides of the point of contact between the curved line and the straight 
auxiliary. These few indications will suffice to show the ample field of 
observation and study afforded by the endless variety of curves that occur 
in the great domain of nature. 
e. Curvilinear Figures are either in themselves sufficiently definite for 
immediate conception by our mind (the simplest being the circle, next the 
ellipse, and then the oval), or they require the application of auxiliary lines 
to determine their forms, and are then to be resolved into their various curves, 
the divergence of each from a straight line being determined as before 
indicated. 
J. Geometrical Bodies. The cube, parallelopipedon, tetrahedron, the 
prism in its various forms, the pyramid, cone, cylinder, sphere, ellipsoid, 
the egg, and the various mineral crystallizations, constitute a series of forms 
from the most definite and easily determinable to the indefinite and difficult, 
similar to that of lines and plane figures before alluded to. Our limited 
space forbids a detailed consideration of these forms and of the manner in 
which those whose forms are definite are used in determining the confor- 
mation of the irregular ones. But we urgently recommend a minute study 
of these forms, inasmuch as they not only exert the greatest influence upon 
our more or less correct appreciation of the plastic conformations in nature, 
but afford us constructive auxiliary bodies to facilitate our transferring the 
bodies produced by nature into a perspective projection or natural drawing. 
With a view of promoting the study of forms, we add the following 
general observations on general outlines, general forms, symmetry, and 
skeleton of axes. 
Most of the forms of natural objects are continuous deviations from such 
geometrical figures as form their basis, and which, when imagined around 
or in a natural body, can be called in the drawing its general outline. To 
find this general outline in any object is the first condition for the determi- 
nation of its form, and the principal auxiliary in its correct representation. 
It is found by trying to circumscribe the object as closely as possible 
with straight lines or geometrical curves, in such a manner that, if need be, 
we either complete some of its parts by auxiliaries (pl. 19, jig. 20), or cut off 
some of its protuberances ( pl. 20, figs. 8-6, 13-15), or inclose them in suitable 
auxiliaries ( pl. 19, figs. 13, 14; pl. 20, figs. 7, 8). Principal parts of whole 
figures can be treated in the same manner (the arms, pl. 21, jigs. 14, 15; 
the skull, pl. 20, figs. 4, 5, 7, 8). Even geometrical figures can be thus 
reduced to their simple fundamental forms ; for instance, a regular octagon 
can be reduced to a square by prolonging its horizontal and vertical sides; 
a regular hexagon to an equilateral triangle by prolonging three of its 
sides; a trapezium to a triangle by prolonging its non-parallel sides 
(pl. 19, fig. 45, cap and base of the pilaster in the building on the left). 
By circumscription the square is shown to be the basis of the circle (pi. 20, 
jig. 8, square and circle over the line 1); the rectangle that of the ellipsis 
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