THE ART OF DRAWING. 139 
smaller or larger than a right angle, are determined by their respective 
proportions to the standard (pl. 20, jig. 4abg right, pgq obtuse angle ; 
Jig. 6 abg right, pgg acute angle). The position of a right angle can vary ; 
it is called normal when its sides are in the chief directions, and oblique 
when its sides are oblique lines ; in the latter case its position is determined 
by auxiliary lines having the chief directions. 
c. Rectilinear Figures. Of rectilinear figures the square is the most 
regular, being formed by four right angles and four sides of equal length 
(pl. 16, fig. 40bwxy). Being the most accurately determined figure it 
serves for the determination of others. Its position, like that of the righ‘ 
angle, can be normal or oblique. 
Next to the square in simplicity is the rectangle, differing from the for 
mer only in being inclosed by two pairs of parallels of unequal length 
(pl. 19, the boundaries of jigs. 41-45.) The proportion of form, 7. e. of the 
height to the breadth of a rectangle, is most simply determined by the 
draughtsman by dividing it into squares (pl. 20, jigs. 18, 14; pl. 21, jigs. 
12-15). The normal position of a rectangle is either the reclining (reversed) 
(pl. 19, figs. 41, 42), or the standing (erect) (jigs. 48, 44). All other 
positions are oblique. 
With regard to definiteness of form to the eye, the next figure to be con- 
sidered is the equzlateral triangle, and after it the dsosceles in its varieties 
(steeple, roof, or gable-shape) arising from different proportions between the 
height and the base. Then follow the regular hexagon, octagon, and other 
polygons, which, like the irregular ones, are determined either by means of 
the above enumerated simple figures, or by division or integration (comple- 
menting). 
d. Curves (or curved lines) are determined as to their form by examining 
whether they be of egual curvature throughout or not. The circle is the 
standard of the former. Of the wnequally curved lines the rule of their 
curvature must be determined, and the places of greatest and relatively inferior 
curvature found. This determines the character of a curve as an ellipse, 
parabola, cycloid, spiral, &c. It is further to be examined in which 
part or division there is a concavity or a convexity, and whether either of 
these is constant or whether concavity alternates with convexity as in wave 
and serpent-lines, and the outlines of a nose, mouth, &e. In the latter case 
the points of recurvature, or the points where concave curves pass into con- 
vex ones, are to be accurately observed. Curves of a freer sweep, as for 
instance the profile lines of organic formation, are determined by compari- 
son with those whose curvature is reducible to geometrical laws. 
Mathematics teach the precise formation of the geometrical curves. But 
we may obtain an immediate knowledge of their form as well as of that of 
the organic curves (of mountains, clouds, plants, animals, &c.) in the follow- 
ing manner. We apply the enumerated rectilinear auxiliary figures either 
between two points of recurvature or the terminal points of a curve, or at 
one point on the convex side of acurve. In the former case the determining 
or auxiliary lines form chords, in the latter tangents, vertical or horizontal 
ones being most available. We then carefully observe the point of the 
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