Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

194

DESCRIPTIVE GEOMETRY

The planes determined by the lines O-X and O-Y, O-Y and
0-Z, and O-Z and O-X are called cobrdinate planes, and the projections of magnitudes lying on these planes between the limiting
axes will fall between the projections of these limiting axes.
The axis O-Y is given a position directly beneath the line P-O.
As a result the isometric axis o'-y' has a vertical position, the
axis o'-x' makes an angle of 30 degrees with a horizontal line
on the right, and the axis o'-z' makes an angle of 30 degrees with
a horizontal line on the left. For this reason the isometric axes
and all straight lines parallel to them are easily represented
upon the drawing board by use of the T-square and the 30-degree
triangle.
Each of the three dimensions - length, breadth, and thickness - of a solid are measured on straight lines perpendicular to
the plane of the other two, corresponding with the three edges of
a right trihedral angle.
It is therefore possible to place a solid in such a position that
its three principal dimension lines shall coincide with the three
coordinate axes O-X, O-Y, and 0-Z of Fig. 167. When the magnitude occupies this position its projection upon the plane V will
reveal the characteristics of three dimension faces of the object,
and the projection is called isometric.
Whenever a solid is projected upon a plane to which its principal dimension lines are equally inclined, the projection is called
isometric, since on account of this equality of inclination the projections of equal distances measured upon these dimension lines,
or upon lines parallel to them, will be equal.
The projection of any magnitude may be said to be isometric
whenever this projection is determined by reference to isometric
axes which themselves are the isometric projections of the three
coordinate axes to which the magnitude is referred, coordinates
with reference to the isometric axes appearing as the isometric
projections of the corresponding coordinates used in connection
with the original coordinate axes.
430. The Isometric Scale. The inclination of each of the three
coordinate axes O-X, O-Y, and 0-Z to the plane of projection is
35~.16'. By trigonometry the isometric projection of one foot