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.

ISOMETRIC PROJECTION

197

Of course the same result will be obtained if after drawing the line
a'-d' we lay off upon it the remaining coordinate a'-dt equal to ot-b'.
The axes to which the point is referred may be assumed in coincidence with O-X and 0- Y, or in coincidence with O-Z and 0- Y.
434. Problem 299. To find the b'
isometric projection of a point whose, av
coordinates with reference to three \
rectangular coordinate planes are
known. '
In Fig. 169 let ot-x', o'-y', and o'-z'
represent the isometric axes.
Place the three coordinate axes,
to whose planes the point is referred,
in coincidence with O-X, O-Y, and
FIG. 169
O-Z respectively. Then o'-xl, o'-y',
and ot-z' are the isometric projections of the coordinate axes.
Make o'-a' equal to the distance of the point from the plane
Z-O-Yand through a' draw al-b' parallel to o'-z. Make a-b' equal
to the distance of the point from the plane X-O-Y, and through
b' draw b'-d' parallel to o'-y'. Make b'-d' equal to the distance of
the point from the plane Z-O-X.
The point d' is the isometric pro^^~~r H^^I.^jection of the point in question.
// l ~The lines el-d', df-fl, and bt-df
I~ o | ~ / are the isometric projections of
A/I~ ^the three coordinate lines of the
I Y I point D.
435. Problem 300. To find the
) I |isometric projection of a straight
N ' j line when the coordinates of two of
>\ 1I~ its points with reference to three
rectangular coordinate planes are
FIG. 170 no
known.
In Fig. 170 let o'-x', o-y', and o'-z' represent the isometric axes.
Place the coordinate axes to whose planes the line is referred
in coincidence with O-X, O- Y, and 0-Z. Then o-xl, o'-y', and o'-z'
are the isometric projections of these coordinate axes.