This is called the direct orthogonal substitution, because the sense of rotation from the axis of X i to the axis of X, is the same as that from that of x i to that of x 2.

Clerk Maxwell, who showed amongst other things that a reciprocal can always be drawn to any figure which is the orthogonal projection of a plane-faced polyhedron.

Orthogonal System.-In particular, if we consider the transformation from one pair of rectangular axes to another pair of rectangular axes we obtain an orthogonal system which we will now briefly inquire into.

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Previous to continuing the general discussion it is useful to have before us the orthogonal invariants and covariants of the binary linear and quadratic forms.

If we project both polyhedra orthogonally on a plane perpendicular to the axis of the paraboloid, we obtain two figures which are reciprocal, except that corresponding lines are orthogonal instead of parallel.

It may denote a simultaneous orthogonal invariant of forms of orders n i, n2, n3,...; degree 0 of the covariant in the coefficients.

By means of the orthogonal relations (15).

The orthogonal projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix.

The area of the ellipse is 7rab, where a, b are the semi-axes; this result may be deduced by regarding the ellipse as the orthogonal projection of a circle, or by means of the calculus.

Such a determinant is of importance in the theory of orthogonal substitution.