- The " centres of **similitude** " of two circles may be defined as the intersections of the common tangents to the two circles, the direct common tangents giving rise to the " external centre," the transverse tangents to the " internal centre."

The circle on the line joining the internal and external centres of **similitude** as diameter is named the " circle of **similitude**."

With a system of three circles it is readily seen that there are six centres of **similitude**, viz.

The theory of centres of **similitude** and coaxal circles affords elegant demonstrations of the famous problem: To describe a circle to touch three given circles.

Hence T, the point of intersection of Pp and Qq, must be the centre of **similitude** and must be on the common directrix.

Again, Moses differs from all other prophets in that Yahweh speaks to him face to face, and he sees the **similitude** of Yahweh.

That returns from the bottomless pit, "that was, and is not, and yet is"; the head "as it were wounded to death" that lives again; the gruesome **similitude** of the Lamb that was slain, and his adversary in the final struggle.

John Casey, professor of mathematics at the Catholic university of Dublin, has given elementary demonstrations founded on the theory of **similitude** and coaxal circles which are reproduced in his Sequel to Euclid; an analytical solution by Gergonne is given in Salmon's Conic Sections.

In this paper Vieta made use of the centre of **similitude** of two circles.