In this paper, Vieta made use of the center of similitude of two circles.
2.
The circumcenter of the tangential triangle, and the center of similitude of the orthic and tangential triangles, are on the Euler line.
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Any two disjoint spheres in three dimensional space, with different radii, have two bitangent double cones, the apexes of which are called the centers of similitude.
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The same argument can be applied to the other pairs of circles, so that three centers of similitude for the given three circles must lie on the radical axes of pairs of solution circles.
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And if four spheres are given, with their centers non-coplanar, then they determine 12 centers of similitude and 16 axes of similitude, which together form an instance of the Reye configuration.
6.
If three spheres are given, with their centers non-collinear, then their six centers of similitude form the six points of a complete quadrilateral, the four lines of which are called the axes of similitude.
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