Her husband and children accompanied her to Portugal, where she figured among the "reconciled" in the auto-da **fd** of the 9th of July 1713, after undergoing the torment only.

He went through the great auto-da **fd** held on the 23rd of October in the presence of King John V.

Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -**fD** = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.

In the triangle **FDC**, let **FD** be tangent to the curvelFC vertical, and Dqhorizontal; these three sides will necessarily be proportional respectively.to_the FIG.

Other words, by a non-Euclidean construction he trisected the angle AOC, for it is readily seen that, since **FD**' = FO = OC, the angle FOB = 2 AOC. 6 This couplet of constructions is as important from the calculator's point of view as it is interesting geometrically.

For a single pulley of diameter D, turning on a fixed pin of diameter d, the relation of the effort E to the load W, where f is the coefficient of friction, is expressed by E/W = (D-pfd)/(D - **fd**) _ 1 +2fd/D approximately.