A sequel to the first six books of the Elements of Euclid, containing an easy introduction to modern geometry, with numerous examples. By John Casey.

52 A SEQUEL TO EUCLID.
45. If a G touch a semicircle and two ordinates to its diameter,
the rectangle under the remote segments of the diameter is equal
to the square of the 1 from the centre of the ( on the diameter
of the semicircle.
46. If AB be the diameter of a semicircle, and AC, BD two
chords intersecting in 0, the ( about the A OCD intersects the
semicircle orthogonally.
47. If the sum or difference of the tangents from a variable
point to two Os be equal to the part of the common tangent of
the two Os between the points of contact, the locus of the point
is a right line.
48. If pairs of common tangents be drawn to three Os, and if
one triad of common tangents be concurrent, the other triad will
also be concurrent.
49. The distance between the feet of I s from any point in the
circumference of a ( on two fixed radii is equal to the I fiom
the extremity of either of these radii on the other.