Below we give a list of theorems obtained by inverting the corresponding theorems respecting a conic. In these theorems any circle through the pole is called a nodal circle, any chord through the pole is called a nodal chord, and the line through the pole perpendicular to the axis of the curve is called the latus rectum. The letters _e_ and _p_ signify respectively the eccentricity and half the latus rectum of the inverted conic. The locus of the point of intersection of two tangents to a parabola which cut one another at a constant angle is a hyperbola having the same focus and directrix as the original parabola. The locus of the point of intersection of two nodal tangent circles to a cardioid which cut each other at a constant angle is a limaçon having the same double point and director circle. The sum of the reciprocals of two focal chords of a conic at right angles to each other is constant. The sum of any two nodal chords of a limaçon at right angles to each other is constant. P Q is a chord of a conic which subtends a right angle at the focus. The locus of the pole of P Q and the locus enveloped by P Q are each conics whose latera recta are to that of the original conic as √2 : 1 and 1 : √2 respectively. If P and Q be two points on a limaçon such that they intercept a right angle at the node, then the locus of the point of intersection of the two nodal circles tangent at P and Q respectively, is a limaçon whose latus rectum is to that of the original limaçon as ½√2 : 1. And the envelope of the circle described on P Q as a diameter is a limaçon, whose latus rectum is to that of the original limaçon as 1 : ½√2. If two conics have a common focus, two of their common chords will pass through the point of intersection of their directrices. If two limaçons have a common node, two nodal circles passing each through two points of intersection of the limaçons, will pass through the point of intersection of their base circles. Two conics have a common focus about which one of them is turned; two of their common chords will touch conics having the fixed focus for focus. Two limaçons have a common node about which one of them is turned; two of the nodal circles through two of their points of intersection will envelope limaçons having fixed node for node.