218 



and circle directly, without the intervention of the cone. He thus 

 removes the conic sections altogether from the geometry of solids 

 into the geometry of planes, according to the modern method, with- 

 ont separating them from the family of the circle to which they 

 properly belong. 



The definition from which he sets out is this : If between a given 

 circle and its tangent straight line there be traced a curve whose dis- 

 tance from the circle shall bear a constant proportion to its distance 

 from the straight line, that curve is a conic section, and according 

 as the given ratio is one of equality, deficiency, or excess, the cone 

 becomes a parabola, ellipse, or hyperbola. 



The author shews with how much facility the other properties of 

 the curve follow from this constitution : he gives examples of some 

 of these, shews a new and remarkable property of the tangents of 

 the conic sections, and proves that they may be readily identified 

 with the sections of the cone from the constructive property alone, 

 without the intervention of any derived property. 



[The Meetings were adjourned till the first Monday in No- 

 vember.] 



