In this paper the author institutes an examination of the various methods of conceiving and constructing the conic sections, the different standards of comparison to which they have been referred, and the means by which their properties have been developed and expressed in the ancient and modern schools of mathematics. He finds that the constitution of the curves in plano by means of their remarkable properties, and the demonstration of their other properties from the constitution so obtained; have been noticed by Eutocius in the 6th century, and by him referred to Apollonius, although the formal adoption of the plane method is generally referred to a recent date.