CONIC sections, as the name imports, are such curve lines as are produced by the mutual intersection of a vlane and the surface of a solid cone. The, nature and properties of these figures were the subject of an extensive branch of the an cient geometry, and formed a speculation well suited to the subtle genius of the Greeks. In modern times the conic geo metry is intimately connected with every part of the higher mathematics and natu ral philosophy. A knowledge of those discoveries, that do the greatest h onourto the last and the present centuries, cannot be attained without a familiar acquaint ance with the figures that are now to en gage our attention.
We are chiefly indebted to the pre servation of the writings of Apollonius for a knowledge of the theory of the an cient geometricians concerning the conic sections. Apollonius was born at Perga, a town of Phamphylia, and he is said to have lived under Ptolemy Philopater, about forty years posterior to Archime des. Besides his great work on the conic sections, he published many smaller trea tises, relating chiefly to the geometrical analysis, which have all perished. The treatise of Apollonius on the conic sec tions is written in eight books, and it was esteemed a work of so much merit by his contemporaries, as to procure for its author the title of the great geometri cian Only the four first books have come down to us in the original Greek. On the revival of learning, the lovers of the ma thematics had long to regret the original of the four last books In the year 1658, Borelli, passing through Florence, found an Arabic manuscript in the library of the Medici family, which he judged to be a translation of all the eight books of the conics of Apollonius : but on ex amination, it was found to contain the first seven books only. Two other Ara
bic translations of the conics of Apollo nius have been discovered by the indus try of learned men : and as they all agree in the want of the eighth book, we may now regard that part of the treatise as irrecoverably lost. The work of Apollonius contains a very extensive, if not a complete, theory of the conic sec tions. The best edition of it is that published by Dr. Halley, in 1710: to which the learned author has added a re storation of the eighth book, executed with so much ability as to leave little room to regret the original.
Since the revival of learning, the theory of the conic sections has been mach cul tivated, and is the subject of a great va riety of ingenious writings. Dr. Wallis, in his treatise " Dr SeCI1011;b1IS Conicis," published at Oxford, in 1655, deduced the properties of the curves from a de scription of them on a plane. Since this tirne•authors have been much divided as to the best way of defining the curves, and demonstrating their elementary pro perties ; many, in imitation of the ancient geometricians, making the cone the groundwork of their theories ; while °fliers have followed the example of Dr. WLIis.