APOLLONIUS, of Perga, a city in Pamphilia, wa.s a celebrated geometrician, who flourished in the reign of Ptolemy Euergetes, about 240 years before Christ; being about 60 years after Euclid, and 30 years later than Archimedes. Ite studied a long time in Alexandria under the disci ples of Euclid ; and afterwards he com posed several curious and ingenious geo metrical works, of which only his books of Conic Sections are now extant, and even these not perfect. For it appears from the author's dedicatory epistle to Eudemus, a geometrician in Pergarnus, that this work consisted of eight books ; only seven of which however has come down to us.
From the Collections of Papus, and the Commentaries of Eutocius, it appears that Apollonius was the author of various pieces in geometry, on account of which he acquired the title of the great geome trician. His Conics was the principal of them. Some have thought that Apollo nius appropriated the writings and disco veries of Archimedes; Heraclius, who wrote the life of Archimedes, affirms it ; though Eutocius endeavours to refute him. Although it should be allowed a groundless supposition, that Archimedes was the first who wrote upon conics, not withstanding his treatise on conics was greatly esteemed, yet it is highly proba ble that Apollonius would avail himself of the writings of that author, as well as others who had gone before him ; and, upon the whole, he is allowed the honour of explaining a difficult subject better than had been done before, having made several improvements, both in Archime des's problems, and in Euclid. His work
upon conics was doubtless the most per fect of the kind among the ancients, and in some respects among the moderns also. Before ApoBoning, it had been cu.stoma ry, as we are informed by Eutocius, for the writers on conics to require three dif ferent sorts of cones to cut the three diffe rent sections from; tir.. the parabola from a right-angled cone, the ellipse from an acute, and the hyperbola from an obtuse cone ; because they always supposed the sections made by a plane cutting the cones to be perpendicular to the side of them: but Apollonius cut his sections all from any one cone, by only varying the inclination or position of the cutting plane ; all improvement that has been followed by aU other authors since his dine. But that Archimedes was acquainted with tile same manner of cutting- any cone is suffi ciently proved, against Eutocius, Pappus, and others, by Guido Ubaldus, in the be ginning of his Commentary on the second book of Archimedes's Equiponderantes, published at Pisa in 1588. See CONIC