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The characteristics of the system can be determined when it is known how many there are of these two kinds of degenerate conics in the system, and how often each is to be counted.

Projective Definitions of the Conics.—We now consider the shape of the conics.

Next to Archimedes, he was the most distinguished of the Greek geometricians; and the last four books of his conics constitute the chief portions of the higher geometry of the ancients.

The second greatest contribution of the Greeks was the statics and the conics of which Archimedes was the chief creator in the third century b.c.

Dionysodorus gave a solution by means of conics of the auxiliary cubic equation to which Archimedes reduced this problem; he also found the solid content of a tore or anchor-ring.