But all chords intersecting inside a circle divide one another in this proportion. Other curved lines suggest other purposive solutions of which nothing was thought in the rule that furnished their construction. All conic sections in themselves and when compared with one another are fruitful in principles for the solution of a number of possible problems, however simple is the definition which determines their concept. — It is a true joy to see the zeal with which the old geometers investigated the properties of lines of this class, without allowing themselves to be led astray by the questions of narrow-minded persons, as to what use this knowledge would be.

Thus they worked out the properties of the parabola without knowing the law of gravitation, which would have suggested to them its application to the