Consideration of the special case in which the centre of the eccentric circle lies on the straight line whose points of intersection with the conic are required.

In what follows it will be convenient to abandon the system of lettering adopted by Boscovich which we have hitherto followed, and as far as possible to use that common to modern text books.

Pythagoras was born in Samos about 580 B.C. The statements regarding his masters are destitute of solid historical foundation, and so are the accounts of his travels. It is known, however, that he visited Egypt. He may have taught in Samos, but whether he did not obtain sufficient consideration among his fellow-citizens, or whether he wished to withdraw from the tyranny of Polycrates, he removed to Croton about 540 B.C. There he founded an association, less scientific than politico-religious, which eventually became the nucleus of the aristocratic party.

The extraordinary development, ramification, and specialisation which our generation sees in all science, but especially in the queen of sciences, mathematics, makes imperative a determined attempt to keep connected these new and growing fields.