Paper, 'A memoir on the conditions for the existence of given systems of equalities among the roots of an equation' by A [Arthur] Cayley Subject: Mathematics Published in Philosophical Transactions as 'A memoir on the conditions for the existence of given systems of equalities among the roots of an equation'. Received by the Royal Society on 18 December 1856. Read 8 January 1857. Abstract published in Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London [later Proceedings of the Royal Society of London], Volume 8, 1857. [1856]