Unpublished paper, 'On the extension of the principle of Fermat's theorem (of the polygonal numbers) to the higher orders of series whose ultimate differences are constant - with a new theorem proposed, applicable to all the orders' by Frederick Pollock Pollock attempts to ascertain whether the principle of Fermat’s theorem of the polygonal numbers may not be extended to all orders of series whose ultimate differences are constant. Annotations in pencil throughout. Subject: Mathematics / Calculus Received 4 December 1849. Read 21 February 1850. Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 5 of Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London [later Proceedings of the Royal Society] as 'On the extension of the principle of Fermat’s theorem of the polygonal numbers to the higher orders of series whose ultimate differences are constant. With a new theorem proposed, applicable to all the orders'. December 1849