The Elements of the True Arithmetic of Infinites

To most readers, who consider the present as a very enlightened age, it will doubtless appear monstrous to assert that the greatest of modern mathematicians have been so far from adding anything of importance to the discoveries of ancient mathematicians, that some of their most splendid inventions are either entirely erroneous or are remarkable examples of the possibility of deducing true conclusions from unscientific and false principles. Strange, however, as this assertion may seem, the following elementary treatise demonstrates it to be true by showing that all the leading propositions of the Arithmetic of Infinites of Dr. Wallis are false, and that the Doctrine of Fluxions The mathematical study of continuous change, originally developed by Isaac Newton. is a baseless fabric and, in the language of the ingenious Bishop Berkeley*, "must be considered only as a presumption, as a knack, an art, or rather an artifice, but not a scientific demonstration."

If the following treatise, therefore, only detected the errors of some of the greatest modern mathematicians and vindicated the scientific accuracy of the ancient mathematicians, I should consider that my time was by no means misspent in composing it; but as I presume it will also be found to unfold the nature of the mathematical infinite more satisfactorily than it has been unfolded hitherto, I trust I shall obtain the commendation of the liberal and the wise.

• In his Analyst, p. 41.

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