... containing a full Explication of the Method by which the most celebrated Geometers of the present Age have made such vast Advances in Mechanical Philosophy, A work very useful for those who would know how to apply Mathematics to Nature.

A Preface is expected from every Author, and when tending to inform the Readers of the motives that induced him to write: And of the means they must use to understand what is wrote, is very proper; the former to justify himself from the Imputation of Vanity, and the latter to quicken and forward their Industry.

As to the first, 'Tis manifest, since the World has been convinced of the mischief of Dogmatizing, either in Philosophy or Mathematics, that by allowing themselves a freedom of Thought, and boldly venturing forwards; the Advances in each are equally wonderful, that it is a difficult matter to resolve, whether an easy Acquiescence in all the Ancient Discoveries more obstructed, or the more generous Essays of modern Hero's improved our Knowledge; that since Men resumed their Native privilege, and allowed themselves the Liberty of enquiring freely into things, they have extended their Dominions over all the Earth, and their Knowledge far above the clouds; that these being the undeniable results of Mathematical studies; it is further plain, that they create in us more awful Thoughts and juster Notions of the works of God; and the admirable Harmony which only they discover, both in things in Heaven, and in things in Earth, undeniably prove one and the same great Author; in a word, that by them we create our Riches, enlarge our Power, and improve our reason; these then being some of the great Advantages Mankind receive from Mathematical learning, Who would not incessantly aspire after such useful Knowledge? Who can be blamed for using these endeavours to propagate the same?

As to the ensuing Treatise, the Author has been well assured that there are in England as many Lovers of the Mathematics as in any part of the World; that the multitudes of excellent Judgements and natural Parts, merely for want of a competent Knowledge in other Languages, have hitherto been deprived of the Opportunities of improving them, to the great disadvantage of the most Flourishing Island in the World; that in other Nations the best pieces of Learning are written in their own mother Tongues, for the good of their country which we seem purposely to slight, seeking a little empty applause by writing in a Language not easily attained, as if the Knowledge of things and words had a necessary dependence on each other ...

Magnitude is divisible in 'infinitum', and the Parts after this infinite Division, being infinitely little, are what Analysts call 'Moments' or 'Differences'; And if we consider Magnitude as Indeterminate and perpetually Increasing or Decreasing, then the infinitely little Increment or Decrement is called the Fluxion of that Magnitude or Quantity: And whether they be called Moments, Differences or Fluxions, they are still supposed to have the same Proportion to their Whole's, as a Finite Number has to an Infinite; or as a finite Space has to an infinite Space. Now those infinitely little Parts being extended, are again infinitely Divisible; and these infinitely little Parts of infinitely little Parts of a given Quantity, are by Geometers called 'Infinitesimae Infinitesimarum' or 'Fluxions of Fluxions'. Again, one of those infinitely little Parts may be conceived to be Divided into an infinite Number of Parts which are called Third Fluxions, etc.

Following Muslim scholars who sought to lay down sound chronologies of the very ancient world, Hayes realised that for this it was necessary to establish relationships and links between lists of rulers in different parts of the world.

... Hayes found himself exonerated from that burden, which, though he had long supported it, yet was not altogether suitable to his inclinations.

He devoted the last eight years of his life to a far larger project, a Chronology of Asia and Egypt which he did not finish. In this work he argued that Josephus and the Seventy had had access to texts left out of the Old Testament canon but available to them in the Temple. On the basis of this it was possible to give credence to the testimony of the Letter, and hence also to what was contained in the Septuagint.

If I differed in anything from him, as I could not espouse all his opinions, and never made a compliment of my own, he would reply in so mild a manner, that I never left him without admiring his great fund of learning, the clear method in which he explained his mind, and his sedate and serene temper.