ABSTRACT
WHEN I treated in the foregoing Lecture concerning the Division of the Mathematical Sciences, I affirmed the Whole of Mathematics to be in some sort contained and circumscribed within the Bounds of Geometry. And indeed concerning the other Sciences then mentioned, I imagine no Body will much deny, but they are conveniently enough reduced to Geometry. But now I have brought a harder Task upon myself, to shew allowable and fit Causes for expunging Arithmetic out of the List of Mathematical Sciences, and as it were degrading the most noble Science from the Degree which it has been to long possessed of. Albeit I am conscious to myself that I have committed no such Fault. Be it far from me to take away or seclude a Science so excellent and profitable as that of Numbers from the Mathematics. I will rather restore it into its lawful Place, as being removed out of its proper Seat, and ingrass and unite it again into its native Geometry, the Stock from whence it has been plucked. Nay, my Conscience would not permit me to oppose so illustrious and venerable an Authority, and obtrude such a monstrous Paradox upon you, if I did not put great Confidence in the Cause I have undertaken, and thought it very much to the Purpose of Mathematics, that Arithmetic be accounted not only like and of kin to Geometry in Nature (or, according to the Saying of f Archytas of Tarentum, that antient Pythagorean Philosopher, its Sister) but more nearly conjoined, yea altogether the same, and wholly indistinct from it. For I am convinced that Number really differs nothing from what is called Continued Quantity, but is only formed to express and declare it; and consequently that Arithmetic and Geometry are not conversant about different Matters, but do both equally demonstrate Properties common to one and the same Subject; and very many, and very great Improvements will appear to be derived from hence upon the Republic of Mathematics.
