The Doctrine of Permutations and Combinations, Being an Essential and Fundamental Part of the Doctrine of Chances : As It Is Delivered by Mr. James Bernoulli, in His Excellent Treatise on the Doctrine of Chances, Intitled, Ars Conjectandi, and by the Celeb

Excerpt from The Doctrine of Permutations and Combinations, Being an Essential and Fundamental Part of the Doctrine of Chances: As It Is Delivered by Mr. James Bernoulli, in His Excellent Treatise on the Doctrine of Chances, Intitled, Ars Conjectandi, and by the Celebrated Dr. John Wallis, of Oxford, in a Tract Intitled From the Subject

The next Traél: in this Colleé'tion relates to the Rational Numbers that will exprefs the Sides of Right-angled Tri angles, and contains two methods of finding as many fets of numbers as we pleafe that fhail have this propeny. The firft of thefe methods begins in page-417, and ends in page 431, and the fecond reaches from page 431 to page 448 after which I have inferred a Table of the Squares of the feveral natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 81c, as far as 100, together with two additional columns adjoining to the column of the faid fquares, in the former of which I have fet down the differences of the faid fquares, and in the latter the differences of thofe differences, or the fecond differences of the fquares'themfelves; which fecond differences are all equal to each Other, and to the number 2. This Table begins in page 449, and is aecom panied with fome remarks which extend 19 page 4. 57. This Trad has a confiderable refemblance to fome parts of the foregoing Difcourfe of Dr. Wallis, and may afford fome amufement to fuch readers as are fond of contemplating the properties of numbers.

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