## 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, and Published at the End of His Treatise on Algebra: in the Former of which Tracts is Contained, a Demonstration of Sir Isaac Newton's Famous Binomial Theorem, in the Cases of Integral Powers, and of the Reciprocals of Integral Powers. Together with Some Other Useful Mathematical Tracts. Published by Francis Maseres, Esq |

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added adeoque æquationis æquationum alſo approximation autem becauſe beginning called caſe co-efficients combinations conſequently contained continued Cube cube-root denoted divided Diviſors equal equation erit eſt example exponent expreſſion fifth figurate numbers firſt firſt term five foregoing former four fourth fractions funt greater igitur inſtead inter laſt leſs letters manner means method Multiplied muſt natural numbers obtained omnes permutations powers Prime prodit propoſed quæ quam quantity quod quot quotient radices radicum radix rational reſpectively root ſaid ſame ſecond ſeries ſet ſeveral ſhall ſides ſome Square ſuch ſum ſunt taken termini terminorum theſe things third thoſe tion true value unitate valores vertical column whole number

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Page 36 - ... to form on all the subjects we reflect upon, whether they relate to the knowledge of Nature, or the merits and motives of human actions. It must therefore be acknowledged that that art which affords a cure to this weakness or defect of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, and that we may be certain that we have not omitted any one arrangement of them that can lead to the object of our enquiry,...

Page 421 - Geometry ; where it is proved, that the fquare of the hypothenufe, or longeft fide of a right-angled triangle, is equal to the fum of the fquares of the bafe and perpendicular, or the other two fides.

Page 117 - ... dû l'égarer. Les quantités négatives de la seconde espèce montrent tout à la fois, et la richesse de cette science qui fait trouver dans la solution du problème jusqu'aux choses qu'on ne demandait pas, et en même temps, si on ose le dire, l'imperfection du calcul, qui , en donnant ce qu'on ne cherche pas et qu'on ne lui demande point, ne donne pas toujours ce qu'on lui demande avec toute la perfection qu'on pourrait exiger. C'est ce qui n'arrive que trop dans les questions algébriques;...

Page 35 - Nature and in the actions of man, and which constitutes the greatest part of the beauty of the Universe, is owing to the multitude of different ways in which its several parts are mixed with, or placed near, each other.

Page 273 - By John Wallis, DD, Professor of Geometry in the University of Oxford, and a member of the Koyal Society, London.

Page 568 - ... to be performed : and, as to the negative roots of an equation, they are in truth the real and pofitive roots of another equation confiding of the fame terms as the firft equation, but with different figns + and — prefixed to fome of them ; fo that, when writers of Algebra...

Page 35 - ... part of the beauty of the Universe, is owing to the multitude of different ways in which its several parts are mixed with, or placed near, each other. But because the number of causes that concur in producing a given event, or effect, is oftentimes so immensely great, and the causes themselves are so different one from another, that it is extremely difficult to reckon up all the different ways in which they may be arranged or combined together, it often happens that men, even of the best understandings...

Page 567 - Unherfalis, with great attention, and to endeavour to make themfelves mafters of it, by going carefully through all the examples given in it, and performing all the arithmetical operations contained in them. And I will venture to fay that they will thereby acquire more ufeful knowledge in Algebra, towards the...

Page 593 - Icfs than the leaft root of the original equation, if it really has (as it appears to have,) more than one real and affirmative root ; or it will be lefs than the only root of the original equation, if (notwithftanding the appearances to the contrary,) it really has but one root. When the root of this fécond, or curtailed, equation, has been difcovered, it may be called...