# The Elements of Universal Mathematics, Or Algebra: To which is Added, A Specimen of a Commentary on Sir Isaac Newton's Universal Arithmetic. Containing, Demonstrations of His Method of Finding Divisors, and of His Rule for Extracting the Root of a Binomial. Also A New Rule for Determining the Form of an Assum'd Infinite Series

S. Paterson, 1752 - Algebra - 187 pages

### Popular passages

Page 36 - If four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. Thus...
Page 97 - I. When the given point, A, is in the circumference. HINT. — What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. \ Construction. Join A, and 0 the center of the given circle. On OA as a diameter, construct a circumference...
Page 97 - Propojition a Line may be divided into any Number of equal Parts, by taking the fame Number of equal Parts at pleafure on another Line.
Page 71 - The Value of the unknown Quantity is called the Root of the Equation, and it is evident that an Equation of two Dimenfions has two Roots. 214. And as a Negative Quantity may be de-* t1'd by a Letter, the Root is fometimes nega-» e ; there are therefore four different Cafes.
Page 142 - Quantity will not admit of a Divifor of two Dimenfions. The fame Method may be extended to the Invention of Divifors of more Dimenfions, by feeking in the aforefaid...
Page 133 - Ternary or three of them, each £)uatetrary, &c. and you will alfa hau: all the compounded Divifors. As, if all the Divifors of the Number 60 are required, divide it by 2, and the Quotient 30 by 2, and the Quotient 15 by 3, and there will remain the indivifible Quotient 5. Therefore the prime Divifors are i, 2, 2, 3, 5 ; thofe compofed of the Pairs 4, 6, 10, 15 ; of the Ternaries 12, 20, 30 ; and of all of them 60.
Page 141 - Difference between 27 and 17, that is, 10, divides 170; but the Difference between 12 and — 13, that is, 25, does not divide 190. Wherefore I reject the latter Progreffion. According to the former, If С is — 7, and If В is nothing ; the Terms of the Progreffion having no Difference.