...quantity is introduced into the calculus by affecting it with the sign V , and it is written thus, V^Sa64. Quantities of this kind are called radical quantities,...quantities, or simply radicals of the second degree. 84. These expressions may sometimes be simplified, upon the principle that the square root of the product...

...is introduced into the calculus by affecting it with the sign V , and it is written thus, V98ab°. Quantities of this kind are called radical quantities,...simplified, upon the principle that, the square root of tlie product of two or more factors is equal to the product of the square roots of these factors ;...

...quantity is introduced into the calculus by affecting it with the sign -\/ , and it is written thus : Quantities of this kind are called radical quantities,...quantities, or simply radicals of the second degree. They are also, sometimes called Surds. These expressions may often be simplified, upon the principle...

...simply radicals of the second degree. They are also, sometimes called Surds. These expressions may often be simplified, upon the principle that, the square root of the product of two or more factors w equal to the product of the square roots of these factors ; or, in algebraic language, Jyabcd . ....

...quantity is introduced into the calculus by affecting it with the sign -y/ , and it is written thus: Quantities of this kind are called radical quantities,...quantities, or simply radicals of the second degree. They are also, sometimes called Surds. These expressions may often be simplified, upon the principle...

...rule for the involution of monomials, let the following proposition be demonstrated, viz. : The power of the product of two or more factors is equal to the product of their powers. Let («6)2 represent the second power of the product of two factors, And a262 the product...

...introduced into the calculus by affecting it with the radical sign y' , and written thus, y'sQab*. Quantities of this kind are called radical quantities,...quantities, or simply radicals of the second degree, These expressions may sometimes be simplified. For, by the definition of the square root, we have X...

...rule for the involution of monomials, let the following proposition be demonstrated, viz.: The power of the product of two or more factors is equal to the product of their powers. Let (ab) 2 represent the second power of the product of two factors, And aV the product...

...together, NN'=a'a" =a"+" .-. by definition, r+x' is the logarithm of NN' ; that is to say, The logarithm of the product of two or more factors is equal to the sum of the logarithms of those factors. II. Divide equation (1) by (2). N_o« N'=o" =a'-". .•. by...

...+ x' is the index of that power of the base a which is equal to NN' j that is to say, The logarithm of the product of two or more factors is equal to the sum of the logarithms of tho2e factors. Hence \ve see that if it is required to multiply two or more...