...the conditions of the question proposed, since in order to obtain the value of x, we must extract the root of a negative quantity, which is impossible....product of these parts may be the greatest possible. Let us represent the given number by p, the product of the two parts by q, and the difference of the two...

...the conditions of the question proposed, since in order to obtain the value of x, we must extract the root of a negative quantity, which is impossible....product of these parts may be the greatest possible. > EQUATIONS OF THE SECOND DEGREE. 153 greater part will then be - -f- - and the less , and we 22 22...

...conditions of the question proposed, since in order to obtain the vaiue of z, we imiot extmet the loot of a negative quantity, which is impossible. In order to see in \\iial this absurdity consists, let us exucuine into what two parts a given number should be divided,...

...the radical part is ^/ — q-\-p'1. Now when q is greater than p", this is essentially negative, and we are required to extract the square root of a negative quantity, which is impossible (Art. 193). Hence, when q is greater than p-, that is, when the known term is negative, and greater...

...forms, the radical part is I/ — 2+pa. Now, if q is greater than p', this is essentially negative, and we are required to extract the square root of a negative quantity, which is impossible. See Art. 195. Therefore, in the third and fourth forms, when q is greater than p2, that is, when the...

...the conditions of the question proposed, since in order to obtain the value of x, we must extract the root of a negative quantity, which is impossible....product of these parts may be the greatest possible. Let us represent the given number by p, the product of the two parts by q, and the difference of the two...

...the conditions of the question proposed, since in order to obtain the value of x, we must extract the root of a negative quantity, which is impossible....product of these parts may be the greatest possible. Let us represent the given number by p, the product of the two parts by q, and the difference of the two...

...the conditions of the question proposed, since in order to obtain the value of x, we must extract the root of a negative quantity, which is impossible....divided, in order that the product of these parts may We the greatest possible. Let us represent the given number by p, the product of the two parts by q,...

...fourth forms, the radical part, I/ — Jj-p2, will be further considered. If q is greater than p-, we are required to extract the square root of a negative quantity, which is impossible. See Art. 195. Therefore, In the third and fourth forms, when q is greater thanp2, that is, when the...

...the radical part is ^/ — q-\-p3. Now when q is greater than p1, this is essentially negative, and we are required to extract the square root of a negative quantity, which is impossible (Art. 193). Hence, when q is greater than p1, that is, when the known term is negative, and greater...