## The British encyclopedia, or, Dictionary of arts and sciences, Volume 3C. Whittingham, 1809 |

### From inside the book

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**equation**ay m + n_ n . ( ax ) " . bx m Of these there are several sorts : thus , if a y3bx2 ( ax ) it is a cubical ellip- toid ; and if a y1 = bx2 ( a — x ) , it de . ellipsis of the third order in respect of the notes a biquadratic ... Page

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**equation**3 a = b , in algebraical charac- ters . See ALGEBRA .**EQUATIONS**, construction of , in algebra , is the finding the roots or unknown quanti- tities of an**equation**, by geometrical con- 1 struction of right lines or curves , or ... Page

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**equation**. The roots of any**equation**may be determined , that is , the**equation**may be constructed , by the intersections of a straight line with another line or curve of the same dimensions as the**equation**to be constructed : for the ... Page

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**equation**one dimension lower , whose roots are b and c . Ex . One root of x ' + 1 = 0 , or x + 1 = and the**equation**may be depressed to a quadratic in the following manner : x + 1 ) x3 + 1 ( x2 − x + 1 x2 + x2**EQUATIONS**, nature of ... Page

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**equation**becomes a3 + b ' + r = 0 , also , since 3 a b - q = 0 , b = q3 and by substitution , a3 + + r = 0 , 27 a3 q Sa ' or a3 + ra ' + 22 = 0 , an**equation**of a quadratic form ; and by completing the p.2 q3 and a3 + square , a + ra3 + ...### Common terms and phrases

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