A Course of Mathematics: In Two Volumes. For the Use of the Royal Military Academy, Volume 1Gilberte and Rivington, 1841 - Mathematics |
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Page 170
... side of the equation ; those which follow it , the second member or the second side . The resolution of equations , is the finding the value of the ... sides , in order to get all the unknown terms on one 170 ALGEBRA . Simple equations.
... side of the equation ; those which follow it , the second member or the second side . The resolution of equations , is the finding the value of the ... sides , in order to get all the unknown terms on one 170 ALGEBRA . Simple equations.
Page 172
... side when it is the square root ; cube each side when it is the cube root ; and so on , which removes that radical from the equation . Thus , if √x 34 : then transposing 3 , gives x = 7 ; and squaring both sides gives x = 49 . Also ...
... side when it is the square root ; cube each side when it is the cube root ; and so on , which removes that radical from the equation . Thus , if √x 34 : then transposing 3 , gives x = 7 ; and squaring both sides gives x = 49 . Also ...
Page 185
... sides : then we a Add the square of half the co - efficient of x , viz . of have x2 + b a b2 b2 C b2-4ac x + = 4a2 4a2 a --- = 4a2 , and the first side is a complete square . Extract the roots , and resolve the resulting simple equation ...
... sides : then we a Add the square of half the co - efficient of x , viz . of have x2 + b a b2 b2 C b2-4ac x + = 4a2 4a2 a --- = 4a2 , and the first side is a complete square . Extract the roots , and resolve the resulting simple equation ...
Page 238
... sides of the equation being of different forms , and those of the first side given , we may proceed to equate those ... sides by 1 + x + x2 , and multiply the two factors of the numerator together . This gives - 1 - Ох - x2 + 2x3 · x1 ...
... sides of the equation being of different forms , and those of the first side given , we may proceed to equate those ... sides by 1 + x + x2 , and multiply the two factors of the numerator together . This gives - 1 - Ох - x2 + 2x3 · x1 ...
Page 243
... sides to the qth power : then we have 1 ± pv + B , v2 + ... = 1 + qv ( A , + B „ v + ... . . ) + B2 v2 ( An + B2 v + ... sides , ... · n 1+ y . } ; n ( 1 + y ) " = ( 1 + y ) { n + 2A , y + 3A , y2 + ... ( r + 1 ) A ‚ + 1 3 ′′ + ...
... sides to the qth power : then we have 1 ± pv + B , v2 + ... = 1 + qv ( A , + B „ v + ... . . ) + B2 v2 ( An + B2 v + ... sides , ... · n 1+ y . } ; n ( 1 + y ) " = ( 1 + y ) { n + 2A , y + 3A , y2 + ... ( r + 1 ) A ‚ + 1 3 ′′ + ...
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Common terms and phrases
ABCD algebraic altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients common cone cosec cube root decimal denominator denoted diagonal diameter difference dihedral angle distance divided divisor draw drawn equal equation equiangular EXAMPLES expression figure fraction frustum geometrical given line greater hence inscribed integer intersection join length less lineation logarithms mantissa measure meeting method multiplied parallel parallel ruler parallelogram perpendicular plane polygon prism PROBLEM proportional quantity quotient radii radius ratio rectangle Reduce right angles rule Scholium segment sides sine solid angle solution square root straight line subtraction tangent THEOREM third trapezium triangle ABC u₁ vulgar fraction Whence