A Course of Mathematics: In Two Volumes. For the Use of the Royal Military Academy, Volume 1 |
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Page 170
The quantities which precede the mark of equality , are often called together the first member or the first side of the equation ; those which follow it , the second member or the second side . The resolution of equations , is the ...
The quantities which precede the mark of equality , are often called together the first member or the first side of the equation ; those which follow it , the second member or the second side . The resolution of equations , is the ...
Page 172
Thus , if n x – 3 = 4 : then transposing 3 , gives na = 7 ; and squaring both sides gives a = 49 . ... V. When that side or member of the equation which contains the unknown quantity is a complete power , or can easily be reduced to one ...
Thus , if n x – 3 = 4 : then transposing 3 , gives na = 7 ; and squaring both sides gives a = 49 . ... V. When that side or member of the equation which contains the unknown quantity is a complete power , or can easily be reduced to one ...
Page 185
They are alike in principle , which is that of so modifying the first side as to render it a complete square ; and by ... viz . of to both sides : then we have b 62 62 62 4ac 2 + X + 4ao 4a ? and the first side is a complete square .
They are alike in principle , which is that of so modifying the first side as to render it a complete square ; and by ... viz . of to both sides : then we have b 62 62 62 4ac 2 + X + 4ao 4a ? and the first side is a complete square .
Page 238
Assume the root to be in positive powers of x ; or v1 + 2 = A + Bx + Then squaring both sides , 1 + x2 = A ? + ABX + ... + + The coefficients of the two sides of the equation being of different forms , and those of the first side given ...
Assume the root to be in positive powers of x ; or v1 + 2 = A + Bx + Then squaring both sides , 1 + x2 = A ? + ABX + ... + + The coefficients of the two sides of the equation being of different forms , and those of the first side given ...
Page 243
Then , as before , assume that 9 ( 1 + o ) = l + A , 0 + B , v2 + Ch 03 + Raise both sides to the qth power : then we have 1 + pv + B , v2 + ... = l + qu ( A. + B , 0 + ... ) + B , v2 ( A , + B , 0 + .. ) + and equating the homologous ...
Then , as before , assume that 9 ( 1 + o ) = l + A , 0 + B , v2 + Ch 03 + Raise both sides to the qth power : then we have 1 + pv + B , v2 + ... = l + qu ( A. + B , 0 + ... ) + B , v2 ( A , + B , 0 + .. ) + and equating the homologous ...
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A Course of Mathematics: Composed for the Use of the Royal Military Academy Charles Hutton No preview available - 2015 |
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added algebraic angle answer applied arithmetical base called centre circle coefficients common compound contained continued cube decimal denominator denote describe diameter difference distance divided division divisor double draw drawn equal equation EXAMPLES expression extremes factors figure former four fraction functions give given greater half hence interest intersection join latter length less manner means measure meeting method Multiply obtained operation opposite parallel parallelogram perpendicular plane position principal PROBLEM proportional quantity question quotient radius ratio rectangle Reduce remainder respectively result right angles root rule sides signs simple solution square subtract successive supposing taken THEOREM third triangle Whence whole yards