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 131
... Whence the quotient is 205 y 2 3 5 for the exterior term . 23 { 1 + 2 + ( ~ ) 2 + ( ~ ) 2 + ( ~ ) ' 5 or x + ( ~ ) 2 + x2 + x1y3 + xy2 + x2y3 + xy1 + y5 . 262 263 264 + a a2 a3 + .... = 1 + 2x + 3x2 + 4x3 + 5x4 + 2. Prove that 2ab a + b ...
... Whence the quotient is 205 y 2 3 5 for the exterior term . 23 { 1 + 2 + ( ~ ) 2 + ( ~ ) 2 + ( ~ ) ' 5 or x + ( ~ ) 2 + x2 + x1y3 + xy2 + x2y3 + xy1 + y5 . 262 263 264 + a a2 a3 + .... = 1 + 2x + 3x2 + 4x3 + 5x4 + 2. Prove that 2ab a + b ...
Page 134
... Whence as Qm , Qm_1 , and Q - 2 are integral , X - 2 is divisible by Xm + 1 . ...... m - 19 Whence Xm + 1 .... Xm . In the same way , we find that in succession all the preceding Xm - 3 , X m - 49 X4 , X3 , X2 , X1 , X , are divisible ...
... Whence as Qm , Qm_1 , and Q - 2 are integral , X - 2 is divisible by Xm + 1 . ...... m - 19 Whence Xm + 1 .... Xm . In the same way , we find that in succession all the preceding Xm - 3 , X m - 49 X4 , X3 , X2 , X1 , X , are divisible ...
Page 149
... - 8a4 16a6 ენ 16a5 - ... } , or } . 6a5 + 21a1 44a363a54a + 27 . - Here there are three columns , and the condition is fulfilled for the application of the rule . Whence ( III ) ( 11 ) 1 1 1 2-23 INVOLUTION AND EVOLUTION . 149.
... - 8a4 16a6 ენ 16a5 - ... } , or } . 6a5 + 21a1 44a363a54a + 27 . - Here there are three columns , and the condition is fulfilled for the application of the rule . Whence ( III ) ( 11 ) 1 1 1 2-23 INVOLUTION AND EVOLUTION . 149.
Page 157
... Whence the proposition is true . ( 2 ) . One quadratic surd cannot be the sum or difference either of a rational quantity and a quadratic surd , or two quadratic surds . For , first , assume √ = x ± √y ; then squaring , z = x2 + 2 x ...
... Whence the proposition is true . ( 2 ) . One quadratic surd cannot be the sum or difference either of a rational quantity and a quadratic surd , or two quadratic surds . For , first , assume √ = x ± √y ; then squaring , z = x2 + 2 x ...
Page 158
... Whence , √a ± √b = √a ± - 2 It is quite obvious that , except √a2 - b he a rational quantity , the formula , on the right side of the equation here obtained , is far less convenient than that on the left . If this criterion be ...
... Whence , √a ± √b = √a ± - 2 It is quite obvious that , except √a2 - b he a rational quantity , the formula , on the right side of the equation here obtained , is far less convenient than that on the left . If this criterion be ...
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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