A Course of Mathematics, Volume 1Longman, Rees, 1836 - Mathematics |
From inside the book
Results 1-5 of 100
Page 159
... side in the bottom : the sides or faces in either the triangular or square piles , are called arithmetical triangles ; and the numbers contained in these , are called triangular numbers : ABC , fig . 1 , EFG , fig . 2 , are arithmetical ...
... side in the bottom : the sides or faces in either the triangular or square piles , are called arithmetical triangles ; and the numbers contained in these , are called triangular numbers : ABC , fig . 1 , EFG , fig . 2 , are arithmetical ...
Page 180
... side when it is the square root ; cube each side when it is the cube root ; & c . which removes that radical from the equation . Thus , if x - 3 = 4 ; then transposing 3 , gives √x = 7 ; And squaring both sides gives x = 49 . And , if ...
... side when it is the square root ; cube each side when it is the cube root ; & c . which removes that radical from the equation . Thus , if x - 3 = 4 ; then transposing 3 , gives √x = 7 ; And squaring both sides gives x = 49 . And , if ...
Page 197
... side either + or — , which will give two roots of the equation , or two values of the unknown quantity . Note 1. The ... sides ; the first side will then be a complete square . Extract the root , and the value of the unknown quantity ...
... side either + or — , which will give two roots of the equation , or two values of the unknown quantity . Note 1. The ... sides ; the first side will then be a complete square . Extract the root , and the value of the unknown quantity ...
Page 213
... sides . 3. When the coefficient of the fourth term divided by that of the second term , gives for a quotient the square root of the last term : then , to complete the square , add the square of half the coefficient of the second term to ...
... sides . 3. When the coefficient of the fourth term divided by that of the second term , gives for a quotient the square root of the last term : then , to complete the square , add the square of half the coefficient of the second term to ...
Page 239
... sides ; then- 1 + x2 = a2 + ABX + Aсx2 + ADX3 + AEX1 + B2x2 + всx3 + BDX1 + + Aсx2 + Bсx3 + c2x2 + ABX + ADX3 + BDX4 + + AEX1 + ... and making equal the coefficients of the like powers of x , we have- 2ACB2 1 , or c = A2 = 1 , or a ...
... sides ; then- 1 + x2 = a2 + ABX + Aсx2 + ADX3 + AEX1 + B2x2 + всx3 + BDX1 + + Aсx2 + Bсx3 + c2x2 + ABX + ADX3 + BDX4 + + AEX1 + ... and making equal the coefficients of the like powers of x , we have- 2ACB2 1 , or c = A2 = 1 , or a ...
Common terms and phrases
AB² ABCD Algebra altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients contained Corol cube root decimal denominator denote diagonal diameter distance divide dividend division divisor draw drawn equal equation equiangular EXAMPLES expression feet figure fraction frustum geometrical geometrical progression given number gives greater half height Hence improper fraction inches infinite series integer intersect length less logarithms measure method multiply number of terms parallel parallelogram perpendicular plane polygon PROBLEM proportional Q. E. D. THEOREM quadratic equation QUEST quotient radius ratio rectangle Reduce remainder right angles right-angled triangle rule segment sides sine solid angle square root straight line subtract surd tangent third triangle ABC u₁ VULGAR FRACTIONS yards