A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα 3
Charles Brooke. To extract the square root of a + √b : Assume then a + √b = √x + √y ; x = } { a + ( a2 − b ) } } , — y = { { a — ( a2 —b ) * } . - ~ and y are rational only when a2 - b is a complete square . surd . ( W. 258 ; Bour ...
Charles Brooke. To extract the square root of a + √b : Assume then a + √b = √x + √y ; x = } { a + ( a2 − b ) } } , — y = { { a — ( a2 —b ) * } . - ~ and y are rational only when a2 - b is a complete square . surd . ( W. 258 ; Bour ...
Σελίδα 31
... Assume a --- - - a ( a , b ) + ( a , b ) + & e . b a b 2 b1 + & c . .b1 = c , aq - .b2 = = C1 , & c . = & c . proceeding as before , the second quotient will be b + b1 + & c . 1 c + c1 + & c . ? b == b -- - · c2 ) + ( b - 2 + & c . + C1 ...
... Assume a --- - - a ( a , b ) + ( a , b ) + & e . b a b 2 b1 + & c . .b1 = c , aq - .b2 = = C1 , & c . = & c . proceeding as before , the second quotient will be b + b1 + & c . 1 c + c1 + & c . ? b == b -- - · c2 ) + ( b - 2 + & c . + C1 ...
Σελίδα 33
... assume xe + x1 ≈ being > e but < e + 1 , then a1x2 + b1x + a = 0 , = 1 in which equation a , ae2 + be + c , from ( 2 ) , X1 = b1 = 2ae + b ; 1 2a1 - ( − b1 + b2 — 4 a.a1 1 Xo " and so on . ( 2 ) b2-4acb - 4a.a , b - 4a , .a2 = & c ...
... assume xe + x1 ≈ being > e but < e + 1 , then a1x2 + b1x + a = 0 , = 1 in which equation a , ae2 + be + c , from ( 2 ) , X1 = b1 = 2ae + b ; 1 2a1 - ( − b1 + b2 — 4 a.a1 1 Xo " and so on . ( 2 ) b2-4acb - 4a.a , b - 4a , .a2 = & c ...
Σελίδα 38
... assume x = y + c , and by substituting this value of x in p ( x ) = 0 , we obtain roots are a1 - n ( n - 1 ) . + ( n - 1 ) a - 1C y " + nc yn - 1 + c2 yn - 2 + & c . 1 2 + aμ - 1 + + n = 0 ; α - cn - 1 -2 + ( n − 1 ) an− 1 c2 — 2 n- + ...
... assume x = y + c , and by substituting this value of x in p ( x ) = 0 , we obtain roots are a1 - n ( n - 1 ) . + ( n - 1 ) a - 1C y " + nc yn - 1 + c2 yn - 2 + & c . 1 2 + aμ - 1 + + n = 0 ; α - cn - 1 -2 + ( n − 1 ) an− 1 c2 — 2 n- + ...
Σελίδα 39
... assume x = - y 9 we obtain a1 yn + -1 yn - 1 + ... + an - 2 y2 + an - 1 y + 1 = = 0 . a a a a ( W. 280-97 ; Bour . 275-80 ; G. 310-25 . ) To take away the coefficient of yn - m + 1 , assume m S , n — m + r r - 1 ጥ -- .1 --- ɑn − m + r ...
... assume x = - y 9 we obtain a1 yn + -1 yn - 1 + ... + an - 2 y2 + an - 1 y + 1 = = 0 . a a a a ( W. 280-97 ; Bour . 275-80 ; G. 310-25 . ) To take away the coefficient of yn - m + 1 , assume m S , n — m + r r - 1 ጥ -- .1 --- ɑn − m + r ...
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Άλλες εκδόσεις - Προβολή όλων
A Synopsis of the Principal Formulae and Results of Pure Mathematics ... Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
A Synopsis of the Principal Formulae and Results of Pure Mathematics Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a-log a.sin a₁ a² a² angle arcs Assume ax² axis ay² B.cos B.sin b₁ Biot Bour c₁ centre circle co-ordinates conjugate diameters const continued fraction converging fraction cosec cosine curve cx² determined differential coefficients e₁ ellipse formula functions G. G. A. Ch given equation hyperbola integral intersection Let the equation log Cot log Sin log Sin Blog logarithmic m₁ method modulus negative obtained parabola perpendicular plane possible root prime number primitive equation quadratic divisor quadratic equation quotients R₁ radius reduced remainders sin x sine solution square straight line substituting subtangent Suppose surface tana tangent ternary divisor ternary form theorem triangle u₁ unknown quantities values vers x₁ y-y₁ y₁ απ
Δημοφιλή αποσπάσματα
Σελίδα 112 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Σελίδα 4 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Σελίδα 4 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 347 - Si, the formula assigned by Thomson to the mineral from Ireland, named " Anhydrous silicate of iron." Now, this slag had evidently been in a position favourable to the absorption of oxygen, namely, the...
Σελίδα 4 - To reduce a fraction to its lowest terms, divide both the numerator and denominator by their greatest common divisor.
Σελίδα 4 - The same quantity may be added to, or subtracted from, both sides of an equation. To...
Σελίδα 343 - The immutability, no less than the symmetry of its notation, (which should ever be guarded with a jealousy commensurate to its vital importance,) facilitates the translation of an expression into common language at any stage of an operation, - disburdens the memory of all the load of the previous steps, - and at the same time, affords it a considerable assistance in retaining the results.
Σελίδα 46 - These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given...
Σελίδα 161 - Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig.
Σελίδα 2 - Tiie square root of a quantity cannot be partly rational and partly a quadratic surd. If possible, let...