A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα 3
... equal to nothing ; the last divisor will be the greatest common divisor required . If any divisor contains a factor not contained in both the given quantities , that factor may be rejected . ( Bour . 34—41 , 258-74 ; W.90 ; E. 451-60 ...
... equal to nothing ; the last divisor will be the greatest common divisor required . If any divisor contains a factor not contained in both the given quantities , that factor may be rejected . ( Bour . 34—41 , 258-74 ; W.90 ; E. 451-60 ...
Σελίδα 14
... equal ; the coefficient of every term is an integer ; n 1 + 1 1 n + + n ( n - 1 ) 1 2 • n ( n - 1 ) 1 • + & c . = 2n ; & c . = 0 , or 2 1 + n ( n - 1 ) ( n . -2 ) ( n − 3 ) + + & c . 1 2 1.2 . 3 4 • n n ( n − 1 ) ( n − 2 ) + 1 • 1 2 3 • ...
... equal ; the coefficient of every term is an integer ; n 1 + 1 1 n + + n ( n - 1 ) 1 2 • n ( n - 1 ) 1 • + & c . = 2n ; & c . = 0 , or 2 1 + n ( n - 1 ) ( n . -2 ) ( n − 3 ) + + & c . 1 2 1.2 . 3 4 • n n ( n − 1 ) ( n − 2 ) + 1 • 1 2 3 • ...
Σελίδα 40
... equals the number of separate systems of values that satisfy the given equations . If the last remainder is independent of the unknown quan- tities , the equations are incompatible . Further observations , and their application to ...
... equals the number of separate systems of values that satisfy the given equations . If the last remainder is independent of the unknown quan- tities , the equations are incompatible . Further observations , and their application to ...
Σελίδα 43
... equal roots . If ( x ) = 0 has m equal roots , ' ( x ) = 0 has m - 1 of them : hence these two equa- tions will have a common divisor ( x - a ) -1 , which may be found , and the original equation thus reduced to another of ( nm ) ...
... equal roots . If ( x ) = 0 has m equal roots , ' ( x ) = 0 has m - 1 of them : hence these two equa- tions will have a common divisor ( x - a ) -1 , which may be found , and the original equation thus reduced to another of ( nm ) ...
Σελίδα 50
... so on : those divisors which give always an integral quotient , will be found to be roots of the equation ; which may therefore be reduced as many degrees . If there are equal roots , this method will only 50 ALGEBRA .
... so on : those divisors which give always an integral quotient , will be found to be roots of the equation ; which may therefore be reduced as many degrees . If there are equal roots , this method will only 50 ALGEBRA .
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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...