A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 17
... possible ( 26. ) values of a1 Τι a2 13 a3 ( 1.2.3 ... ) ( 1.2.3 ... r ) ( 1.2.3 ... ) ... subject to the condition that ..... r1 + r2 + r 3 + ... + rm = n ; arm m ( 1.2.3 ... ) the values of 1 , T , & c . being either 0 , or a positive ...
... possible ( 26. ) values of a1 Τι a2 13 a3 ( 1.2.3 ... ) ( 1.2.3 ... r ) ( 1.2.3 ... ) ... subject to the condition that ..... r1 + r2 + r 3 + ... + rm = n ; arm m ( 1.2.3 ... ) the values of 1 , T , & c . being either 0 , or a positive ...
Σελίδα 23
... of logarithms , of which the above is the only possible one . n > n Sm log = log P , δ loga x x , m Pmx , -1 Sm ( - ( − 1 ) m −1 . m . ( x - 1 ) m m - 1 ( a− 1 ) m S „ ( − 1 ) TM – m m 1 ( x - 1 ) 2 log , x LOGARITHMS . 23.
... of logarithms , of which the above is the only possible one . n > n Sm log = log P , δ loga x x , m Pmx , -1 Sm ( - ( − 1 ) m −1 . m . ( x - 1 ) m m - 1 ( a− 1 ) m S „ ( − 1 ) TM – m m 1 ( x - 1 ) 2 log , x LOGARITHMS . 23.
Σελίδα 37
... possible root , which has the same sign as - α . If n is even , and a negative , the equation has two possible roots , one positive , the other negative . a : m - 1 , n ε m - 1 - a If a is positive , there is an even , GENERAL ...
... possible root , which has the same sign as - α . If n is even , and a negative , the equation has two possible roots , one positive , the other negative . a : m - 1 , n ε m - 1 - a If a is positive , there is an even , GENERAL ...
Σελίδα 38
... possible roots . If a + Vẞ is a root of an equation of which the coefficients are rational , ẞ not being a complete square , then a - VB is also a root . ( W. 280-97 ; Bour . 275-80 ; L. 178-94 . ) TRANSFORMATION OF EQUATIONS . ( 33 ...
... possible roots . If a + Vẞ is a root of an equation of which the coefficients are rational , ẞ not being a complete square , then a - VB is also a root . ( W. 280-97 ; Bour . 275-80 ; L. 178-94 . ) TRANSFORMATION OF EQUATIONS . ( 33 ...
Σελίδα 45
... possible transpositions of the products of the roots taken m at a time , the several roots in each transposition being raised to the rth , r , & c , r powers respectively . th m th Sr + r2 + T ( a , " 1 . α ̧ ” 1 ) ; ST .. ST2 = r1tr2 2 ...
... possible transpositions of the products of the roots taken m at a time , the several roots in each transposition being raised to the rth , r , & c , r powers respectively . th m th Sr + r2 + T ( a , " 1 . α ̧ ” 1 ) ; ST .. ST2 = r1tr2 2 ...
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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...