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 20.
Σελίδα 33
... suppose ; then = b - dvd - b1 b1 = 2a.e + b 2a , = > e , and < e , + 1 ; 2 a 2a , b2 - dvd - b b2 = 2α1 . e1 + b1 | 2α2 : > e , and < e , + 1 ; 201 2a b3 - dvd - b b = 2α2 . e2 + b2 | 2α2 = = > e , and < e , + 1 . 2 2a2 2a3 & c . & c ...
... suppose ; then = b - dvd - b1 b1 = 2a.e + b 2a , = > e , and < e , + 1 ; 2 a 2a , b2 - dvd - b b2 = 2α1 . e1 + b1 | 2α2 : > e , and < e , + 1 ; 201 2a b3 - dvd - b b = 2α2 . e2 + b2 | 2α2 = = > e , and < e , + 1 . 2 2a2 2a3 & c . & c ...
Σελίδα 51
... Suppose the difference between any two possible roots > 1 . [ 1 ] Lagrange's Method . Find a number b , such that one of the roots is > b1 , but < b1 + 1 , and for a substitute b1 + given equation . The resulting equation in a least one ...
... Suppose the difference between any two possible roots > 1 . [ 1 ] Lagrange's Method . Find a number b , such that one of the roots is > b1 , but < b1 + 1 , and for a substitute b1 + given equation . The resulting equation in a least one ...
Σελίδα 52
... Suppose the difference between two possible 1 Determine the inferior limit of the positive roots of the ī equation of differences , and let k be the least integer > √1 : transform the given equation into one whose roots are k times as ...
... Suppose the difference between two possible 1 Determine the inferior limit of the positive roots of the ī equation of differences , and let k be the least integer > √1 : transform the given equation into one whose roots are k times as ...
Σελίδα 64
... Suppose 4 , negative , then the number of possible solutions cannot exceed the number of values of un < B1 Ꭺ ( W. 367-9 ; E. Pt . 11. 1-23 ; Bour . 122-9 . ) Second Method . [ 1 ] Let the equation be ax - by = ± 1 . α Convert the ...
... Suppose 4 , negative , then the number of possible solutions cannot exceed the number of values of un < B1 Ꭺ ( W. 367-9 ; E. Pt . 11. 1-23 ; Bour . 122-9 . ) Second Method . [ 1 ] Let the equation be ax - by = ± 1 . α Convert the ...
Σελίδα 67
... suppose therefore that they are all three positive ; in which case the number is finite . To determine the number of solutions : let k ; f1 , f2 , & c . fk be respectively the integral parts of e e - c B b m -- e - c a Am e 2c Bm e- -2c ...
... suppose therefore that they are all three positive ; in which case the number is finite . To determine the number of solutions : let k ; f1 , f2 , & c . fk be respectively the integral parts of e e - c B b m -- e - c a Am e 2c Bm e- -2c ...
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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...