A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα v
... 48 41 . Commensurable roots 50 42 . Incommensurable roots 51 • 43 . Quadratic factors " 53 44 . Impossible roots ib . 45 . Application of the theory of equations to surds . 54 The equation y " + p = 0 General solution.
... 48 41 . Commensurable roots 50 42 . Incommensurable roots 51 • 43 . Quadratic factors " 53 44 . Impossible roots ib . 45 . Application of the theory of equations to surds . 54 The equation y " + p = 0 General solution.
Σελίδα vii
... impossible quantities Formulæ for the sums of arcs , and multiple arcs Powers of the sine and cosine of an arc Sums of trigonometrical series . . 129 130 ib . • 131 . 136 . 137 Resolution of trigonometrical quantities into factors . 140 ...
... impossible quantities Formulæ for the sums of arcs , and multiple arcs Powers of the sine and cosine of an arc Sums of trigonometrical series . . 129 130 ib . • 131 . 136 . 137 Resolution of trigonometrical quantities into factors . 140 ...
Σελίδα 2
... impossible quantities . 1 ( + a ) 3 = ± a3 . 2m ( -a ) TM m : * = ± a2 . ( −1 ) . ( E. 139—51 . ) 2m- α has the same sign as a , ( 6. ) Nature of squares , and square roots . ( E. 123-38 . ) Nature of cubes , and cube roots . ( E. 152 ...
... impossible quantities . 1 ( + a ) 3 = ± a3 . 2m ( -a ) TM m : * = ± a2 . ( −1 ) . ( E. 139—51 . ) 2m- α has the same sign as a , ( 6. ) Nature of squares , and square roots . ( E. 123-38 . ) Nature of cubes , and cube roots . ( E. 152 ...
Σελίδα 48
... impossible roots : if b is positive , the roots are all possible , when b2 and b are positive , and b1 , b , b , negative ; otherwise they are all impossible . 2 To obtain the equation of differences by elimination : for ≈ substitute x ...
... impossible roots : if b is positive , the roots are all possible , when b2 and b are positive , and b1 , b , b , negative ; otherwise they are all impossible . 2 To obtain the equation of differences by elimination : for ≈ substitute x ...
Σελίδα 53
... Impossible quantities of all degrees may be reduced to the form 4+ B - 1 , A and B being possible quantities . To find the impossible roots : substitute y +/- 1 for a in the given equation , and another equation will be obtained 4 + B ...
... Impossible quantities of all degrees may be reduced to the form 4+ B - 1 , A and B being possible quantities . To find the impossible roots : substitute y +/- 1 for a in the given equation , and another equation will be obtained 4 + B ...
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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...