A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα 165
... conjugate diameters . T R L F K M If CD is conjugate to CP , conversely CP is conjugate to CD . A tangent at P is parallel to CD . The axes are the only conjugate diameters that are perpen- dicular to each other . The equation to an ...
... conjugate diameters . T R L F K M If CD is conjugate to CP , conversely CP is conjugate to CD . A tangent at P is parallel to CD . The axes are the only conjugate diameters that are perpen- dicular to each other . The equation to an ...
Σελίδα 166
... conjugate diameters , 19 2 a12 + b12 = a2 + b2 . The area of all circumscribing parallelograms is constant , = 4CD . PF - 4AC . BC . If a1 = b1 , then a1 = { ( a2 + b2 ) | * ; and 2ab sin a , b1 = a2 + b2 · b tan a1 , a = . a ( See Fig ...
... conjugate diameters , 19 2 a12 + b12 = a2 + b2 . The area of all circumscribing parallelograms is constant , = 4CD . PF - 4AC . BC . If a1 = b1 , then a1 = { ( a2 + b2 ) | * ; and 2ab sin a , b1 = a2 + b2 · b tan a1 , a = . a ( See Fig ...
Σελίδα 167
... conjugate to each other . tan APa = 2ab2 Y1 ( a2 — b2 ) ( H. C. S. 127-64 ; Hust . Prop . 13-8 ; Biot , 161-90 . ) CD2 Radius of curvature = ; PF Chord of curvature through C = 2 CD2 CP 2CD2 Chord through the focus : = ( Hust . Prop ...
... conjugate to each other . tan APa = 2ab2 Y1 ( a2 — b2 ) ( H. C. S. 127-64 ; Hust . Prop . 13-8 ; Biot , 161-90 . ) CD2 Radius of curvature = ; PF Chord of curvature through C = 2 CD2 CP 2CD2 Chord through the focus : = ( Hust . Prop ...
Σελίδα 169
... conjugate diameters . The locus of the points of bisection of all parallel chords is a diameter . The co - ordinates of the points of intersection of any diameter y = ax with the curve are x = ± - ab ( b2 — a3 a2 ) + ' aba y = ± - ( b2 ...
... conjugate diameters . The locus of the points of bisection of all parallel chords is a diameter . The co - ordinates of the points of intersection of any diameter y = ax with the curve are x = ± - ab ( b2 — a3 a2 ) + ' aba y = ± - ( b2 ...
Σελίδα 170
... conjugate to b1 , b1 is conjugate to a 1 The equation to the diameter passing through ( x1 , y1 ) is y = Y1 -- . X1 the equation to the conjugate diameter is b2 X1 a . y = a2 Yı The equation to an hyperbola referred to the centre , and ...
... conjugate to b1 , b1 is conjugate to a 1 The equation to the diameter passing through ( x1 , y1 ) is y = Y1 -- . X1 the equation to the conjugate diameter is b2 X1 a . y = a2 Yı The equation to an hyperbola referred to the centre , and ...
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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...