A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα 157
... axes in the original system .are rectangular , and in the new system , oblique , the above formulæ become x = x1 COS x1 , x + y1 cos y 19x , 1 y = x1 sin x1 , x + y1 sin y1 , x . If the original axes are oblique , and the new ones rect ...
... axes in the original system .are rectangular , and in the new system , oblique , the above formulæ become x = x1 COS x1 , x + y1 cos y 19x , 1 y = x1 sin x1 , x + y1 sin y1 , x . If the original axes are oblique , and the new ones rect ...
Σελίδα 158
... axis to which u is referred makes with the axis of x , then x = a + u y = b + u - sin { x , y — ( 0 + a ) } sin x , y sin ( 0+ a ) sin x , y If the axes are rectangular , these formulæ become x = a + u cos ( 0 + a ) , y = b + u sin ( 0 ...
... axis to which u is referred makes with the axis of x , then x = a + u y = b + u - sin { x , y — ( 0 + a ) } sin x , y sin ( 0+ a ) sin x , y If the axes are rectangular , these formulæ become x = a + u cos ( 0 + a ) , y = b + u sin ( 0 ...
Σελίδα 159
... axes are rectangular , - X1 --- - y - y1 = ( x − x1 ) , or Y1 xx1 + yy1 = r2 . To draw a tangent from a given point ( x , y ) without the circle : the co - ordinates 1 , y1 , of the point of contact may be determined by the solution of ...
... axes are rectangular , - X1 --- - y - y1 = ( x − x1 ) , or Y1 xx1 + yy1 = r2 . To draw a tangent from a given point ( x , y ) without the circle : the co - ordinates 1 , y1 , of the point of contact may be determined by the solution of ...
Σελίδα 160
... axis . Let S be the focus , P any point in the curve , and PQ perpendicular to EQ the directrix , then PSPQ . N T E A p S Let PT be a tangent at the point P , and PG the normal . If the origin is at the vertex , and the axis coincides ...
... axis . Let S be the focus , P any point in the curve , and PQ perpendicular to EQ the directrix , then PSPQ . N T E A p S Let PT be a tangent at the point P , and PG the normal . If the origin is at the vertex , and the axis coincides ...
Σελίδα 161
... axis AY in the same point . SP.SA - SY2 . Let Z be the intersection of the tangent with the directrix , SZ is perpendicular to SP . ( H. C. S. 63–71 ; Hust . Prop . 8. ) X ( 13. ) The parabola referred to any diameter . CONIC SECTIONS ...
... axis AY in the same point . SP.SA - SY2 . Let Z be the intersection of the tangent with the directrix , SZ is perpendicular to SP . ( H. C. S. 63–71 ; Hust . Prop . 8. ) X ( 13. ) The parabola referred to any diameter . CONIC SECTIONS ...
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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...