A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 σελίδες |
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Αποτελέσματα 1 - 5 από τα 32.
Σελίδα 8
... give a geometrical definition of a curve and deduce from that definition an appropriate equation ; this will likewise appear as we proceed ; we shall take successively different curves , define them , deduce their equations , and then ...
... give a geometrical definition of a curve and deduce from that definition an appropriate equation ; this will likewise appear as we proceed ; we shall take successively different curves , define them , deduce their equations , and then ...
Σελίδα 10
... give an expression for the area of a triangle in terms of the polar co - ordinates of its angular points . Also obtain the result directly from the figure . 7. A and B are two points and O is the origin ; express the area of the ...
... give an expression for the area of a triangle in terms of the polar co - ordinates of its angular points . Also obtain the result directly from the figure . 7. A and B are two points and O is the origin ; express the area of the ...
Σελίδα 12
... applicable . We shall now give separate investigations of these two cases . axes . To investigate the equation to a line parallel to one of the X B ID P # M X First suppose the line parallel to the axis of x 12 EQUATION TO A STRAIGHT LINE .
... applicable . We shall now give separate investigations of these two cases . axes . To investigate the equation to a line parallel to one of the X B ID P # M X First suppose the line parallel to the axis of x 12 EQUATION TO A STRAIGHT LINE .
Σελίδα 37
... give for DE a positive value . We may also obtain the value of DE thus ; draw the ordi- nate DM meeting the line AB in H ; then Now DE = DH sin DHE – DH cos HAM . = НАМ . OM = h ; .. HM = mh + c , and DM = k ; .. DH - k - mh - c . 1 ...
... give for DE a positive value . We may also obtain the value of DE thus ; draw the ordi- nate DM meeting the line AB in H ; then Now DE = DH sin DHE – DH cos HAM . = НАМ . OM = h ; .. HM = mh + c , and DM = k ; .. DH - k - mh - c . 1 ...
Σελίδα 40
... give another investigation of the expression for the perpendicular from a given point on the line ( p , a ) . Let AB represent the line ( p , a ) , O the origin , P the point ( x , y ) , so that P and O are on opposite sides of AB ...
... give another investigation of the expression for the perpendicular from a given point on the line ( p , a ) . Let AB represent the line ( p , a ) , O the origin , P the point ( x , y ) , so that P and O are on opposite sides of AB ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a²b² a²b³ a²y abscissa asymptotes ax² axes axis of x b²x² bisects centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant Crown 8vo cy² denote directrix distance Edition ellipse equa equal Examples external point find the equation find the locus fixed point focal chord focus given lines given point Hence the equation inclined latus rectum Let the equation line drawn line joining lines meet lines which pass major axis meet the curve middle point negative normal ordinate origin parabola parallel perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition radical axis radius ratio rectangular required equation respectively right angles shew shewn sides Similarly student suppose tangent tion triangle vertex x₁ y₁
Δημοφιλή αποσπάσματα
Σελίδα 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 304 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Σελίδα 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Σελίδα 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Σελίδα 189 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.