An Elementary Treatise on Graphs

Capa
Macmillan and Company, limited, 1904 - 183 páginas
 

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Página 146 - PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant.
Página 147 - In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.
Página 48 - A can do a piece of work in 3 days, and B can do it in 5 days.
Página 149 - conic' is the locus of a point P which moves so that its distance from a fixed point S, called the 'focus,' is in a constant ratio to its distance from a fixed line called the 'directrix.
Página 135 - ... according as this limit does or does not exist. The geometry of curves is merely one of many departments of mathematics in which the idea of a derivative finds an application. Another important application is in dynamics. Suppose that a particle is moving in a straight line in such a way that at time t its distance from a fixed point on the line is <p(t). Then the 'velocity of the particle at time t' is by definition the limit of ) -#(0 h Examples XXXIX.
Página 101 - Art. 12O3. in which/ is the pressure in pounds per square inch, and V the volume in cubic feet of a pound of steam at the given pressure. •WORK DONE IN THE CYLINDER OF A STEAM ENGINE. Let P = the pressure on the piston in pounds per sq. ft. ; p = pressure on piston in pounds per sq. in. ; V = volume swept through by the- piston; W '=• work in foot-pounds.
Página 55 - ... 6 am, 9 am, 12 Noon, 3 pm, 6 pm, 9 pm...
Página 115 - An open tank is to be constructed with a square base and vertical sides so as to contain a given quantity of water. Show that the expense of lining it with lead will be least if the depth is made half of the width.
Página 156 - Prove that the area of the parallelogram formed by the tangents at the extremities of two conjugate diameters of an ellipse is constant, and is equal to 4 06.
Página 49 - Noon 1 PM 2 PM 3 PM 4 PM 5 PM 6 PM 7 PM 8 PM 9 PM 10 PM...

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