Cambridge Problems: Being a Collection of the Printed Questions Proposed to the Candidates for the Degree of Bachelor of Arts at the General Examinations, from 1801 to 1820, InclusiveJ. Deighton and sons, 1821 - 425 páginas |
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Página 3
... density is that of itself ; compare the velocity of projection with that remaining in the sphere after describing a space equal to eight diame- ters ; the resistance to the motion arising only from the inertia of the medium . Third and ...
... density is that of itself ; compare the velocity of projection with that remaining in the sphere after describing a space equal to eight diame- ters ; the resistance to the motion arising only from the inertia of the medium . Third and ...
Página 7
... density of the rays at different points . 8. Given the Sun's alt . at 6 o'clock , and the alt . when due east ; find the lat . of the place . 9. Given the mean horary motion of a planet in its orbit ; shew the method of finding the ...
... density of the rays at different points . 8. Given the Sun's alt . at 6 o'clock , and the alt . when due east ; find the lat . of the place . 9. Given the mean horary motion of a planet in its orbit ; shew the method of finding the ...
Página 10
... densities of the earth and sun . 6. aż = yu + 4y , where x is the arc of a cer- tain curve , and y the ordinate ; determine the rela- tion between the ordinate and abscissa . 7. Prove that the solid generated by the revolu- tion of an ...
... densities of the earth and sun . 6. aż = yu + 4y , where x is the arc of a cer- tain curve , and y the ordinate ; determine the rela- tion between the ordinate and abscissa . 7. Prove that the solid generated by the revolu- tion of an ...
Página 17
... density varying inversely as the distance , and the centripetal force as the square of the density , to be deprived of its angular motion at a given distance from the centre ; compare the time of its descent to the centre in a straight ...
... density varying inversely as the distance , and the centripetal force as the square of the density , to be deprived of its angular motion at a given distance from the centre ; compare the time of its descent to the centre in a straight ...
Página 29
... density increases as the depth , with its base contiguous to the surface of the fluid ; find upon which of the ordinates to the axis there is the greatest pressure . 3. Solve the equation x3- px2 + qx ― r = 0 , whose roots are in ...
... density increases as the depth , with its base contiguous to the surface of the fluid ; find upon which of the ordinates to the axis there is the greatest pressure . 3. Solve the equation x3- px2 + qx ― r = 0 , whose roots are in ...
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Cambridge Problems: Being a Collection of the Printed Questions Proposed to ... Vista completa - 1821 |
Términos y frases comunes
abscissa altitude angular velocity axis base body fall body is projected body revolve center of force center of gravity chord circumference Compare conic section convex convex lens curve cycloid cylinder density descend described diameter distance earth ellipse equal equation FIFTH AND SIXTH Find the fluents Find the fluxion Find the sum Find the value fluid fluxion focal length focus force varying inversely FOURTH CLASSES geometric geometrical progression given point greatest horizontal plane inclined plane latus rectum lens logarithmic spiral Monday moon's motion orbit ordinate orifice oscillation parabola paraboloid parallel pendulum perpendicular Problems.-Mr Prove quantity radius ratio rays reflector refraction Required proof required to determine required to find right ascension shew sides SIXTH CLASSES space specific gravity sphere spherical spherical reflector straight line Sum the following Sum the series supposed surface tangent triangle velocity acquired vertex vertical vessel
Pasajes populares
Página 112 - The rectangle contained by the diagonals of a quadrilateral ,figure inscribed in a circle, is equal to both the rectangles contained by i'ts opposite sides.
Página 318 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Página 69 - ... move in its intersection with the other. 19. Let the position of the "axis of a spherical surface of known refracting power, perpendicular to, and bisecting, a very distant object, be given, and in it the position of the eye and image, and also the apparent magnitudes of the object and image; to determine the magnitude and position of the refracting surface. 20. A body is projected in a given direction, at a known distance from an horizontal plane, with a given velocity, acted on by a force perpendicular...
Página 304 - Shew that the sum of the products of each body into the square of its velocity is a minimum, when the velocities are reciprocally proportional to the quantities of matter in the bodies.
Página 280 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Página 89 - If a body revolves in an ellipse it is required to find the law of the centripetal force tending to the focus of the ellipse . . . . . . And therefore the centripetal force is inversely as the square of the distance.
Página 191 - Find the inclination of the bar to the horizon, upon supposition that the semi-circle is devoid of weight. 2. Prove, from a property of the circle, that if four quantities are proportionals, the sum of the greatest and least is greater than the sum of the other two. 3. Given the area of any plane surface, it is required to find the content of a solid, formed ' by drawing lines from a given point without the plane, to every part of its surface.
Página 328 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.
Página 421 - A sets off from London to York, and B at the same time from York to London : they travel uniformly; A reaches York 16 hours, and B London 36 hours, after they have met on the road ; find in what time each has performed the journey.
Página 364 - ... in the ratio of the sine of incidence to the sine of refraction (Art. 881.) when the light passes from water into air.