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acquired altitude angle apply axis base body circle circular circumference CLASSES common Compare Construct curve cycloid cylinder declination density descend described determine diameter difference direction distance drawn earth ellipse equal equation Explain expression extremity fall feet Find Find the fluents fluid fluxion focus force force varying formed FOURTH given gravity greatest half horizon incidence inclined interest latitude least length lens less logarithmic mean method Monday moon motion moving nature object orbit oscillation parabola parallel passing periodic perpendicular plane position principle produced proportional Prove quantity radius ratio rays refraction Required Required proof resistance rest revolve roots round shew sides sine solid space specific gravity sphere spherical spiral square star straight line string sun's supposed surface tangent THIRD triangle velocity vertex vertical vessel weight whole
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.