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acted altitude angle angular apply attraction axes axis ball base body centre of force centre of gravity chord circle common Compare construction contained convex curvature curve cylinder density descends described determine diameter direction distance drawn Earth elastic ellipse equal equation equilibrium Explain extremity fall feet fixed fluid focal length focus force given point greatest horizontal plane incident inclined inclined plane inversely latitude least length lens light magnitude mean method motion moving nearly object observed orbit oscillation parabola parallel particle passing perpendicular placed position pressure principle projected proportional prove quantity radius ratio rays reflected refraction respectively rest revolve roots round shew sides sine space specific gravity sphere spherical square star straight line string Sun's supposed surface tangent tending triangle TRINITY COLLEGE uniform varies velocity vertex vertical vessel weight whole
Page 211 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 137 - If a body be acted on by a given force and revolve in a circle, the arc described .in any given time is a mean proportional between the diameter of the circle and the space through which a body would descend in the same time from rest if acted on by the same force.
Page 211 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Page 247 - Prove that the pressure upon any portion of a vessel filled with a fluid of uniform density is equal to the weight of a column of fluid whose base is the area of the surface pressed, and...
Page 139 - In the logarithmic spiral find an expression for the time of a body's descent from a given point to the centre, and prove that the times of successive revolutions are in geometrical progression. 7. A body acted on by a force varying as (dist...
Page 245 - Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and conversely, triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Page 231 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Page 231 - If a straight line touch a circle, and from the point of contact a...
Page 236 - Csesar and Pope Gregory. 18. Give the theory of the Trade Winds. 19. Prove that part of the equation of time which arises from the obliquity of the ecliptic to be a maximum when the longitude of the Sun equals the complement of its right ascension. 20. Compare the surface of a sphere with the area of its great circle, and its magnitude with that of its circumscribing cylinder. VOL. II.
Page 196 - when a body revolves on an axis, and a force is impressed, tending to make it revolve on another, it will revolve on neither, but on a line in the same plane with them, dividing the angle which they contain so that the sines of the parts are in the inverse ratio of the angular velocities with which the body would have revolved about the said axes separately.