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angles apply asymptotes axes axis beam becomes called cardioid centre chord circle coincide condition cone conic conicoids conjugate consequently consider constant containing coordinates corresponding cubic curve denote described determined developable surface diameter direction distance drawn ellipse ellipsoid equal equation expressed extremities figure fixed force function Geometry given gives Hence inclined infinity intersection joining limit line of curvature locus meet method multiplication negative normal obtained opposite origin parallel passes period perpendicular places plane polar pole position problem projection PROP properties radius reference represent respect right angles sides similar similarly sphere straight line suppose surface tangent tangent plane theorem third triangle vect vector vertical volume
Page 47 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 185 - ABCD, (fig. 49), the plane of which is vertical, rests with its side AD in contact with a rough vertical wall, which is perpendicular to the plane of the board ; the side AB resting...
Page 113 - Zbafy + 3cxif + dif into its canonical form, = (\x + p.yf + (\.'x + ii!y)*. 6. State, and prove analytically, the general theorem obtainable by projection from the theorem " the middle points of the three diagonals of a complete quadrilateral lie in a line." 7. Explain the meaning of the expressions, (1) polar of a point in relation to a conic ; (2) rth polar of a point in relation to a curve of the with order.
Page 160 - ... the length of the perpendicular from the centre on the tangent plane.
Page 72 - The perpendiculars from the vertices of a triangle on the opposite sides are concurrent.
Page 47 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Page 160 - ... the former is equal to the volume of the latter. Since the conditions furnished by the equations of the surface and by the equations of the tangent planes at the extremities of the conjugate diameters, as exhibited in last proposition...
Page 43 - A conic always touches four given straight lines ; prove that the chord of intersection of the circle, described about any one of the triangles formed by three of these straight lines, with the circle which is the locus of the intersection of two tangents to the conic at right angles to each other, always passes through a fixed point.
Page 244 - In discussing the stability of position of masonry towers, let the distance of the centre of pressure from the centre of figure of the section of the pier be denoted by q. If this latter does not exceed q (the limit of safety for q"), which may be ascertained by determining the line of resistance for the pier, stability of position will be secured. It is supposed, of course, that 0 has some value greater than zero ; otherwise q...