Calendar: 1871-1872 Page 578

578 the school Through given point planes are drawn and from another given point perpendiculars are let fall upon them find the locus of the feet of these perpendiculars 13 The perpendicular let fall from the vertex of regular tetrahedron upon the opposite base is three times that from its own foot upon any of the other bases algebra Show that Ο ζ χ yr -χ y4 zY χ yz or that y2 z" yz xz xy Explain clearly the principle upon which factors are omitted in finding the of two algebraical expressions Find the of x3 aA β2 χ a'A and x2 cb c2 χ c2A Find the limits between which ---lie's for real 2i 2x values of Find the conditions that the two expressions x3 -j- βί -f bx and x3 x1 A'x -j- c' may have common quadratic factor Solve the equations bx a2 J- ax A2 ο י fit ax Ay If xiy ζ zQt log logy log ζ then ylz" x"y" Find the condition that ax2 Ay2 2a'y 2A2 ry may be the product of two linear factors in χ and If the roots