Calendar: 1880-1881 Page 643

GENERAL LITERATURE AND SCIENCE 643 XIX -4&comttn Define rhombus and prove that its diagonals bisect one another at right angles If straight line falling on two other straight lines makes the alternate angles equal to one another the two straight lines shall be parallel to one another Half the base of triangle is greater than equal to or less than the line drawn from the vertical angle to bisect the base according as that angle is greater than equal to or less than right angle To describe parallelogam equal to given rectilineal figure and having an angle equal to given rectilineal angle To describe square that shall be equal to given rectilineal figure The opposite angles of any quadrilateral figure inscribed in circle are together equal to two right angles If two circles intersect and through the points of inter- section any two lines are drawn terminated at both ends by the circumferences of the circles the lines joining the ends are parallel If from any point without circle two straight lines be drawn one of which cuts the circle and the other touches it the rectangle contained by the whole line which cuts the circle and the part of it without the circle shall be equal to the square on the line which touches it The sides about the equal angles of triangles which are equiangular to one another are proportionals and those which are opposite to the equal angles are homologous sides 10 If perpendiculars be drawn from any point on the circumference of circle to two tangents and their chord of contact the square on the perpendicular to the chord is equal to the rectangle under the other two perpendiculars 11 If the tangent to the parabola at any point ρ intersect the directrix in the point then sz will be at right angles to sp hp