Calendar: 1884-1885 Page 643

GENERAL LITERATURE AND SCIENCE 637 If an equal triangle be also described upon the other side of the given line what figure will the two triangles form Construct triangle of which the sides shall be equal to three given straight lines but any two whatever of these must be together greater than the third Is similar limitation in every case necessary with respect to the three angles The opposite sides and angles of parallelogram are qual to one another and the diameter divides it into two qual parts Prove this If either diameter of four-sided figure divide it into two equal triangles is the figure necessarily parallelogram Prove your answer Prove that if straight line be divided into any two arts the square on the whole line is equal to the squares on the two parts together with twice the rectangle contained by the parts In what sense is the area of triangle said to be equal to half the product of its base and its altitude Prove this from Euclid Describe square that shall be equal to given recti- lineal figure If the given rectilineal figure were right-angled triangle whose sides were represented by and what number would represent the side of square of the same area Define accurately the terms radius-arc-circumference chord-secant of circle How does sector differ in 'form from segment of circle Are they in any case coincident If the chord of an arc of circle whose diameter is 8£ inches be inches what is the length of the chord of double the arc of the same circle 10 Prove that the angle at the centre of circle is double the angle at the circumference upon the same base Hence prove that the angle in semicircle is right angle 11 If from point without circle there be drawn two straight lines one of which cuts the circle and the other ו meets it if the rectangle contained by the whole line which