Calendar: 1884-1885 Page 688

682 WARNEFORD SCHOLARSHIPS What is postulate Mention an additional postulate that would render any of Euclid's propositions unnecessary If two obtuse-angled triangles ABC DEF have the two sides AB BC of the one equal to the two sides BE EF of the other each to each and likewise the angle not included CB equal to the angle DFE prove that the triangles are equal in all respects What are alternate angles Prove that they are equal What is problem Mention problem that the following theorem enables you to solve The straight line that bisects parallelogram also bisects its diagonal Prove the theorem and also solve the problem you mention What is gnomon Prove that he difference between the two gnomons in the figure of Euclid II is the rectangle under the sum and difference of the two parts into which any side of the square is divided What is chord of circle Equal chords are drawn in unequal circles prove that chords through their ex- tremities at right angles to them are equidistant from the centres What is an arc of circle Assuming that the arc is always greater than the chord and less than the sum of the two tangents at its extremities show how to find limits between which the ratio of the circumference of circle to its diameter must lie 10 What is sector of circle If the chord of the sector is equal to the radius prove that the sector contains one-sixth of the area of the circle XL-iliflonUScitueu'S rautirtir tt ecatlence fcci JftomawS Translate into English Le nombre du petit peuple presque tout composo d'af- franchis ou de fils d'affranchis devenant incommode on en fit des colonies par le moyen desquelles on s'assura de la