Calendar: 1886-1887 Page 734

736 CLOTHWORKERS' SCIENCE EXHIBITIONS In any right-angled triangle the square which is de- scribed on the side subtending the right angle is equal to the squares described on the sides which contain the right angle In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpen- dicular let fall on it from the opposite angle and the acute angle The sum of the squares on the sides of triangle is equal to twice the square on half the base together with twice the square on the straight line which joins the vertex to the middle point of the base The diameter is the greatest straight line in circle and of all others that which is nearer to the centre is always greater than one more remote and the greater is nearer to the centre than the less Through given point within circle draw the shortest chord The straight line drawn at right angles to the diameter of circle from the extremity of it falls without the circle and no straight line can be drawn from the extremity between that straight line and the circumference so as not to cut the circle If from any point without circle there be drawn two straight lines one of which cuts the circle and the other meets it and if the rectangle contained by the whole line which cuts the circle and the part of it without the circle be equal to the square on the line which meets the circle the line which meets the circle shall touch it To describe circle which shall pass through two given points on the same sides of given straight line and touch that straight line To inscribe an equilateral and equiangular pentagon in given circle If the vertical angle of triangle be bisected by straight line which also cuts the base the segments of the