Calendar: 1858-1859 Page 424

426 GENERAL LITERATURE AND SCIENCE of the whole line is equal to the squares of the two parts to- gether with twice the rectangle contained by the parts To divide given straight line into two parts so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part If straight line drawn through the centre of circle bisect straight line in it which does not pass through the centre it shall cut it at right angles and if it cuts it at right angles it shall bisect it 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 If straight line touches circle and from the point of contact straight line be drawn cutting the circle the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle 10 About given circle to describe triangle equiangular to given triangle 11 To describe an isosceles triangle having each of the angles at the base double of the third angle 12 The sides about the equal angles of equiangular triangles are proportionals and those which are opposite to the equal angles are homologous sides that is are the antecedents or con- sequents of the ratios 13 To divide given straight line similarly to given divided straight line that is into parts that shall have the same ratios to one another which the parts of the divided given straight line have 14 To describe rectilineal figure which shall be similar to one and equal to another given rectilineal figure 15 Find point in the side of triangle from which lines drawn parallel to the other two sides shall be equal 16 Describe parallelogram having its area and perimeter equal to those of given triangle 17 Draw tangent to given circle which shall make given angle with given straight line