# Calendar: 1858-1859 Page 433

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APPLIED SCIENCES 435 II -βπΐίΐίο an& Crigononutrp Triangles on the same base and between the same parallels are equal Describe triangle equal to given quadrilateral figure its base being in the same straight line as the base of the figure and its vertex at one of the angles On given straight line describe rectangle equal to given square and prove that its perimeter is greater than that of the square If straight line is divided into any two parts the squares on the whole and one of the parts are equal to twice the rect- angle contained by the whole and that part together with the square on the other part If straight line be drawn from the vertex of triangle bisecting the base the squares of the two sides of the triangle are together double the squares of the bisecting line and of half the base From given point without circle draw two tangents to the circle and show that they are equal in length Find the relation subsisting between the sides of quadrilateral figure described about circle If two adjacent angles of regular polygon are bisected the lines drawn from the point of intersection of the bisecting lines to any angle of the figure will bisect that angle Divide straight line into parts in the ratio Similar triangles have to one another the duplicate ratio of their homologous sides From given triangle cut off its fifth part by line parallel to one side Describe an isosceles triangle equal to given triangle and having its vertical angle equal to given angle 10 Draw straight line perpendicular to given plane from given point above it 11 Three edges of triangular pyramid are at right angles to one another show that the square of the face opposite to the angle they form is equal to the squares of the faces containing it 12 are three points in the same straight line whose distances from one another are known show how to find the distance of each from point at which Β and BC subtend given angles Ε Ε

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