Calendar: 1884-1885 Page 691

CL0THW0RKERS SCIENCE EXHIBITION 685 To describe parallelogram that shall be equal to given triangle and have one of its angles equal to given rectilineal angle 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 The angles in the same segment of circle are equal to one another If two triangles having their vertical angles equal stand on the same base and on the same side of it they have the same circumscribing circle If straight line touch 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 If from any point in the circumference of circle chord and tangent are drawn the perpendiculars dropped upon them from the middle point of the subtended arc are equal to one another To inscribe an equilateral and equiangular hexagon in given circle The sides about the equal angles of equiangular triangles are proportionals and thosh which are opposite to the equal angles are homologous sides that is are the antecedents or consequents of the ratios The rectangle contained by the sides of triangle is equal to the rectangle contained by the diameter of the circumscribing circle and the perpendicular from the vertex on the base 10 Similar triangles are to one another in the duplicate ratio of their homologous sides 11 If the tangent at any point Ρ of parabola intersect the axis produced in and the tangent at the vertex in Yy then SY will bisect Ρ Τ at right angles If circle be described about the triangle SPNy the tangent to it from is equal to PN