# Calendar: 1875-1876 Page 582

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578 GENERAL LITERATURE AND SCIENCE drawn one of which cots the circle and the other touches it the rectangle contained by the whole line which cuts the circle and the part of it without the circle shall be equal to the square of tbe line which touches it 13 To describe circle in given triangle 14 To describe an isosceles triangle having each of the angles at the base double of the third angle 15 If the angle of triangle be divided into two equal angles by straight line which also cuts the base the segments of the base shall have the same ratio which the other sides of the triangle have to one another and if the segments of the base have the same ratio which the other sides of the triangle have to one another the straight line drawn from the vertex to the point of section divides the vertical angle into two equal angles 16 If four straight lines be proportionals the similar rectilineal figures similarly described upon them shall also be proportionals and if the similar rectilineal figures similarly described upon four straight lines be proportionals those straight lines shall be proportionals 17 If an angle of triangle be bisected by straight line which likewise cuts the base the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base together with the square of the straight line which bisects them 18 With any point in the circumference of given circle an equal circle is described find the area of the intercepted figure FIRST AND SECOND YEAR VII -aigtbra airtl ULrigononutrg Simplify ab x2 al 4'" φ -a -c x- by c-a c-bj x-c

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