Calendar: 1861-1862 Page 517

518 AKNEFORD SCHOLARSHIPS viii -eucito If two triangles have two sides of the one equal to two sides of the other each to each and have likewise the angles contained by those sides equal to each other they shall have their bases or third sides equal and the two triangles shall be equal and their other angles shall be equal each to each viz those to which the equal sides are opposite If two triangles have two sides of the one equal to two sides of the other each to each but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them of the other the base of that which has the greater angle shall be greater than the base of the other Parallelograms upon the same base and between the same parallels are equal to one another If straight line be divided into any two parts the square of the whole line is equal to the squares of the two parts toge- ther with twice the rectangle contained by the parts If straight line be divided into any two parts the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part toge- ther with 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 conversely if it cut it at right angles it shall bisect it In circle the angle in semicircle is right angle hut the angle in segment greater than semicircle is less than right angle and the angle in segment less than semicircle is greater than right angle If from any point without circle two straight lines be drawn one of which cuts 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 the line which touches it