Calendar: 1859-1860 Page 467

468 MEDICAL DEPARTMENT If two triangles have two sides of the one equal to two sides of the other each to each and have likewise their bases equal the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them of the other Parallelograms upon the same base and between the same parallels are equal to one another If the square described upon one of the sides of triangle be equal to the squares described upon the other two sides of it the angle contained by these two sides is right angle If straight line be bisected and produced to any point the rectangle contained by the whole line thus produced and the part of it produced together with the square of half the line bisected is equal to the square of the straight line which is made up of the half and the part produced 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 any point be taken in the diameter of circle which is not the centre of all the straight lines which can be drawn from it to the circumference the greatest is that in which the centre is and the other part of that diameter is the least and of any others that which is nearer to the line which passes through the centre is always greater than one more remote and from the same point there can be drawn only two straight lines that are equal to one another one upon each side of the shortest line 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 If from point without circle there be drawn two straight lines one of which cuts the circle and the other meets it if the rectangle contained by the whole line which cuts the circle and the part of it without the circle be equal to the square of the line which meets it the line which meets shall toucb the circle