Calendar: 1860-1861 Page 487

488 general literature and science III Euclfo "A circle may be described from any centre with any straight line as radius How does this postulate differ from Euclid's and which of his problems is assumed in it To bisect given rectilineal angle that is to divide it into two equal parts The three interior angles of every triangle are together equal to two right angles All the interior angles of any rectilineal figure together with four right angles are equal to twice as many righi angles as the figure has sides Find the angle of regular octagon To given straight line to apply parallelogram which shall be equal to given triangle and have one of its angles equal to given rectilineal angle If straight line be divided into two equal parts and also into two unequal parts the rectangle contained by the unequal parts together with the square on the line between the points of section is equal to the square on half the line Divide straight line into two parts so that the sum of their squares may be the least possible 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 In circle whose diameter is 20 inches will chord whose length is inches be greater or less than chord whose distance from the centre is inches Upon the same straight line and upon the same side of it there cannot be two similar segments of circles not coinciding with one another If straight line touch circle and from the point of contact straight line be drawn meeting 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