### Popular passages

Page 13 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 20 - To make a triangle of which the sides shall be equal to three given straight lines, any two of which are together greater than the third.
Page 22 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Page 19 - I. When the given point, A, is in the circumference. HINT. What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. Construction. Join A and 0 the center of the given circle. On OA as a diameter, construct a circumference intersecting...
Page 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Page 14 - In a given circle, to place a straight line, equal to a given straight line, which is not greater than the diameter of the circle.
Page 45 - We have, incidentally, a proof that the pedal of a circle with respect to a point on its circumference is...
Page 5 - To draw a perpendicular to a given straight line, from a given point without that line.
Page 12 - At a point in a given straight line to make an angle equal to a given angle.
Page 17 - To trisect a given angle. Much time was devoted to this famous problem by the Greeks and the geometers of the Middle Ages ; it has now been shown that it is impossible with only the aid of a pair of compasses and a straight...