PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS. PROPOSITION XXIII. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. the given Let be the given straight line, and the given point in it, and rectilineal angle. It is required, at the given point in the given straight line that shall be equal to the given rectilineal angle to make an angle In, 7 take any points and join ; on make the triangle the sides of which shall be equal to the three straight lines be equal to to and to Then the angle equal to the angle Because to the base ; therefore the angle are equal to each to each, and the base is equal to the angle Wherefore, at the given point in the given straight line is equal , the angle is made equal to the given rectilineal angle PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS. PROPOSITION XXII. To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third. be the three given straight lines, of which any two whatever are greater It is required to make a triangle of which the sides shall be equal to to each. each ; then the triangle make ; from the centre at the dis where the circles cut each other, draw describe to the points shall have its sides equal to the three straight lines Because the point is the centre of the circle therefore is equal to ; but is equal to the straight line ; therefore is the centre of the circle ; therefore also |