RELFE BROTHERS EUCLID SHEETS. ' 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. Let be the given straight line, and the given point in it, and the given rectilineal angle. It is required, at the given point in the given straight line to make an angle that shall be equal to the given rectilineal angle i on In , take any points and join make the triangle the sides of which shall be equal to the three straight lines and Then the angle be equal to shall be , so that to to equal to the angle Because are equal to each to each, and the base is equal to the base ; therefore the angle is equal to the angle Wherefore, at the given point in the given straight line the angle is made equal to the given rectilineal angle RELFE BROTHERS' EUCLID SHEETS. 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. Let be the three given straight lines, of which any two whatever are greater than the third, namely, and greater than ; and and greater than ; and It is required to make a triangle of which the sides shall be equal to each ; then the triangle shall have its sides equal to the three straight lines ; therefore also ; and straight lines, is equal to is equal to ; therefore the three are respectively equal to the three, ; and therehas its three sides equal to the three given fore the triangle straight lines |