Posts tagged 'duplicate-ratio'
G.230 duplicate ratio
When three magnitudes are:term:proportional <G.180>, the first is said to have to the third the:term:**duplicate ratio** <duplicate-ratio> of that which it has to the second.
G.231 similar triangles duplicate
Similar triangles are to one another in the duplicate ratio of the corresponding sides.
G.232 similar polygons divided
Similar polygons are divided into similar triangles, and into triangles equal in multitude and in the same ratio as the wholes, and the polygon has to the polygon a ratio duplicate of that which the corresponding side has to the corresponding side.
G.381 squares segments commensurable
The squares on segments commensurable in length have to one another the ratio which a square number has to a square number; and squares which have to one another the ratio which a square number has to a square number will also have their sides commensurable in length. But the squares on segments incommensurable in length have not to one another the ratio which a square number has to a square number; and squares which have not to one another the ratio which a square number has to a square number will not have their sides commensurable in length either.