A Corollary added by Campane.
H•••••••• it is manifest, th••t two squar•• numbers multiplyed the one into the, other do alwayes produce a squa•••• num••••r.* 1.1 For they are like superficiall numbers, and therefore the num∣ber produced of them, is (by the first of this booke) a square number. But a square num∣ber mul••••plye•• into a number not square, produceth a number not square. For if they should pro∣duce a square number, they should be like superficiall numbers (by this Proposition). But they are not. Wherefore they produce a number not square. But if a square num∣ber multiplyed into an other number produce a square number, that other number shall be a square number. For by this Proposition that other number is like vnto the square number which multiplyeth it, and therefore is a square number. But if a square number multiply∣ed into an other number produce a number not square, neither shall that other number also be a square number. For if it should be a square number, then being multiplyed into the square number it should produce a square number, by the first part of this Corollary.