produce the number EF: agayne let the number CB multipli∣ing
the selfe same number
AB produce the number FG. Now forasmuch as the number
AC multiplying the number
AB produced the number EF: therefore the number AB measu∣reth the number EF by the vnities which are in
AC. Againe for∣asmuch as the number
CB multiplied the number
AB and pro¦duced the number FG: therfore the number
AB measureth the number FG by the vnities which are in the number
CB. But the same number
AB before measured the number EF by the vni∣ties which are in the number
AC. Wherefore the number
AB measureth the whole number
••G by the vnities whcih are in
AB. Farther forasmuch as the number
AB multiplying it selfe pro¦duced the number
D: therefore the number
AB measureth the number
D by the vnities which are in himselfe. Wherfore it mea¦sureth either of these numbers, namely, the number
D, and the number
EG, by the vnities which are in himselfe. Wherfore how multiplex the number
D is to the number
AB, so multiplex is the number
EG to the same number
AB. But numbers which are equemultiplices to one and the selfe same number
•• are equal the one to the other. Wherefore the number
D is equall to the number
EG. And the number
D is the square number made of the number
AB, and the number
EG is composed of the two su∣perficiall numbers produced of
AB into
BC, and of
BA into
AC. Wherefore the square number produced of the number
AB is equall to the superficial numbers, produced of the number AB into the number
BC, and of AB into AC, added together. If therefore a number be deuided into two other numbers &c. which was required to be proued.