shall make the quadrate or square aeio. For it is a parallelogramme, by the grant: Because the opposite sides are parallell: And it is rectangled: because seeing the angle aei, of the perpendicular lines, is a right angle, they shall be all right angles by the [2 e xj]. Then one side ei, is equall to all the rest. First to ao, that over against it, by the [8 e x]. And then to ea, by the grant: And therefore to oi, to that over against it, by the [8 e x].
6 The plaine of a quadrate is an equilater plaine.
Or thus: The plaine number of a square, is a plaine number of equall sides, H.
A quadrate or square number, is that which is equally equall: Or that which is comprehended of two equall numbers, A quadrate of all plaines is especially rationall; and yet not alwayes: But that onely is rationall whose number is a quadrate. Therefore the quadrates of numbers not quadrates, are not rationalls.
Therefore
7 A quadrate is made of a number multiplied by it self.
Such quadrates are the first nine. 1, 4, 9, 16, 25, 36, 49, 64, 81, made of once one, twice two, thrise three, foure times foure, five times five, sixe times sixe, seven times seven, eight times eight, and nine times nine. And this is the summe of the making and invention of a quadrate number of multiplication of the side given by it selfe.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9. | The sides given. |
| 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81. | The quadrates found. |
Hereafter diverse comparisons of a quadrate or square, with a rectangle, with a quadrate, and with a rectangle and a quadrate iointly. The comparison or rate of a quadrate with a rectangle is first.
And