8 If three right lines be proportionall, the quadrate of the middle one, shall be equall to the rectangle of the extremes: And contrariwise: 17. p vj. and 20. p vij.
Or thus: If three lines be proportionall, the square made of the middle line is equall to the right angled parallelogramme made of the two outmost lines: H.
It is a corallary out of the [28. e x]. As in ae, ei, io.
9 If the base of a triangle doe subtend a right angle, the powre of it is as much as of both the shankes: And contrariwise 47, 48. p j.
It is a consectary out of the [11. e viij]. But it is sometime rationall, and to be expressed by a number: yet but in a scalene triangle onely. For the sides of an equicrurall right-angled triangle are irrationall; Whereas the sides of a scalene are sometime rationall; and that after two manners, the one of Pythagoras, the other of Plato, as Proclus teacheth, at the 47. p j. Pythagora's way is thus, by an odde number.
10 If the quadrate of an odde number, given for the first shanke, be made lesse by an unity; the halfe of the remainder shall be the other shanke; increased by an unity it shall be the base.