Here the two triangles aie, and ies, are by the [8 e, viij]. alike; And as se, is unto ei: So is ie, unto ea: And by [25 e, iiij], as se, is to ea: so is the quadrate of se, to the quadrate of ei: And inversly or backward, as ae, is to se: so is the quadrate of ie, to the quadrate of se. But ae, is the triple of se. Therefore the quadrate of ie, is the triple of se. But the quadrate of as, by the grant, and [14 e xij], the quadruple of the quadrate of se. Therefore also it is greater than the quadrate of ie: And the right line as, is greater than ie, and al, therefore is much greater. But al, is by the grant
compounded of the sides of the sexangle and decangle rl, and ar. Therefore by the 1 c. [5 e, 18.] it is cut proportionally: And the greater segment is the side of the sexangle, to wit, rl: And the greater segment of ie, proportionally also cut, is ye. Therefore the said rl, is greeter than ye: And even now it was shewed ul, was equall to rl. Therefore ul, is greater than ye: But ue, the side of the Icosahedrum, by [22. e vj]. is greater than ul. Therefore the side of the Icosahedrum is much greater, then the side of the dodecahedrum.
Of Geometry the twenty seventh Book; Of the Cone and Cylinder.
1 A mingled solid is that which is comprehended of a variable surface and of a base.
For here the base is to be added to the variable surface.
2 If variable solids have their axes proportionall to their bases, they are alike. 24. d xj.
It is a Consectary out of the [19 e, iiij]. For here the axes and diameters are, as it were, the shankes of equall angles, to wit, of right angles in the base, and perpendicular axis.
3 A mingled body is a Cone or a Cylinder.
The cause of this division of a varied or mingled body, is to be conceived from the division of surfaces.