As in these two quinquangles. First the particular triangles are like betweene themselves. For the shankes of aeu and ysm, equall angles are proportionall, by the grant. Therefore the triangles themselves are equiangles, by [14 e vij]. And therefore alike, by the [12 e vij], and so forth of the rest.
The middle triangles, the equall angles being substracted shall have their other angles equall: And therefore they also shall be equiangles and alike, by the same.
Secondarily, the triangles aeu. and ysm: eio and srl; eou, and slm, to wit, alike betweene themselves, are by the [1 e vj], in a double reason of their homologall sides eu, sm, eo, sl, which reason is the same, by meanes of the common sides. Therefore three triangles are in the same reason: And therefore they are proportionall: And, by the third composition, as one of the antecedents is, unto one of the consequents; so is the whole quinquangle to the whole.
5. A triangulate is a Quadrangle or a Multangle.
The parts of this partition are in Euclide, and yet without any shew of a division. And here also, as before, the species or severall kinds have their denomination their angles, although it had beene better and truer to have beene taken from their sides; as to have beene called a Quadrilater, or a Multilater. But in words use must bee followed as a master.
6. A Quadrangle is that which is comprehended of foure right lines. 22 d j.
As here thou seest. But a Quadrangle may also bee a sphearicall, and a conicall, and a cylindraceall, and that
those differences are common, we doe foretell at the [3 e v]. And a Quadrangle may be a plaine, which is not a quadrilater, as here.