coangular to the whole parallelogramme aeio; And let it have the same angle with it at a; like unto the whole and alike situate unto it; I say it is the Diagonall.
Otherwise, let the diverse Diagony be aro: And let lr be parallell against ae: Therefore alrs, shall bee the Diagonall, by the 6 e [[16].] Now therefore it shall be, by 8 e [[17 e,]] as ea is to ai: so is sa unto al: Againe,by the grant, as ea is unto ai: so is sa to au: Therefore the same sa is proportionall to al, and to au: And al is equall to au, the part to the whole, which is impossible.
19. The Complement is a particular parallelogramme, comprehended of the conterminall sides of the diagonals.
Or thus: It is a particular parallelogramme conteined under the next adjoyning sides of the diagonals.
As in this figure, are ur, and sy: For each of them is comprehended of the continued sides of the two diagonals. And therefore are they called Complements, because they doe with the Diagonals complere, that is, fill or make up the whole parallelogramme. Neither in deed may the two diagonals be described, but withall the complements must needes be described.
20. The complements are equall. 43 p j.
As in the same figure, are the sayd ur, and sr: For the triangles aei, and aoi, are equall, by the [12 e]. Item, so are asl, and aul: Item, so are lui, and lri. Therefore if you shall on each side take away equall triangles from those which are
equall, you shall leave the Complements equall betweene themselves.