Otherwise they should not be parallell. This is understood by the perpendiculars, knitting them together, which by the definition are equall betweene two parallells: And if of perpendiculars they bee made oblique, they shall notwithstanding remaine equall, onely the corners will be changed.
And
27. If right lines doe joyntly bound on the same side equall and parallell lines, they are also equall and parallell.
This element might have beene concluded out of the next precedent: But it may also be learned out of those
which went before. As let ae, and io, equall parallels be bounded joyntly of ai, and eo: and let ei be drawn. Here because the right line ei falleth upon the parallels ae, and io, the alterne angles aei and eio, are equall, by the [21 e]. And they are equall in shankes ae, and io, by the grants, and ei, is the common shanke: Therefore they are also equall in base ai, and eo, by the [7 e iij]. This is the first: Then by [21 e], the alterne angles eia, and ieo, are equall betweene themselves: And those are made by ai and eo, cut by the right line ei: Therefore they are parallell; which was the second.
On the same part or side it is sayd, least any man might understand right lines knit together by opposite bounds as here.
28. If right lines be cut joyntly by many parallell right lines, the segments betweene those lines shall bee proportionall one to another, out of the 2 p vj and 17 p xj.