12. Those which divided by a common perpendicle. 14 p xj.
It is a consectary out of the [3], and [6 e]. For if the middle right line be perpendicular to both the plaines, it is also to the right lines on either side cut, perpendicular in the common intersection: And the inner angles on each side, being right angles, will evince them to be parallels.
It is also out of the definition of parallels, at the [15 e ij].
And
13. If two paires of right in them be joyntly bounded, they are parallell. 15 p xj.
Such are the opposite walls in the toppe or ridge of houses. As let aei, and uoy, be plaine which have two payres of
right lines, ea, and ia: Item uo, and yo, joyntly bounded in a, and o: And parallels, to wit ea, against uo: and ia, against yo. I say that the plaines themselves are parallels: For the right lines ue, and oa: item yi, and oa, doe knit together equall parallels, they shal by the [27 e v], be equall and parallels: And so they shall prove the equidistancie.
The same will fall out if thou shalt imagine the joyntly bounded to infinitely drawn out; for the plaines also infinitely extended shall be parallell.
14. If two parallell plaines are cut with another plaine, the common sections are parallels, 16 p xj.