18. If a part of an infinite right line, bee by a periphery for a point given without, cut off a right line from the said point, cutting in two the said part, shall bee perpendicular upon the line given. 12. p j.
Of an infinite right line given, let the part cut off by a periphery of an externall center be ae: And then let io, cut the said part into two parts by the [12. e]. I say that io is perpendicular unto the said infinite right line. For it standeth upright, and maketh aoi, and eoi, equall angles, for the same cause, whereby the next former perpendicular was demonstrated.
19. If two right lines drawne at length in the same plaine doe never meete, they are parallells. è 35. d j.
Thus much of the Perpendicularity of plaine right lines: Parallelissmus, or their parallell equality doth follow.
Euclid did justly require these lines so drawne to be granted paralels: for then shall they be alwayes equally distant, as here ae. and io.
Therefore
20. If an infinite right line doe cut one of the infinite right parallell lines, it shall also cut the other.
As in the same example uy. cutting ae. it shall also cut io. Otherwise, if it should not cut it, it should be parallell unto it, by the [18 e]. And that against the grant.