Linea recta, a straight or right line is that, as Plato defineth it, whose middle points do hinder us from seeing both the extremes at once; As in the eclipse of the Sunne, if a right line should be drawne from the Sunne, by the Moone, unto our eye, the body of the Moone beeing in the midst, would hinder our sight, and would take away the sight of the Sunne from us: which is taken from the Opticks, in which we are taught, that we see by straight beames or rayes. Therfore to lye equally betweene the boundes, that is by an equall distance: to bee the shortest betweene the same bounds; And that the middest doth hinder the sight of the extremes, is all one.
7. A crooked line is touch'd of a right or crooked line, when they both doe so meete, that being continued or drawne out farther they doe not cut one another.
Tactus, Touching is propper to a crooked line, compared either with a right line or crooked, as is manifest out of the 2. and 3. d 3. A right line is said to touch a circle, which touching the circle and drawne out farther, doth not cut the circle, 2 d 3. as here ae, the right line toucheth the periphery iou. And ae. doth touch the helix or spirall.
Circles are said to touch one another, when touching they doe not cutte one another, 3. d 3. as here the periphery doth aej. doth touch the periphery ouy.
Therefore
8. Touching is but in one point onely. è 13. p 3.
This Consectary is immediatly conceived out of the definition; for otherwise it were a cutting, not touching. So Aristotle in his Mechanickes saith; That a round is easiliest mou'd and most swift; Because it is least touch't of the plaine underneath it.
9. A crooked line is either a Periphery or an Helix. This also is such a division, as our Authour could then hitte on.
