Dividing a line from an external point; the straight line defined
Cases of point-to-segment partitions and a definition of the straight line
The page collects several cases of an arc or a line segment together with a point lying off it, with lines radiating from the point to equal partitions of the segment and arcs marking radial distances. In the fullest case the external point is labeled a and the partition boundaries b, c, d, e, and f. A note begins to define a straight line as one whose length can serve as an exact divider of a given line laid off from an external point.
On this page
External point a and partitions b, c, d, e, f
In the last of four cases a point a lies off a segment whose equal partitions are bounded by b, c, d, e, and f; lines run from a to those boundaries and arcs about a indicate the radial distances.
Definition of a straight line
A straight line is described by placing a point beyond it at a distance whose length can be an exact divider of the given line, so that any straight line so laid off measures it evenly.