{ Composite (broken line forming an angle) { Lines { { Forming a figure, or determinate. (Circle, { { ellipse, cissoid.) { Incomposite { Not forming a figure, or indeterminate and { extending without a limit. (Straight { line, parabola, hyperbola, conchoid.) Of course his view of the cissoid, the curve represented by the equation _y_^2(_a_ + _x_) = (_a_ - _x_)^3, is not the modern view. 3. _The extremities of a line are points._ This is not a definition in the sense of its two predecessors. A modern writer would put it as a note under the definition of line. Euclid did not wish to define a point as the extremity of a line, for Aristotle had asserted that this was not scientific; so he defined point and line, and then added this statement to show the relation of one to the other. Aristotle had improved upon this by stating that the "division" of a line, as well as an extremity, is a point, as is also the intersection of two lines. These statements, if they had been made by Euclid, would have avoided the objection made by Proclus, that some lines have no extremities, as, for example, a circle, and also a straight line extending infinitely in both directions. 4. STRAIGHT LINE. _A straight line is that which lies evenly with respect to the points on itself._ This is the least satisfactory of all of the definitions of Euclid, and emphasizes the fact that the straight line is the most difficult to define of the elementary concepts of geometry. What is meant by "lies evenly"? Who would know what a straight line is, from this definition, if he did not know in advance?