Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/29

 33. A rhomboid is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles:

34. All other four-sided figures besides these are called trapeziums.

35. Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways do not meet.

[Note. The terms oblong and rhomboid are not often used. Practically the following definitions are used. Any four-sided figure is called a quadrilateral. A line joining two opposite angles of a quadrilateral is called a diagonal. A quadrilateral which has its opposite sides parallel is called a parallelogram'. The words square and rhombus are used in the sense defined by Euclid; and the word rectangle is used instead of the word oblong.

Some writers propose to restrict the word trapezium to a quadrilateral which has two of its sides parallel; and it would certainly be convenient if this restriction were universally adopted.]

Let it be granted,

1. That a straight line may be drawn from any one point to any other point:

2. That a terminated straight line may be produced to any length in a straight line:

3. And that a circle may be described from any centre, at any distance from that centre.