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

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5
DEFINITIONS.
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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.

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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.]

 

POSTULATES.

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.