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VII. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies.
VIII. A plane angle is the inclination of two lines to each other in a plane which meet together, but not in the same straight line.
IX. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
X. When a straight line standing on another straight line, makes the adjacent angles equal to each other, each of these angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
XV. A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
XVII. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter.
XXIV. Of three-sided figures, an equilateral triangle is that which has three equal sides.
XXX. Of quadrilateral or four-sided figures, a square has all its sides equal and all its angles right angles.
XXXI. An oblong is that which has all its angles right angles, but has not all its sides equal.
XXXII. A rhombus has all its sides equal, but its angles are not right angles.
XXXIII. A rhomboid has its opposite sides equal to each other, but all its sides are not equal, nor its angles right angles.
XXXV. Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
A. A parallelogram is a four-sided figure, of which the opposite sides are parallel: and the diameter or the diagonal is the straight line joining two of its opposite angles.
I. Let it be granted that a straight line may be drawn from any one point to any other point.
II. That a terminated straight line may be produced to any length in a straight line.
III. And that a circle may be described from any centre at any distance from that centre.
I. THINGS which are equal to the same thing are equal to one another.
If equals be added to equals, the wholes are equal.