Euclid

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.

Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three angles acute.

Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.

Sire, there is no royal road to geometry.

Give him threepence, since he must make a gain out of what he learns.

What advantage shall I get by learning these things?

That which is without parts has no magnitude.

A straight line is a line which lies evenly with the points on itself.

A plane surface is a surface which lies evenly with the straight lines on itself.

A plane angle is the inclination of the lines to one another, when two lines meet one another, but are not in the same straight line.

And when the lines containing the angle are straight, the angle is called rectilineal.

Rectilineal figures are those which are contained by straight lines...

Trilateral figures are those contained by three straight lines, quadrilateral those contained by four, and multilateral those contained by more than four straight lines.

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has only two of its sides equal, and a scalene triangle that which has its three sides unequal.

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let all other quadrilaterals besides these be called trapezia.

Let the following be postulated:

To draw a straight line from any point to any point.

To produce a finite straight line continuously in a straight line.

To describe a circle with any centre and radius.

That all right angles are equal to one another.