On the principles known through themselves: and first concerning their definitions.

The most illustrious book of the Elements of the most clear-sighted Euclid: begins most happily in the art of Geometry:

The page is framed by a broad, ornate woodcut border featuring intricate white-on-black scrolling foliage, vines, and floral motifs. In the upper left corner of the text block, there is a large, square woodcut decorative initial 'P' decorated with similar vine patterns.

A point is that which has no part. ¶ A line is length without breadth, whose extremities are indeed two points. ¶ A straight line is the shortest extension from one point to another, receiving each of them into its extremities. ¶ A surface is that which has only length and breadth: its boundaries are indeed lines. ¶ A plane surface is the extension from one line to another, receiving [the lines] into its extremities. ¶ A plane angle is the mutual contact of two lines, whose expansion is upon a surface and whose joining is not in a straight line. ¶ When, however, two straight lines contain an angle, it is called a rectilinear angle. ¶ When a straight line stands upon [another] straight line and the two angles on both sides are equal, each of them will be a right [angle]. ¶ And the line standing upon the other is called the perpendicular. ¶ An angle which is greater than a right angle is called obtuse. ¶ An angle smaller than a right angle is called acute. ¶ A boundary is that which is the end of each thing. ¶ A figure is that which is contained by a boundary or boundaries. ¶ A circle is a plane figure contained by one line, which is called the circumference: in the middle of which is a point, from which all straight lines going out to the circumference are equal to one another. And this point indeed is called the center of the circle. ¶ The diameter of a circle is a straight line which, passing through its center and applying its extremities to the circumference, divides the circle into two halves. ¶ A semicircle is a plane figure contained by the diameter of the circle and half of the circumference. ¶ A portion segment of a circle is a plane figure contained by a straight line and a part of the circumference: being either greater or smaller than a semicircle. ¶ Rectilinear figures are those contained by straight lines: some of which are three-sided, [contained] by three straight lines; some are four-sided, [contained] by four straight lines; and some are many-sided, which are contained by more than four straight lines. ¶ Of three-sided figures: one is the triangle having three equal sides equilateral. Another is the triangle having two equal sides isosceles. Another is the triangle of three unequal sides scalene. Among these again, one is the right-angled triangle original: orthogonium, having, that is, one right angle. Another is the obtuse-angled triangle original: ambligonium, having some obtuse angle. Another is the acute-angled triangle original: oxigonium in which the three angles are acute. ¶ Of quadrilateral figures: One is the square, which is equilateral and right-angled. Another is the long tetragon original: tetragonus longus; a rectangle, which is a right-angled figure, but is not equilateral. Another is the "belmuaym" original: belmuaym; a medieval term derived from Arabic for a rhombus, which is equilateral, but is not right-angled.

Line
Point
plane surface.

Geometric diagram showing a horizontal line, a single point, and a rectangle labeled "plane surface."

plane angle
right angle
perpendicular

Diagram of two intersecting lines forming a right angle, with one vertical line labeled as perpendicular.

Circle
acute
obtuse angle

Diagrams showing a full circle, an acute angle, and an obtuse angle.

Diameter
Major portion
Minor portion
Semicircle

Diagrams of a circle with a diameter line and various circular segments including a semicircle and major/minor portions.

Equilateral
of two equal sides
of three unequal sides

Diagrams of three triangles: equilateral, isosceles, and scalene.

Acute-angled
Right-angled
Obtuse-angled

Diagrams of acute (oxygon), right (orthogon), and obtuse (amblygon) triangles.

Long tetragon
square
belmuaym rhombus

Diagrams of a rectangle (tetragonus longus), a square (quadratus), and a rhombus (belmuaym).