The Elements

7

diameter

A diameter of a circle is any straight line
drawn through the center, and terminated in
each direction by the circumference of the circle,
which also bisects the circle.
A semicircle is the figure contained
by the diameter and the circumference
cut off by it from the circle.
And the center of the semicircle is the same
as that of the circle.
segment

A segment of a circle is the figure contained
by a straight line and the circumference of a circle,
either greater or less than a semicircle. Rectilinear
figures are those contained by straight lines, trilateral
being those contained by three, quadrilateral
those by four, and multilateral
those contained by more than four straight lines.

A circle with a horizontal diameter drawn across its center.

Three triangles illustrating types categorized by sides: equilateral (all sides equal), isosceles (two sides equal), and scalene (all sides unequal).
Of trilateral figures, an equilateral
triangle is that which has its three sides equal, an isosceles
triangle is that which has two sides only equal,
and a scalene triangle is that which has its three sides unequal.
Further, of trilateral figures, a right-angled
the shape of the right-angled triangle

triangle is that which has a right angle, an obtuse-angled
triangle is that which has an obtuse angle,
the shape of the obtuse-angled triangle

and an acute-angled triangle is that which has three acute
the shape of the acute-angled triangle

angles. Of quadrilateral figures, a square
is that which is both equilateral and
right-angled; an oblong is that which is right-angled
but not equilateral; a rhombus is that which is
equilateral but not right-angled; and a rhomboid is that which has
the opposite sides and angles equal to one
another, which is neither equilateral nor
right-angled. And let all other quadrilaterals
be called trapezia. 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. — Postulates
1. Let it be requested to draw a straight line from any point to any point.
2. And to produce a finite straight line continuously in a straight line.
3. And to describe a circle with any center and radius.

Geometric diagrams placed in the right margin and bottom of the page. The margin contains diagrams for a right-angled triangle, an obtuse triangle, a square, an oblong rectangle, a rhombus, and a trapezoid. The bottom margin contains three diagrams illustrating the postulates: Postulate 1 shows a line segment connecting two points; Postulate 2 shows a line segment being extended further along the same line; Postulate 3 shows a circle being generated from a central point using a radius.