Euclid, Elements of Geometry, Book I, Definitions
(Edited by Dionysius Lardner, 1855)
A point is that
which has no part.
A line is
The extremities of a line are points.
A straight line is a line
which lies evenly with the points on itself.
A surface is that
which has length and breadth only.
The extremities of a surface are lines.
A plane surface is a
surface which lies evenly with the straight lines
A plane angle is the
inclination to one another of two lines in a plane
which meet one another and do not lie in a straight line.
And when the lines containing the angle are straight,
the angle is called rectilineal.
When a straight line set up on a straight line makes the
adjacent angles equal to one another, each of the equal
angles is right, and the
straight line standing on the other is called a
perpendicular to that
on which it stands.
An obtuse angle is an
angle greater than a right angle.
An acute angle is an
angle less than a right angle.
A boundary is that which
is an extremity of anything.
A figure is that which is
contained by any boundary or boundaries.
A circle is a plane
figure contained by one line such that all the straight
lines falling upon it from one point among those lying
within the figure are equal to one another;
And the point is called the centre
of the circle.
A diameter of the circle
is any straight line drawn through the centre and
terminated in both directions by the circumference of
the circle, and such a straight line also bisects the
A semicircle is the figure
contained by the diameter and the circumference cut off
by it. And the centre of the semicircle is the same as
that of the circle.
Rectilineal figures are
those which are contained by straight lines,
trilateral figures being
those contained by three,
those contained by four, and
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 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.
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 quadrilaterals other
than these be called
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.
Book I: Euclid, Book I (ed. Sir Thomas L. Heath, 1st Edition, 1908)
Next: Euclid, Book I, Postulates (ed. Sir Thomas L. Heath, 1st Edition, 1908)
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