Euclid
Father of geometry, wrote Elements
Quotes by Euclid
The square on any straight line is equal to the rectangle contained by that line and the line applied to it equal to the sum of the squares on the two segments.
In obtuse- and acute-angled triangles the orthocenter lies outside the triangle.
The nine-point circle passes through the midpoints of the sides, the feet of the altitudes, and the midpoints of the segments from the orthocenter to the vertices.
The power of a point theorem states that for a point P outside a circle, the product of the lengths of two secant segments from P is constant.
In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
The opposite angles of a cyclic quadrilateral sum to 180 degrees.
The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.
The perpendicular bisector of a chord passes through the center of the circle.
Equal chords subtend equal arcs and equal angles at the center.
The angle formed by two chords intersecting inside a circle is equal to half the sum of the intercepted arcs.
A tangent is perpendicular to the radius at the point of tangency.
The length of an arc is proportional to the central angle.
To find the center of a given circle.
The four angles formed by two intersecting straight lines are equal in pairs.
If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
The exterior angle of a triangle is greater than either of the interior opposite angles.
In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles taken together, and the three interior angles of the triangle are equal to two right angles.
Any two sides of a triangle are together greater than their remaining side.
The bisectors of the three angles of a triangle meet in a point.
The medians of a triangle intersect at a point that divides each median in a 2:1 ratio.