Euclid

Mathematics Greek -325 – -265 439 quotes

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.

Elements (Book II, Proposition 12) -300

In obtuse- and acute-angled triangles the orthocenter lies outside the triangle.

Elements (implied in Book I) -300

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.

Elements (advanced implication) -300

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.

Elements (Book III, Proposition 36) -300

In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.

Elements (Book III, implied) -300

The opposite angles of a cyclic quadrilateral sum to 180 degrees.

Elements (Book III, Proposition 22) -300

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

Elements (Book III, Proposition 20) -300

The perpendicular bisector of a chord passes through the center of the circle.

Elements (Book III, Proposition 3) -300

Equal chords subtend equal arcs and equal angles at the center.

Elements (Book III, Proposition 4) -300

The angle formed by two chords intersecting inside a circle is equal to half the sum of the intercepted arcs.

Elements (Book III, Proposition 35) -300

A tangent is perpendicular to the radius at the point of tangency.

Elements (Book III, Proposition 18) -300

The length of an arc is proportional to the central angle.

Elements (Book III, Proposition 27) -300

To find the center of a given circle.

Elements (Book III, Proposition 1) -300

The four angles formed by two intersecting straight lines are equal in pairs.

Elements (Book I, Proposition 15) -300

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.

Elements (Book I, Proposition 27) -300

The exterior angle of a triangle is greater than either of the interior opposite angles.

Elements (Book I, Proposition 16) -300

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.

Elements (Book I, Proposition 32) -300

Any two sides of a triangle are together greater than their remaining side.

Elements (Book I, Proposition 20) -300

The bisectors of the three angles of a triangle meet in a point.

Elements (Book I, Proposition 7 implied) -300

The medians of a triangle intersect at a point that divides each median in a 2:1 ratio.

Elements (implied) -300