Archimedes of Syracuse
A brilliant ancient Greek mathematician, physicist, engineer, inventor, and astronomer, known for his work on buoyancy and levers.
Quotes by Archimedes of Syracuse
The volume of a sphere is equal to four times the volume of a cone whose base is a great circle of the sphere and whose height is equal to the radius of the sphere.
The surface area of a segment of a sphere is equal to the area of a circle whose radius is the chord of the segment.
The center of gravity of a segment of a parabola is on the axis of the parabola, at a distance from the vertex equal to three-fifths of the height of the segment.
The area of a segment of a parabola is to the area of the triangle with the same base and height as 4 is to 3.
The volume of a segment of a hyperboloid of revolution cut off by a plane perpendicular to the axis is equal to the volume of a cylinder whose base is the base of the segment and whose height is equal to the height of the segment multiplied by a certain factor.
The tangent to an Archimedean spiral at any point makes an angle with the radius vector to that point whose tangent is equal to the reciprocal of the angle through which the radius vector has turned.
The area of a sector of an Archimedean spiral is one-third of the area of the circle whose radius is the length of the arc of the sector.
The method of exhaustion is a rigorous method of proof, while the method of mechanical theorems is a heuristic method of discovery.
The value of pi is approximately 22/7.
The center of gravity of a hemisphere is on its axis, at a distance from the base equal to three-eighths of its radius.
The volume of a segment of a sphere is equal to the volume of a cylinder whose base is the base of the segment and whose height is equal to the height of the segment, plus the volume of a cone whose base is the base of the segment and whose height is equal to the height of the segment.
The surface area of a cone is equal to the area of a circle whose radius is the slant height of the cone, plus the area of its base.
The volume of a cone is one-third the volume of a cylinder with the same base and height.
The center of gravity of a paraboloid of revolution is on its axis, at a distance from the vertex equal to two-thirds of its height.
The area of a segment of a hyperbola is equal to the area of a trapezoid whose parallel sides are the ordinates of the endpoints of the segment and whose height is the distance between the ordinates, minus the area of a triangle whose base is the chord of the segment and whose height is the distance from the vertex to the chord.
The tangent to a circle is perpendicular to the radius at the point of tangency.
The area of a polygon inscribed in a circle is less than the area of the circle.
The area of a polygon circumscribed about a circle is greater than the area of the circle.
The volume of a cylinder is equal to the area of its base multiplied by its height.
Any magnitude whatever being given, and any magnitude whatever less than the first being given, it is possible to find a finite number of magnitudes equal to the lesser which shall exceed the greater.