On the Sphere and Cylinder (in two books)
shows the surface area of any sphere is 4 pi r2, and the volume of a sphere is two-thirds that of the cylinder in which it is inscribed, V = 4/3 pi r3
Measurement of the Circle
shows that pi, the ratio of the circumference to the diameter of a circle, is between
3 10/70 and 3 10/71
On Conoids and Spheroids
finds the volumes of solids formed by the revolution of a conic section (circle, ellipse, parabola, or hyperbola) about its axis
On Spirals
develops many properties of tangents to the spiral of Archimedes
Centers of Gravity of Planes (in two books)
finds the centers of gravity of various plane figures and conics, and establishes the "law of the lever"
Quadrature of the Parabola
finds, first by "mechanical" means (Archimedes' "Method") and then by rigorous geometry, the area of any segment of a parabola
The Sand Reckoner
attempts to remedy the inadequacies of the Greek numerical notation system by showing how to express a huge number - the number of grains of sand that it would take to fill the whole of the universe by creating a place-value system of notation, with a base of 100,000,000 (and contains the most detailed surviving description of the heliocentric system of Aristarchus of Samos)
Method Concerning Mechanical Theorems
describes the process of discovery in mathematics
On Floating Bodies (in two books)
finds the positions that various solids will assume when floating in a fluid, and establishes Archimedes' principle (that the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object)