regarded as the first clear statement of the principle of mechanical relativity. Galileo saw that from the point of view of a person standing on the shore, the motion of falling downwards on the ship would be combined with, or added to, the forward motion of the ship. In terms of velocities it can be said that the velocity of the falling body relative to the shore equals the velocity of that body relative to ship plus the velocity of the ship relative to the shore. In general for three objects A (e.g. Galileo on the shore), B (e.g. ship), C (e.g. falling body on ship) the velocity vector of C relative to A (velocity of falling object as Galileo sees it) is the sum of the velocity of C relative to B (velocity of falling object relative to ship) plus the velocity of B relative to A (ship's velocity away from the shore). The addition here is the vector addition of vector algebra and the resulting velocity is usually represented in the form The cosmos of Galileo consists of absolute space and time and the addition of velocities corresponds to composition of Galilean transformations. The relativity principle is called Galilean relativity. It is obeyed by Newtonian mechanics. Special relativity According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. This change is not noticeable at low velocities but as the velocity increases towards the speed of light it becomes important. The addition law is also called a composition law for velocities. For collinear motions, the speed of the object (e.g. a cannonball fired horizontally out to sea) as measured from the ship would be measured by someone standing on the shore and watching the whole scene through a telescope as The composition formula can take an algebraically equivalent form, which can be easily derived by using only the principle of constancy of the speed of light, The cosmos of special relativity consists of Minkowski spacetime and the addition of velocities corresponds to composition of Lorentz transformations. In the special theory of relativity Newtonian mechanics is modified into relativistic mechanics. Standard configuration The formulas for boosts in the standard configuration follow most straightforwardly from taking differentials of the inverse Lorentz