Galileo, in 1590, wrote a treatise on motion that disputed nearly every assumption made by Aristotelian physics. He stated that bodies composed of the same material fall with the same speed through a given medium regardless of weights using arguments based on the principle of Archimedes. Galileo supposedly said that if you dropped two balls of similar material but different weights off the Leaning Tower of Pisa, they would hit the ground at the same time. Galileo introduced the law of the level, claimed that besides Aristotle's division of all motions into natural and forced, there were also neutral motions exemplified by rotating spheres and motions along horizontal planes.

In 1632, Galileo published *Dialogue*, reconciling the earth's motion based on Kepler's proof of the solar system as heliocentric with planets revolving around the sun, with man's experience in everyday life with a stationary earth; with the concept of the relativity of motion, the idea of inertia, the law of uniform acceleration and its application to falling bodies, calling for a unified science of physics and astronomy.

where m equals mass and a equals the acceleration. Newton's third law presents conservation of momentum, the product of mass and velocity. Since gravity is a natural force that is either slowing motion or speeding it up, Newton introduced his universal law of gravitational force.

Gottfried Wilhelm Leibniz began publishing papers in calculus in 1684 and first introduced the integral. Leibniz introduced the concept of vis viva (living force) which attempted to quantify life force. It is similar to Newton's conservation of momentum, but velocity is squared. Mathematically vis viva was expressed as:

There is a definite relationship between size and velocity. The power of a bullet to pierce with its small mass but fast velocity has a lot of vis viva, as does an elephant whose mass is enough to make the ground tremble even at slow speeds. A leaf which is both small and slow has little vis viva, but leaves falling in mass as they do in Autumn have vis viva. (Guillen 1995)

Eventually vis viva was replaced by kinetic energy, the energy of motion, with a proportionality constant of ½ expressed as:

where the ½v² accounts for friction becoming a velocity triangle such as the kind that a rock makes skipping through the water. The derivative of kinetic energy becomes mass times acceleration which works in harmony with Newton's force of F = ma. Newton's force can be integrated to become kinetic energy. Note vis viva can not be derived from Newton's force. Other types of energies were derived such as work (mechanical), thermal, electrical, solar and so on.

Today, however, kinetics is also associated with kinetic theories based on the observation that minute particles of a substance are in vigorous motion due to temperature.

Daniel Bernoulli (1700-1782) received his doctorate
in medicine. As a professor he taught anatomy, mathematics and
physics. Bernoulli chief work was his book
*Hydrodynamica* published in 1738. Bernoulli was fascinated with the flow of blood through the veins. He eventually realized that when the heart pumped
blood, the pressure in the veins increases and the velocity of the
blood flow decreased. Inversely when the heart relaxes, blood pressure
decreases so the speed of the blood flow increases.

Daniel's father, Johann (1667-1748), was also a
professor of mathematics and a personal friend of Leibniz and part of
a group promoting a Law of Conservation of Vis Viva:

which was eventually changed to a conservation of
energy law more line with Newton's force

Here the kinetic energy is the energy applied to say a ball to toss it in the air. The potential energy is the initial position of the ball. The higher the initial position of the ball, the less kinetic energy needed to reach a specified height. Drop the ball, it losses potential until it rests upon the ground and returns to the beginning point.

Daniel changed mass to density and altitude to
pressure to create:

which was eventually changed to:

and was grouped under conservation of energy. The Bernoulli effect also describes the reason airplanes and jets fly. The top part of the wing is curved with a flat underside. Air is forced to move faster over the top of the wing, reducing pressure, to create lift. (Guillen, 1995)

Though vis viva was forgotten for a time in favor of energies that could be integrated with Newton's force, it would resurface in the work of Albert Einstein. Einstein and his wife Mileva Maritsch recognized the mathematical importance of the speed of light as a constant and used it to express the relationship between energy and mass in the Specific Theory of Relativity (1905) by changing v² in the original vis viva equation to c², where c is the speed of light traveling through the vacuum of space:

This equation expresses the ability of light to move back and forth between a wave and a particle and is used in quantum mechanics through measurements made by particle accelerators that enable conversion of small subatomic masses into an energy equilivent where all external reactions are kept to a minimum so as to approach the effects of a vacuum (Hawkins 1988). Results are showing an expected increase of mass at high speed. A conceptual reason for this may be electrically charged particles induces a magnetic field that could increase density. The proportionality constant equals 1, because there is little resistance in space and the speed of light is at its maximum. Since the universe is in a state of expansion, gravity acts as a break to degrade and slow light. Einstein developed theories of gravity in his General Theory of Relativity where gravity bends light. Einstein's general theory of gravity allows a more accurate prediction of the orbit of Mercury which is closer to a gravity source, but Newton's and Einstein's theories of gravity are equally effective for planets farther away from the sun such a Pluto.

©