Archimedes is the only physicist before Galileo.
His contributions to the development of mechanics have come to us by some incomplete chapters of his work "The princples of mechanics".
It is owing to Archimedes the theory of the lever, that is fundamental for the realization of all the machines.
We remember, by the way, his famous sentence : "Da mihi ubi consistam et terram movebo - Give me a fulcrum and I will lift the world", that refers to the possibility of balancing by means of a lever very strong resistent forces with motive forces which are the weaker, the greater is the distance between the fulcrum of the lever and the point to which these have been applied.
By enunciating his hydrostatic principle ( a body immersed in a liquid is pushed up by a force equal to the weight of the volume of liquid removed by it ), created the statics of the fluids.
He applied it to the equilibrium of the bodies floating in liquids, and invented a method for the determination of the specific weight of the bodies.
He is considered one of the precursors of the infinitesimal calculus, since calculated an approximate value of p , between 21/7 and 22/7, by the method of the polygons subscribed and circumscribed to a circumference, applied through many phases of successive approximations, by increasing the number of sides .
He is the founder of the modern science and the inventor of the experimental method
(inductive-deductive ), by him assumed as the base on which the scientific progress is
After Archimedes, there has been a scientific gap of about 18 centuries; in fact the scientific progress was rigidly stopped by the action of unconditional faith in the Aristotelian theories, that are founded exclusively on the deductive method, denying any validity to experiments, that were a priori excluded, thinking that to explain the natural phenomena it was enough not to contradict the Aristotelian "ipse dixit", and to deduce the observed facts from the wrong and rigid Aristotelian statements.
The experimental method introduced by Galileo, realizes a cyclic working method consisting in leaving from the observation of the experimental data of a physical phenomenon, in advancing a hypothesis of a law that is able to explain the observed results ( inductive phase, from the experiment to the law ) and in verifying the hypothesized law, by means of its application ( deductive phase, from the law to the experiment ) to the description of the observed phenomenon.
By varying of time in time the experiment parameters of the physical phenomenon that has to be studied, it is possible to check the correspondence among the theoretical forecasts made by the hypothesized law and the experimental results that have been obtained.
We observe the throwing of a bullet,while measuring the coordinates x and y along its parabolic trajectory, in correspondence of some instants. We hypotesize a motion law, that takes account both of the rectilinear and uniform motion of the bullet in horizontal sense, and of the vertical motion with a constant acceleration (the gravity acceleration).
By means of the motion equations derived from our hypotesis, we calculate the coordinates of the bullet in determined instants, leaving from the knowledge of the velocity and of the throwing angle.
We throw again the bullet, measuring its coordinates in the instants selected to verify the motion law .
If the experimental values of the coordinates are matching, within the limits of the measure errors, with the calculated values , the motion-law hypothesis transforms in a motion law, otherwise another hypothesis of motion law is formulated.
Galileo applied his research method to several mechanical phenomena, that had been always described empirically, that is without applying any laws expressed by mathematical formulae, and therefore he is considered the founder of mechanics as a science, since he rejected entirely the Aristotelian theses on the motion, according to which the pregalileian philosophers thought blindly, without do any experiments, that a force applied to a body determined its velocity instead of its acceleration, as Galileo experimentally evidenced.
Galileo gave fundamental contributions to mechanics:
he obtained experimentally the motion laws of free-falling bodies, operating from the top of the Pisa tower, and above all he, using an inclined plane, studied the motion of bullets and enunciated the first two fundamental laws of dynamics ( the inertia principle and the law of proportionality between the force and the acceleration of a body) and the Galileo relativity principle, that concerns the invariance of mechanics laws with respect to two observers which are moving with a rectilinear and uniform motion, each in comparison with the other one.
He invented besides the terrestrial telescope, that, differently from the astronomic telescope of Keplero, furnishes not turned upside-down images.
In astronomy he discovered sunspots (1611 ) and four of the twelve satellites of Jupiter ( Io, Europa, Ganymede and Callisto ), and validated the heliocentric theory enunciated by Nicoḷ Copernico, in opposition to the geocentric one of Aristotle and Ptolomy, paying serious limitations of his freedom, till the abnegation before the Holy Office, for his great loving science.
He is the physicist that by the publication (1687) of his principal work
"Philosophiae naturalis principia mathematica" continued the Galileo work,
providing the physical-mathematical bases to develope modern mechanics.
Newton's contributions to the development of physics are enormous.
Enunciated the third principle of dynamics (the so-called action and reaction principle) and the universal gravitation law.
Invented, independently from Leibnitz, the infinitesimal calculus, that served him to formulate exactly the second law of mechanics and to derive from it and from the universal gravitation law the laws of Keplero describing to the motion of planets.
It must be said that Keplero, who didn't know the law of force among the Sun and his planets, found his laws exclusively on mathematical calculations, by means of the data of astronomic observations.
Newton gave besides several contributions to optics:
the formula of lenses, the reflecting telescope, the corpuscular theory of light, the study of the interference fringes produced by white light passing across thin glass layers , the discovery of the chromatic dispersion of the white light passing across a prism (study of the sunlight spectrum), and of the simultaneous reconversion of the coloured spectral lines into white light, by means of a second prism
(spectral analysis and synthesis of the white light ).