results by stating the triangle of forces. These pioneers were followed by a host of lesser investigators, and by the middle of the sixteenth century this activity had resulted in the establishment of that branch of mechanics which is now called statics.
The next step was the introduction of the fundamental elements of time and mass in an attempt to investigate the laws of motion. At first little progress was made, as the misconception prevailed that a constant supply of force was necessary to keep a body in motion. Prolonged experiment and investigation, however, gradually resulted in a clearer understanding of these phenomena, and finally led to a correct statement of the first law of motion by the great Italian philosopher Galileo Galilei. Subsequent investigation of the motion of projectiles and falling bodies led Galileo to the two great ideas of inertia and the accelerating action of force, and enabled him to also state the second and third laws of motion. In addition to these great discoveries, Galileo generalized the law of equilibrium by stating the principle of virtual velocities, thus giving the first general solution of all problems in statics.
For the next century the development of mechanics consisted chiefly in an application of the principles of statics to liquids and gases. The only notable advance in mechanical principles during this period was made by Hu} r ghens, who, in connection with his invention of the pendulum clock, investigated the center of oscillation and was thus led to a more general statement of the third law of motion.
The four fundamental ideas of space, time, force and mass were now firmly established, but until the time of Newton found expression only in an inorganic mass of facts and principles. Newton's discovery of gravitation, however, led to such a broad generalization of these ideas as to make possible a systematic treatment of the subject, and mechanics as a science may be said to date from the publication of his famous Principia in 1686. Newton's claim to preeminence, therefore, rests not on the discovery of new mechanical principles, but on the immeasurably greater service of bringing all natural phenomena under the reign of universal law.
Only one element was now lacking to complete the series of independent fundamental statements necessary to constitute the foundation of a complete system of mechanics. There still remained the establishment of a general relation between these fundamental concepts, and after eighty years of experiment and investigation along the lines indicated by Newton, this relation was furnished by d'Alembert in the statement of his famous principle.
This closed the first stage of development. The image was now complete, and henceforth a system of mechanics based on this foundation must be a purely deductive science. The subsequent history of