_As to method_, Galileo objected to formal logic, that it is not a means of discovering new truth, although valuable as a corrective of thought. New truth is discovered when we frame an hypothesis from certain experiences, and then infer the truth of other cases from that hypothesis. The hypothesis is first formed by induction from a few characteristic cases; the inference to other cases is made by deduction. He therefore linked induction and deduction closely together, and conceived them as necessarily complementary in scientific investigation. Either induction or deduction alone is absurd and impossible. By induction alone we should be obliged to examine all cases, an impossible undertaking. By deduction alone we should be in the same straits as the Scholastics, and never discover new laws. We must begin with our perceptual experiences and make an induction from them; then we must bring mathematics into use in constructing the hypothesis from which to deduce (calculate) new cases. This is the true, modern method and reveals the great genius of Galileo. A mathematical law never exactly coincides with any particular concrete relations. A mathematical law is an hypothesis or ideal construction. What value, then, has a mathematical law for science? The orbits of planets[8] are described as ellipses, but no actual planet moves in a perfect ellipse. The ellipse is an hypothetical, mathematical orbit for a planet which has no disturbing influences upon it. We get at such a law by the method of concomitant variations;[9] and the value of it consists in the simplification and system that it gives the facts. For example, knowing that a planet would move in an ellipse if it suffered no perturbations, and then knowing the influences upon any particular planet, we can calculate its orbit. Mathematical law, although ideal, is the common rule under which all nature phenomena can be brought. However, only by measurements founded on the tests of observation and experiment can we know how far the claims of such deduction are supported. Measure everything measurable, and calculate the measurement of those things not directly measurable. Nature, therefore, must be called upon to explain her own phenomena. Since the laws of nature are found by investigating nature phenomena as we experience them, the laws must be a part of nature and can be found nowhere else. To explain nature phenomena by referring them to spiritual influence is no real explanation. To say that God moves the planets is to involve the subject in mystery. Here is where Galileo shows that he does not belong to the Scholastics or the Mystics or the Humanists. He searched for some constant element, and not for a “vital force” behind nature phenomena. He declared this constant element to be motion――measurable motion. He is the author of the theory that mechanics is the mathematical theory of motion. Science was therefore taken by him out of the paralyzing grip of the theologian.