that of the Earth could not possibly be a parabola, but he nevertheless maintained that for distances up to the range of the artillery of his day, the deviation of a projectile's trajectory from a parabola would be only very slight. Mathematization Scientific knowledge, according to the Aristotelians, was concerned with establishing true and necessary causes of things. To the extent that medieval natural philosophers used mathematical problems, they limited social studies to theoretical analyses of local speed and other aspects of life. The actual measurement of a physical quantity, and the comparison of that measurement to a value computed on the basis of theory, was largely limited to the mathematical disciplines of astronomy and optics in Europe. In the 16th and 17th centuries, European scientists began increasingly applying quantitative measurements to the measurement of physical phenomena on the Earth. Galileo maintained strongly that mathematics provided a kind of necessary certainty that could be compared to God's: "...with regard to those few [mathematical propositions] which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty..." Galileo anticipates the concept of a systematic mathematical interpretation of the world in his book Il Saggiatore: In 1591 François Viète published In Artem Analyticem Isagoge, which gave the first symbolic notation of parameters in algebra. Newton's development of infinitesimal calculus opened up new applications of the methods of mathematics to science. Newton taught that scientific theory should be coupled with rigorous experimentation, which became the keystone of modern science. Mechanical philosophy Aristotle recognized four kinds of causes, and where applicable, the most important of them is the "final cause". The final cause was the aim, goal, or purpose of some natural process or man-made thing. Until the Scientific Revolution, it was very natural to see such aims, such as a child's growth, for example, leading to a mature adult. Intelligence was assumed only in the purpose of man-made artifacts; it was not attributed to other animals or to nature. In "mechanical philosophy" no field or action at a distance is permitted, particles or corpuscles of matter are fundamentally inert. Motion is caused by direct physical collision. Where natural substances had previously been understood organically, the mechanical philosophers viewed them as machines. As a result, Newton's theory seemed like some kind of throwback to "spooky action at a distance". According to Thomas Kuhn, Newton and Descartes held the teleological principle