12.
Pythagoras: *
Pythagoras' Theorem: In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides.
13.
Descartes:
Cartesian coordinates are a coordinate system that specifies a point uniquely in a plane with 2 numerical coordinates, the signed distances to the point from two fixed perpendicular reference lines called the coordinate axes; where they meet is its origin, at (0, 0). The same principles can specify the position of a point in 3-D space using 3 coordinates.
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He developed analytic geometry by using algebra to describe geometry, in effect elevating it above geometry; he invented the notation of representing unknowns by x, y & z, and knowns by a, b & c; pioneered superscripts to show the powers or exponents; challenged the idea that equations of degree higher than the 3rd were unreal- the assumption that 3-D forms (e.g. a cube), occupied the largest dimension of reality; provide the framework for Newton & Leibniz to develop calculus & proceeded Leibniz in seeing algebra as a symbolic language, a method to automate reasoning, especially in finding abstract, unknown quantities, (the basis of 20th & 21st century computational algorithms ).
14.
perspective: *
Rays of light travel from the object, through the picture plane, and to the viewer's eye. This is the basis for graphical perspective.
